From c51a6bd3e1ee41e2dc71d7829cc15e85cecea8ab Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Wed, 15 Jul 2009 11:54:04 +0000 Subject: [PATCH] ... --- .../eligible_unit_equality_problems | 343 + .../binaries/matitaprover/log.90.fixed-order | 46155 +++++++++++++++ .../matitaprover/log.90.fixed-order.2 | 46518 ++++++++++++++++ .../binaries/matitaprover/matitaprover.ml | 8 +- 4 files changed, 93021 insertions(+), 3 deletions(-) create mode 100644 helm/software/components/binaries/matitaprover/eligible_unit_equality_problems create mode 100644 helm/software/components/binaries/matitaprover/log.90.fixed-order create mode 100644 helm/software/components/binaries/matitaprover/log.90.fixed-order.2 diff --git a/helm/software/components/binaries/matitaprover/eligible_unit_equality_problems b/helm/software/components/binaries/matitaprover/eligible_unit_equality_problems new file mode 100644 index 000000000..75568e133 --- /dev/null +++ b/helm/software/components/binaries/matitaprover/eligible_unit_equality_problems @@ -0,0 +1,343 @@ +BOO007-2.p +BOO007-4.p +BOO031-1.p +BOO072-1.p +BOO073-1.p +BOO074-1.p +COL003-12.p +COL003-17.p +COL003-18.p +COL003-19.p +COL011-1.p +COL034-1.p +COL037-1.p +COL041-1.p +COL044-1.p +COL049-1.p +COL057-1.p +GRP014-1.p +GRP167-1.p +GRP167-2.p +GRP178-1.p +GRP178-2.p +GRP181-3.p +GRP184-2.p +GRP185-1.p +GRP185-2.p +GRP200-1.p +GRP201-1.p +GRP202-1.p +GRP404-1.p +GRP405-1.p +GRP410-1.p +GRP411-1.p +GRP419-1.p +GRP422-1.p +GRP423-1.p +GRP429-1.p +GRP444-1.p +GRP452-1.p +GRP469-1.p +GRP470-1.p +GRP471-1.p +GRP475-1.p +GRP476-1.p +GRP477-1.p +GRP478-1.p +GRP479-1.p +GRP480-1.p +LAT168-1.p +LCL109-2.p +LCL138-1.p +LCL159-1.p +RNG019-6.p +RNG021-6.p +RNG025-6.p +ROB005-1.p +BOO019-1.p +BOO030-1.p +BOO032-1.p +BOO033-1.p +COL003-20.p +COL004-3.p +COL005-1.p +COL038-1.p +COL046-1.p +COL047-1.p +COL060-1.p +COL061-1.p +COL062-1.p +COL071-1.p +COL073-1.p +GRP024-5.p +GRP114-1.p +GRP167-4.p +GRP177-2.p +GRP179-3.p +GRP180-2.p +GRP181-4.p +GRP183-1.p +GRP183-3.p +GRP183-4.p +GRP184-1.p +GRP184-3.p +GRP185-3.p +GRP185-4.p +GRP186-2.p +GRP204-1.p +GRP205-1.p +GRP207-1.p +GRP399-1.p +GRP420-1.p +GRP453-1.p +HWC004-1.p +LAT007-1.p +LAT016-1.p +LAT024-1.p +LAT025-1.p +LAT046-1.p +LAT047-1.p +LAT048-1.p +LAT049-1.p +LAT050-1.p +LAT051-1.p +LAT052-1.p +LAT054-1.p +LAT062-1.p +LAT063-1.p +LAT098-1.p +LAT100-1.p +LAT101-1.p +LAT102-1.p +LAT103-1.p +LAT104-1.p +LAT105-1.p +LAT106-1.p +LAT107-1.p +LAT108-1.p +LAT109-1.p +LAT111-1.p +LAT112-1.p +LAT113-1.p +LAT114-1.p +LAT115-1.p +LAT116-1.p +LAT117-1.p +LAT119-1.p +LAT120-1.p +LAT121-1.p +LAT122-1.p +LAT123-1.p +LAT124-1.p +LAT125-1.p +LAT126-1.p +LAT127-1.p +LAT128-1.p +LAT129-1.p +LAT130-1.p +LAT131-1.p +LAT132-1.p +LAT133-1.p +LAT134-1.p +LAT135-1.p +LAT136-1.p +LAT137-1.p +LAT171-1.p +LCL136-1.p +LCL137-1.p +LCL165-1.p +RNG019-7.p +RNG020-6.p +RNG020-7.p +RNG021-7.p +RNG025-4.p +RNG025-8.p +RNG025-9.p +BOO023-1.p +BOO034-1.p +COL004-1.p +COL006-6.p +COL036-1.p +COL063-1.p +GRP167-3.p +GRP179-1.p +GRP179-2.p +GRP180-1.p +GRP183-2.p +GRP186-1.p +LAT017-1.p +LAT020-1.p +RNG025-5.p +RNG025-7.p +COL006-1.p +COL006-5.p +COL006-7.p +COL044-6.p +COL044-7.p +COL064-1.p +COL065-1.p +GRP181-1.p +GRP181-2.p +GRP187-1.p +GRP505-1.p +GRP507-1.p +GRP508-1.p +LAT080-1.p +LAT083-1.p +LAT092-1.p +LAT093-1.p +LAT094-1.p +LAT095-1.p +LAT096-1.p +LAT097-1.p +LAT146-1.p +LAT148-1.p +LAT156-1.p +LAT160-1.p +LCL160-1.p +RNG009-5.p +RNG009-7.p +RNG026-6.p +RNG026-7.p +BOO076-1.p +COL003-1.p +COL042-1.p +COL043-3.p +COL044-8.p +COL044-9.p +GRP506-1.p +LAT053-1.p +LAT081-1.p +LAT084-1.p +LAT086-1.p +LAT087-1.p +LAT099-1.p +LAT110-1.p +LAT118-1.p +LAT142-1.p +LAT147-1.p +LAT154-1.p +LAT155-1.p +LAT170-1.p +RNG031-6.p +RNG031-7.p +SYN305-1.p +COL043-1.p +COL066-1.p +LAT018-1.p +LAT082-1.p +LAT085-1.p +LAT144-1.p +LAT150-1.p +LAT151-1.p +LAT152-1.p +LAT159-1.p +LAT162-1.p +LAT164-1.p +LAT169-1.p +LAT174-1.p +RNG027-5.p +RNG027-7.p +RNG027-8.p +RNG027-9.p +RNG028-5.p +RNG028-7.p +RNG028-8.p +RNG028-9.p +RNG029-5.p +RNG029-6.p +RNG029-7.p +ROB006-1.p +ROB006-2.p +ROB026-1.p +GRP164-1.p +GRP164-2.p +GRP196-1.p +LAT070-1.p +LAT138-1.p +LAT140-1.p +LAT145-1.p +LAT149-1.p +LAT153-1.p +LAT157-1.p +LAT158-1.p +LAT163-1.p +LAT165-1.p +LAT166-1.p +LAT167-1.p +LAT172-1.p +LAT173-1.p +LAT175-1.p +LAT176-1.p +RNG035-7.p +BOO077-1.p +BOO078-1.p +BOO079-1.p +BOO080-1.p +BOO081-1.p +BOO082-1.p +BOO083-1.p +BOO084-1.p +BOO085-1.p +BOO086-1.p +BOO087-1.p +BOO088-1.p +BOO089-1.p +BOO090-1.p +BOO091-1.p +BOO092-1.p +BOO093-1.p +BOO094-1.p +BOO095-1.p +BOO096-1.p +BOO097-1.p +BOO098-1.p +BOO099-1.p +BOO100-1.p +BOO101-1.p +BOO102-1.p +BOO103-1.p +BOO104-1.p +BOO105-1.p +BOO106-1.p +BOO107-1.p +BOO108-1.p +COL067-1.p +COL068-1.p +COL069-1.p +COL087-1.p +GRP177-1.p +LAT071-1.p +LAT072-1.p +LAT073-1.p +LAT074-1.p +LAT075-1.p +LAT076-1.p +LAT077-1.p +LAT078-1.p +LAT079-1.p +LAT139-1.p +LAT141-1.p +LAT161-1.p +LAT177-1.p +RNG010-5.p +RNG010-6.p +RNG010-7.p +RNG030-6.p +RNG030-7.p +RNG032-6.p +RNG032-7.p +RNG033-6.p +RNG033-7.p +RNG033-8.p +RNG033-9.p +RNG036-7.p +ROB001-1.p +ROB007-1.p +ROB007-2.p +ROB020-1.p +ROB020-2.p +ROB024-1.p +ROB027-1.p +ROB031-1.p +ROB032-1.p diff --git a/helm/software/components/binaries/matitaprover/log.90.fixed-order b/helm/software/components/binaries/matitaprover/log.90.fixed-order new file mode 100644 index 000000000..4cd2bb2d6 --- /dev/null +++ b/helm/software/components/binaries/matitaprover/log.90.fixed-order @@ -0,0 +1,46155 @@ +CLASH, statistics insufficient +4578: Facts: +4578: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +4578: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +4578: Id : 4, {_}: + add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +4578: Id : 5, {_}: + add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +4578: Id : 6, {_}: + multiply (add ?16 ?17) ?18 + =<= + add (multiply ?16 ?18) (multiply ?17 ?18) + [18, 17, 16] by distributivity3 ?16 ?17 ?18 +4578: Id : 7, {_}: + multiply ?20 (add ?21 ?22) + =<= + add (multiply ?20 ?21) (multiply ?20 ?22) + [22, 21, 20] by distributivity4 ?20 ?21 ?22 +4578: Id : 8, {_}: + add ?24 (inverse ?24) =>= multiplicative_identity + [24] by additive_inverse1 ?24 +4578: Id : 9, {_}: + add (inverse ?26) ?26 =>= multiplicative_identity + [26] by additive_inverse2 ?26 +4578: Id : 10, {_}: + multiply ?28 (inverse ?28) =>= additive_identity + [28] by multiplicative_inverse1 ?28 +4578: Id : 11, {_}: + multiply (inverse ?30) ?30 =>= additive_identity + [30] by multiplicative_inverse2 ?30 +4578: Id : 12, {_}: + multiply ?32 multiplicative_identity =>= ?32 + [32] by multiplicative_id1 ?32 +4578: Id : 13, {_}: + multiply multiplicative_identity ?34 =>= ?34 + [34] by multiplicative_id2 ?34 +4578: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +4578: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +4578: Goal: +4578: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +4578: Order: +4578: nrkbo +4578: Leaf order: +4578: additive_identity 4 0 0 +4578: multiplicative_identity 4 0 0 +4578: inverse 4 1 0 +4578: add 16 2 0 multiply +4578: multiply 20 2 4 0,2add +4578: c 2 0 2 2,2,2 +4578: b 2 0 2 1,2,2 +4578: a 2 0 2 1,2 +CLASH, statistics insufficient +4579: Facts: +4579: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +4579: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +4579: Id : 4, {_}: + add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +4579: Id : 5, {_}: + add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +4579: Id : 6, {_}: + multiply (add ?16 ?17) ?18 + =<= + add (multiply ?16 ?18) (multiply ?17 ?18) + [18, 17, 16] by distributivity3 ?16 ?17 ?18 +4579: Id : 7, {_}: + multiply ?20 (add ?21 ?22) + =<= + add (multiply ?20 ?21) (multiply ?20 ?22) + [22, 21, 20] by distributivity4 ?20 ?21 ?22 +4579: Id : 8, {_}: + add ?24 (inverse ?24) =>= multiplicative_identity + [24] by additive_inverse1 ?24 +4579: Id : 9, {_}: + add (inverse ?26) ?26 =>= multiplicative_identity + [26] by additive_inverse2 ?26 +4579: Id : 10, {_}: + multiply ?28 (inverse ?28) =>= additive_identity + [28] by multiplicative_inverse1 ?28 +4579: Id : 11, {_}: + multiply (inverse ?30) ?30 =>= additive_identity + [30] by multiplicative_inverse2 ?30 +4579: Id : 12, {_}: + multiply ?32 multiplicative_identity =>= ?32 + [32] by multiplicative_id1 ?32 +4579: Id : 13, {_}: + multiply multiplicative_identity ?34 =>= ?34 + [34] by multiplicative_id2 ?34 +4579: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +4579: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +4579: Goal: +4579: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +4579: Order: +4579: kbo +4579: Leaf order: +4579: additive_identity 4 0 0 +4579: multiplicative_identity 4 0 0 +4579: inverse 4 1 0 +4579: add 16 2 0 multiply +4579: multiply 20 2 4 0,2add +4579: c 2 0 2 2,2,2 +4579: b 2 0 2 1,2,2 +4579: a 2 0 2 1,2 +CLASH, statistics insufficient +4580: Facts: +4580: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +4580: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +4580: Id : 4, {_}: + add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +4580: Id : 5, {_}: + add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +4580: Id : 6, {_}: + multiply (add ?16 ?17) ?18 + =>= + add (multiply ?16 ?18) (multiply ?17 ?18) + [18, 17, 16] by distributivity3 ?16 ?17 ?18 +4580: Id : 7, {_}: + multiply ?20 (add ?21 ?22) + =>= + add (multiply ?20 ?21) (multiply ?20 ?22) + [22, 21, 20] by distributivity4 ?20 ?21 ?22 +4580: Id : 8, {_}: + add ?24 (inverse ?24) =>= multiplicative_identity + [24] by additive_inverse1 ?24 +4580: Id : 9, {_}: + add (inverse ?26) ?26 =>= multiplicative_identity + [26] by additive_inverse2 ?26 +4580: Id : 10, {_}: + multiply ?28 (inverse ?28) =>= additive_identity + [28] by multiplicative_inverse1 ?28 +4580: Id : 11, {_}: + multiply (inverse ?30) ?30 =>= additive_identity + [30] by multiplicative_inverse2 ?30 +4580: Id : 12, {_}: + multiply ?32 multiplicative_identity =>= ?32 + [32] by multiplicative_id1 ?32 +4580: Id : 13, {_}: + multiply multiplicative_identity ?34 =>= ?34 + [34] by multiplicative_id2 ?34 +4580: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +4580: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +4580: Goal: +4580: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +4580: Order: +4580: lpo +4580: Leaf order: +4580: additive_identity 4 0 0 +4580: multiplicative_identity 4 0 0 +4580: inverse 4 1 0 +4580: add 16 2 0 multiply +4580: multiply 20 2 4 0,2add +4580: c 2 0 2 2,2,2 +4580: b 2 0 2 1,2,2 +4580: a 2 0 2 1,2 +Statistics : +Max weight : 22 +Found proof, 16.914436s +% SZS status Unsatisfiable for BOO007-2.p +% SZS output start CNFRefutation for BOO007-2.p +Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32 +Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22 +Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28 +Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34 +Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24 +Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80 +Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14 +Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6 +Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18 +Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10 +Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3 +Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3 +Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2 +Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3 +Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3 +Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3 +Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2 +Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2 +Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3 +Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2 +Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3 +Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3 +Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3 +Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3 +Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3 +Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3 +Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3 +Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3 +Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2 +Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2 +Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2 +Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2 +Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3 +Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2 +Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3 +Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2 +Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3 +Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3 +Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2 +Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3 +Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3 +Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3 +Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2 +Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2 +Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2 +Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3 +Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2 +Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2 +Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2 +Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3 +Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3 +Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2 +Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2 +Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3 +Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2 +Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2 +Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2 +Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3 +Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3 +Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3 +Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3 +Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2 +Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2 +Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2 +Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3 +Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3 +Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2 +Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3 +Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3 +Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3 +Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2 +Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3 +Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2 +Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2 +Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3 +Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2 +Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3 +Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3 +Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3 +Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2 +Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3 +Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2 +Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3 +Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2 +Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2 +Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3 +Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2 +Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3 +Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3 +Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3 +Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3 +Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3 +Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3 +Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3 +Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2 +Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3 +Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3 +Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3 +Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2 +Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3 +Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3 +Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3 +Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2 +Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3 +Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2 +Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3 +Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2 +Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity +% SZS output end CNFRefutation for BOO007-2.p +4579: solved BOO007-2.p in 8.372523 using kbo +4579: status Unsatisfiable for BOO007-2.p +CLASH, statistics insufficient +4588: Facts: +4588: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +4588: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +4588: Id : 4, {_}: + add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +4588: Id : 5, {_}: + multiply ?12 (add ?13 ?14) + =<= + add (multiply ?12 ?13) (multiply ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +4588: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +4588: Id : 7, {_}: + multiply ?18 multiplicative_identity =>= ?18 + [18] by multiplicative_id1 ?18 +4588: Id : 8, {_}: + add ?20 (inverse ?20) =>= multiplicative_identity + [20] by additive_inverse1 ?20 +4588: Id : 9, {_}: + multiply ?22 (inverse ?22) =>= additive_identity + [22] by multiplicative_inverse1 ?22 +4588: Goal: +4588: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +4588: Order: +4588: nrkbo +4588: Leaf order: +4588: inverse 2 1 0 +4588: multiplicative_identity 2 0 0 +4588: additive_identity 2 0 0 +4588: add 9 2 0 multiply +4588: multiply 13 2 4 0,2add +4588: c 2 0 2 2,2,2 +4588: b 2 0 2 1,2,2 +4588: a 2 0 2 1,2 +CLASH, statistics insufficient +4589: Facts: +4589: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +4589: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +4589: Id : 4, {_}: + add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +4589: Id : 5, {_}: + multiply ?12 (add ?13 ?14) + =<= + add (multiply ?12 ?13) (multiply ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +4589: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +4589: Id : 7, {_}: + multiply ?18 multiplicative_identity =>= ?18 + [18] by multiplicative_id1 ?18 +4589: Id : 8, {_}: + add ?20 (inverse ?20) =>= multiplicative_identity + [20] by additive_inverse1 ?20 +4589: Id : 9, {_}: + multiply ?22 (inverse ?22) =>= additive_identity + [22] by multiplicative_inverse1 ?22 +4589: Goal: +4589: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +4589: Order: +4589: kbo +4589: Leaf order: +4589: inverse 2 1 0 +4589: multiplicative_identity 2 0 0 +4589: additive_identity 2 0 0 +4589: add 9 2 0 multiply +4589: multiply 13 2 4 0,2add +4589: c 2 0 2 2,2,2 +4589: b 2 0 2 1,2,2 +4589: a 2 0 2 1,2 +CLASH, statistics insufficient +4590: Facts: +4590: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +4590: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +4590: Id : 4, {_}: + add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +4590: Id : 5, {_}: + multiply ?12 (add ?13 ?14) + =>= + add (multiply ?12 ?13) (multiply ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +4590: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +4590: Id : 7, {_}: + multiply ?18 multiplicative_identity =>= ?18 + [18] by multiplicative_id1 ?18 +4590: Id : 8, {_}: + add ?20 (inverse ?20) =>= multiplicative_identity + [20] by additive_inverse1 ?20 +4590: Id : 9, {_}: + multiply ?22 (inverse ?22) =>= additive_identity + [22] by multiplicative_inverse1 ?22 +4590: Goal: +4590: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +4590: Order: +4590: lpo +4590: Leaf order: +4590: inverse 2 1 0 +4590: multiplicative_identity 2 0 0 +4590: additive_identity 2 0 0 +4590: add 9 2 0 multiply +4590: multiply 13 2 4 0,2add +4590: c 2 0 2 2,2,2 +4590: b 2 0 2 1,2,2 +4590: a 2 0 2 1,2 +Statistics : +Max weight : 25 +Found proof, 23.495904s +% SZS status Unsatisfiable for BOO007-4.p +% SZS output start CNFRefutation for BOO007-4.p +Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114 +Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10 +Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22 +Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14 +Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18 +Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6 +Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20 +Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64 +Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3 +Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3 +Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3 +Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3 +Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3 +Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3 +Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3 +Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3 +Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3 +Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3 +Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2 +Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2 +Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2 +Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3 +Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2 +Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3 +Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3 +Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2 +Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2 +Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3 +Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3 +Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2 +Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2 +Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3 +Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2 +Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2 +Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2 +Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2 +Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2 +Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3 +Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3 +Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2 +Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3 +Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3 +Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3 +Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3 +Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3 +Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3 +Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3 +Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3 +Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3 +Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3 +Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3 +Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3 +Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2 +Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2 +Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3 +Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3 +Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3 +Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3 +Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3 +Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3 +Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3 +Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3 +Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3 +Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2 +Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2 +Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3 +Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3 +Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2 +Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3 +Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3 +Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2 +Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3 +Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2 +Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3 +Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2 +Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3 +Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2 +Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3 +Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3 +Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2 +Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3 +Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2 +Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3 +Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3 +Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2 +Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2 +Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3 +Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2 +Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3 +Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2 +Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3 +Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2 +Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity +% SZS output end CNFRefutation for BOO007-4.p +4589: solved BOO007-4.p in 11.664728 using kbo +4589: status Unsatisfiable for BOO007-4.p +CLASH, statistics insufficient +4606: Facts: +4606: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =>= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +4606: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +4606: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +4606: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +4606: Id : 6, {_}: + multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 + [19, 18, 17] by l2 ?17 ?18 ?19 +4606: Id : 7, {_}: + multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 + [23, 22, 21] by l4 ?21 ?22 ?23 +4606: Id : 8, {_}: + add (multiply ?25 (inverse ?25)) ?26 =>= ?26 + [26, 25] by property3_dual ?25 ?26 +4606: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +4606: Id : 10, {_}: + multiply ?30 (inverse ?30) =>= n0 + [30] by multiplicative_inverse ?30 +4606: Id : 11, {_}: + add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34) + [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +4606: Id : 12, {_}: + multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38) + [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +4606: Goal: +4606: Id : 1, {_}: + multiply a (add b c) =<= add (multiply b a) (multiply c a) + [] by prove_multiply_add_property +4606: Order: +4606: nrkbo +4606: Leaf order: +4606: n0 1 0 0 +4606: n1 1 0 0 +4606: inverse 4 1 0 +4606: multiply 22 2 3 0,2add +4606: add 21 2 2 0,2,2multiply +4606: c 2 0 2 2,2,2 +4606: b 2 0 2 1,2,2 +4606: a 3 0 3 1,2 +CLASH, statistics insufficient +4607: Facts: +4607: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =>= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +4607: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +4607: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +4607: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +4607: Id : 6, {_}: + multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 + [19, 18, 17] by l2 ?17 ?18 ?19 +4607: Id : 7, {_}: + multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 + [23, 22, 21] by l4 ?21 ?22 ?23 +4607: Id : 8, {_}: + add (multiply ?25 (inverse ?25)) ?26 =>= ?26 + [26, 25] by property3_dual ?25 ?26 +4607: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +4607: Id : 10, {_}: + multiply ?30 (inverse ?30) =>= n0 + [30] by multiplicative_inverse ?30 +4607: Id : 11, {_}: + add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) + [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +CLASH, statistics insufficient +4608: Facts: +4608: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =>= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +4608: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +4608: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +4608: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +4608: Id : 6, {_}: + multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 + [19, 18, 17] by l2 ?17 ?18 ?19 +4608: Id : 7, {_}: + multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 + [23, 22, 21] by l4 ?21 ?22 ?23 +4608: Id : 8, {_}: + add (multiply ?25 (inverse ?25)) ?26 =>= ?26 + [26, 25] by property3_dual ?25 ?26 +4608: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +4608: Id : 10, {_}: + multiply ?30 (inverse ?30) =>= n0 + [30] by multiplicative_inverse ?30 +4608: Id : 11, {_}: + add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) + [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +4607: Id : 12, {_}: + multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) + [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +4607: Goal: +4607: Id : 1, {_}: + multiply a (add b c) =<= add (multiply b a) (multiply c a) + [] by prove_multiply_add_property +4607: Order: +4607: kbo +4607: Leaf order: +4607: n0 1 0 0 +4607: n1 1 0 0 +4607: inverse 4 1 0 +4607: multiply 22 2 3 0,2add +4607: add 21 2 2 0,2,2multiply +4607: c 2 0 2 2,2,2 +4607: b 2 0 2 1,2,2 +4607: a 3 0 3 1,2 +4608: Id : 12, {_}: + multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) + [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +4608: Goal: +4608: Id : 1, {_}: + multiply a (add b c) =<= add (multiply b a) (multiply c a) + [] by prove_multiply_add_property +4608: Order: +4608: lpo +4608: Leaf order: +4608: n0 1 0 0 +4608: n1 1 0 0 +4608: inverse 4 1 0 +4608: multiply 22 2 3 0,2add +4608: add 21 2 2 0,2,2multiply +4608: c 2 0 2 2,2,2 +4608: b 2 0 2 1,2,2 +4608: a 3 0 3 1,2 +Statistics : +Max weight : 29 +Found proof, 44.648027s +% SZS status Unsatisfiable for BOO031-1.p +% SZS output start CNFRefutation for BOO031-1.p +Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23 +Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30 +Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26 +Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191 +Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15 +Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4 +Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60 +Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12 +Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130 +Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19 +Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8 +Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2 +Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2 +Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2 +Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2 +Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2 +Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2 +Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2 +Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2 +Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2 +Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2 +Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3 +Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2 +Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2 +Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3 +Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2 +Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3 +Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2 +Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2 +Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2 +Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3 +Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2 +Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2 +Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2 +Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2 +Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2 +Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2 +Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2 +Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2 +Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3 +Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2 +Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3 +Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2 +Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3 +Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2 +Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2 +Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2 +Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3 +Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3 +Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3 +Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2 +Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2 +Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2 +Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2 +Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2 +Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2 +Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3 +Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2 +Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3 +Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3 +Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3 +Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2 +Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2 +Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2 +Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2 +Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3 +Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3 +Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3 +Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2 +Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2 +Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3 +Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2 +Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3 +Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2 +Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2 +Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2 +Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2 +Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2 +Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2 +Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2 +Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2 +Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2 +Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2 +Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3 +Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2 +Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2 +Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3 +Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2 +Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2 +Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3 +Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2 +Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3 +Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3 +Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2 +Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3 +Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2 +Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2 +Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2 +Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2 +Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2 +Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2 +Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2 +Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2 +Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2 +Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3 +Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2 +Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2 +Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3 +Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3 +Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3 +Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3 +Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3 +Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3 +Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2 +Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property +% SZS output end CNFRefutation for BOO031-1.p +4607: solved BOO031-1.p in 22.309393 using kbo +4607: status Unsatisfiable for BOO031-1.p +NO CLASH, using fixed ground order +4619: Facts: +4619: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4619: Goal: +4619: Id : 1, {_}: add b a =>= add a b [] by huntinton_1 +4619: Order: +4619: nrkbo +4619: Leaf order: +4619: inverse 7 1 0 +4619: add 8 2 2 0,2 +4619: a 2 0 2 2,2 +4619: b 2 0 2 1,2 +NO CLASH, using fixed ground order +4620: Facts: +4620: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4620: Goal: +4620: Id : 1, {_}: add b a =>= add a b [] by huntinton_1 +4620: Order: +4620: kbo +4620: Leaf order: +4620: inverse 7 1 0 +4620: add 8 2 2 0,2 +4620: a 2 0 2 2,2 +4620: b 2 0 2 1,2 +NO CLASH, using fixed ground order +4621: Facts: +4621: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4621: Goal: +4621: Id : 1, {_}: add b a =>= add a b [] by huntinton_1 +4621: Order: +4621: lpo +4621: Leaf order: +4621: inverse 7 1 0 +4621: add 8 2 2 0,2 +4621: a 2 0 2 2,2 +4621: b 2 0 2 1,2 +Statistics : +Max weight : 70 +Found proof, 56.468020s +% SZS status Unsatisfiable for BOO072-1.p +% SZS output start CNFRefutation for BOO072-1.p +Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10 +Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2 +Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2 +Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2 +Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2 +Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2 +Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2 +Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2 +Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2 +Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2 +Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2 +Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2 +Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2 +Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2 +Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2 +Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2 +Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2 +Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2 +Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2 +Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2 +Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2 +Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2 +Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2 +Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3 +Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2 +Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2 +Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2 +Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2 +Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2 +Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3 +Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2 +Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3 +Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2 +Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2 +Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2 +Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2 +Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3 +Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2 +Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2 +Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2 +Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2 +Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2 +Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3 +Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3 +Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2 +Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2 +Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2 +Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2 +Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2 +Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3 +Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2 +Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3 +Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3 +Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2 +Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2 +Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2 +Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2 +Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2 +Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2 +Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2 +Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2 +Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2 +Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2 +Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2 +Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2 +Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2 +Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2 +Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3 +Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2 +Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3 +Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3 +Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2 +Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3 +Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3 +Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3 +Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3 +Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3 +Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3 +Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2 +Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2 +Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2 +Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2 +Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3 +Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2 +Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3 +Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3 +Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3 +Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3 +Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2 +Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2 +Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2 +Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3 +Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2 +Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3 +Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3 +Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3 +Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3 +Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2 +Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2 +Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3 +Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3 +Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3 +Id : 21981, {_}: add a b === add a b [] by Demod 1 with 21454 at 2 +Id : 1, {_}: add b a =>= add a b [] by huntinton_1 +% SZS output end CNFRefutation for BOO072-1.p +4619: solved BOO072-1.p in 9.46059 using nrkbo +4619: status Unsatisfiable for BOO072-1.p +NO CLASH, using fixed ground order +4637: Facts: +4637: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4637: Goal: +4637: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2 +4637: Order: +4637: nrkbo +4637: Leaf order: +4637: inverse 7 1 0 +4637: c 2 0 2 2,2 +4637: add 10 2 4 0,2 +4637: b 2 0 2 2,1,2 +4637: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +4638: Facts: +4638: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4638: Goal: +4638: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2 +4638: Order: +4638: kbo +4638: Leaf order: +4638: inverse 7 1 0 +4638: c 2 0 2 2,2 +4638: add 10 2 4 0,2 +4638: b 2 0 2 2,1,2 +4638: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +4639: Facts: +4639: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4639: Goal: +4639: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2 +4639: Order: +4639: lpo +4639: Leaf order: +4639: inverse 7 1 0 +4639: c 2 0 2 2,2 +4639: add 10 2 4 0,2 +4639: b 2 0 2 2,1,2 +4639: a 2 0 2 1,1,2 +% SZS status Timeout for BOO073-1.p +NO CLASH, using fixed ground order +4666: Facts: +4666: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4666: Goal: +4666: Id : 1, {_}: + add (inverse (add (inverse a) b)) + (inverse (add (inverse a) (inverse b))) + =>= + a + [] by huntinton_3 +4666: Order: +4666: nrkbo +4666: Leaf order: +4666: add 9 2 3 0,2 +4666: b 2 0 2 2,1,1,2 +4666: inverse 12 1 5 0,1,2 +4666: a 3 0 3 1,1,1,1,2 +NO CLASH, using fixed ground order +4667: Facts: +4667: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4667: Goal: +4667: Id : 1, {_}: + add (inverse (add (inverse a) b)) + (inverse (add (inverse a) (inverse b))) + =>= + a + [] by huntinton_3 +4667: Order: +4667: kbo +4667: Leaf order: +4667: add 9 2 3 0,2 +4667: b 2 0 2 2,1,1,2 +4667: inverse 12 1 5 0,1,2 +4667: a 3 0 3 1,1,1,1,2 +NO CLASH, using fixed ground order +4668: Facts: +4668: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +4668: Goal: +4668: Id : 1, {_}: + add (inverse (add (inverse a) b)) + (inverse (add (inverse a) (inverse b))) + =>= + a + [] by huntinton_3 +4668: Order: +4668: lpo +4668: Leaf order: +4668: add 9 2 3 0,2 +4668: b 2 0 2 2,1,1,2 +4668: inverse 12 1 5 0,1,2 +4668: a 3 0 3 1,1,1,1,2 +Statistics : +Max weight : 70 +Found proof, 17.395929s +% SZS status Unsatisfiable for BOO074-1.p +% SZS output start CNFRefutation for BOO074-1.p +Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10 +Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2 +Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2 +Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2 +Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2 +Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2 +Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2 +Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2 +Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2 +Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2 +Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2 +Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2 +Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2 +Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2 +Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2 +Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2 +Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2 +Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2 +Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2 +Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2 +Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2 +Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2 +Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2 +Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2 +Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3 +Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2 +Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2 +Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2 +Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2 +Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2 +Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3 +Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2 +Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3 +Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2 +Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2 +Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2 +Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2 +Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3 +Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2 +Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2 +Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =?= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2 +Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2 +Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2 +Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2 +Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2 +Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2 +Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2 +Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2 +Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2 +Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2 +Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3 +Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3 +Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2 +Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2 +Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2 +Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2 +Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2 +Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2 +Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3 +Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2 +Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2 +Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2 +Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2 +Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2 +Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2 +Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2 +Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3 +Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2 +Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3 +Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3 +Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2 +Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3 +Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3 +Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3 +Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3 +Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3 +Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3 +Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3 +Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2 +Id : 18644, {_}: a === a [] by Demod 18643 with 1733 at 2 +Id : 18643, {_}: inverse (inverse a) =>= a [] by Demod 18642 with 1761 at 2 +Id : 18642, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18641 with 18480 at 1,2,2 +Id : 18641, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2 +Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3 +% SZS output end CNFRefutation for BOO074-1.p +4666: solved BOO074-1.p in 8.672542 using nrkbo +4666: status Unsatisfiable for BOO074-1.p +NO CLASH, using fixed ground order +4673: Facts: +4673: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4673: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4673: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)) + [] by strong_fixed_point +4673: Goal: +4673: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4673: Order: +4673: nrkbo +4673: Leaf order: +4673: w 4 0 0 +4673: b 6 0 0 +4673: apply 19 2 3 0,2 +4673: fixed_pt 3 0 3 2,2 +4673: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +4674: Facts: +4674: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4674: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4674: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)) + [] by strong_fixed_point +4674: Goal: +4674: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4674: Order: +4674: kbo +4674: Leaf order: +4674: w 4 0 0 +4674: b 6 0 0 +4674: apply 19 2 3 0,2 +4674: fixed_pt 3 0 3 2,2 +4674: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +4675: Facts: +4675: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4675: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4675: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)) + [] by strong_fixed_point +4675: Goal: +4675: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4675: Order: +4675: lpo +4675: Leaf order: +4675: w 4 0 0 +4675: b 6 0 0 +4675: apply 19 2 3 0,2 +4675: fixed_pt 3 0 3 2,2 +4675: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL003-12.p +NO CLASH, using fixed ground order +4697: Facts: +4697: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4697: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4697: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b + [] by strong_fixed_point +4697: Goal: +4697: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4697: Order: +4697: nrkbo +4697: Leaf order: +4697: w 4 0 0 +4697: b 7 0 0 +4697: apply 20 2 3 0,2 +4697: fixed_pt 3 0 3 2,2 +4697: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +4698: Facts: +4698: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4698: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4698: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b + [] by strong_fixed_point +4698: Goal: +4698: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4698: Order: +4698: kbo +4698: Leaf order: +4698: w 4 0 0 +4698: b 7 0 0 +4698: apply 20 2 3 0,2 +4698: fixed_pt 3 0 3 2,2 +4698: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +4699: Facts: +4699: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4699: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4699: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b + [] by strong_fixed_point +4699: Goal: +4699: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4699: Order: +4699: lpo +4699: Leaf order: +4699: w 4 0 0 +4699: b 7 0 0 +4699: apply 20 2 3 0,2 +4699: fixed_pt 3 0 3 2,2 +4699: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL003-17.p +NO CLASH, using fixed ground order +4971: Facts: +4971: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4971: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4971: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply (apply b (apply w w)) (apply b w))) + (apply (apply b b) b) + [] by strong_fixed_point +4971: Goal: +4971: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4971: Order: +4971: nrkbo +4971: Leaf order: +4971: w 4 0 0 +4971: b 7 0 0 +4971: apply 20 2 3 0,2 +4971: fixed_pt 3 0 3 2,2 +4971: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +4972: Facts: +4972: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4972: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4972: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply (apply b (apply w w)) (apply b w))) + (apply (apply b b) b) + [] by strong_fixed_point +4972: Goal: +4972: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4972: Order: +4972: kbo +4972: Leaf order: +4972: w 4 0 0 +4972: b 7 0 0 +4972: apply 20 2 3 0,2 +4972: fixed_pt 3 0 3 2,2 +4972: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +4973: Facts: +4973: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +4973: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +4973: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply (apply b (apply w w)) (apply b w))) + (apply (apply b b) b) + [] by strong_fixed_point +4973: Goal: +4973: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +4973: Order: +4973: lpo +4973: Leaf order: +4973: w 4 0 0 +4973: b 7 0 0 +4973: apply 20 2 3 0,2 +4973: fixed_pt 3 0 3 2,2 +4973: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL003-18.p +NO CLASH, using fixed ground order +7458: Facts: +7458: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +7458: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +7458: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b + [] by strong_fixed_point +7458: Goal: +7458: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +7458: Order: +7458: nrkbo +7458: Leaf order: +7458: w 4 0 0 +7458: b 7 0 0 +7458: apply 20 2 3 0,2 +7458: fixed_pt 3 0 3 2,2 +7458: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +7459: Facts: +7459: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +7459: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +7459: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b + [] by strong_fixed_point +7459: Goal: +7459: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +7459: Order: +7459: kbo +7459: Leaf order: +7459: w 4 0 0 +7459: b 7 0 0 +7459: apply 20 2 3 0,2 +7459: fixed_pt 3 0 3 2,2 +7459: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +7460: Facts: +7460: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +7460: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +7460: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b + [] by strong_fixed_point +7460: Goal: +7460: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +7460: Order: +7460: lpo +7460: Leaf order: +7460: w 4 0 0 +7460: b 7 0 0 +7460: apply 20 2 3 0,2 +7460: fixed_pt 3 0 3 2,2 +7460: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL003-19.p +CLASH, statistics insufficient +9903: Facts: +9903: Id : 2, {_}: + apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4) + [4, 3] by o_definition ?3 ?4 +9903: Id : 3, {_}: + apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7) + [8, 7, 6] by q1_definition ?6 ?7 ?8 +9903: Goal: +9903: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +9903: Order: +9903: nrkbo +9903: Leaf order: +9903: q1 1 0 0 +9903: o 1 0 0 +9903: apply 10 2 1 0,3 +9903: combinator 1 0 1 1,3 +CLASH, statistics insufficient +9904: Facts: +9904: Id : 2, {_}: + apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4) + [4, 3] by o_definition ?3 ?4 +9904: Id : 3, {_}: + apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7) + [8, 7, 6] by q1_definition ?6 ?7 ?8 +9904: Goal: +9904: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +9904: Order: +9904: kbo +9904: Leaf order: +9904: q1 1 0 0 +9904: o 1 0 0 +9904: apply 10 2 1 0,3 +9904: combinator 1 0 1 1,3 +CLASH, statistics insufficient +9905: Facts: +9905: Id : 2, {_}: + apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4) + [4, 3] by o_definition ?3 ?4 +9905: Id : 3, {_}: + apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7) + [8, 7, 6] by q1_definition ?6 ?7 ?8 +9905: Goal: +9905: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +9905: Order: +9905: lpo +9905: Leaf order: +9905: q1 1 0 0 +9905: o 1 0 0 +9905: apply 10 2 1 0,3 +9905: combinator 1 0 1 1,3 +% SZS status Timeout for COL011-1.p +CLASH, statistics insufficient +9926: Facts: +9926: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9926: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +9926: Id : 4, {_}: + apply (apply t ?9) ?10 =>= apply ?10 ?9 + [10, 9] by t_definition ?9 ?10 +9926: Goal: +9926: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9926: Order: +9926: nrkbo +9926: Leaf order: +9926: t 1 0 0 +9926: m 1 0 0 +9926: b 1 0 0 +9926: apply 13 2 3 0,2 +9926: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9927: Facts: +9927: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9927: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +9927: Id : 4, {_}: + apply (apply t ?9) ?10 =>= apply ?10 ?9 + [10, 9] by t_definition ?9 ?10 +9927: Goal: +9927: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9927: Order: +9927: kbo +9927: Leaf order: +9927: t 1 0 0 +9927: m 1 0 0 +9927: b 1 0 0 +9927: apply 13 2 3 0,2 +9927: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9928: Facts: +9928: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9928: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +9928: Id : 4, {_}: + apply (apply t ?9) ?10 =?= apply ?10 ?9 + [10, 9] by t_definition ?9 ?10 +9928: Goal: +9928: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9928: Order: +9928: lpo +9928: Leaf order: +9928: t 1 0 0 +9928: m 1 0 0 +9928: b 1 0 0 +9928: apply 13 2 3 0,2 +9928: f 3 1 3 0,2,2 +Goal subsumed +Statistics : +Max weight : 62 +Found proof, 1.513358s +% SZS status Unsatisfiable for COL034-1.p +% SZS output start CNFRefutation for COL034-1.p +Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2 +Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2 +Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2 +Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3 +Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2 +Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3 +Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL034-1.p +9926: solved COL034-1.p in 0.528032 using nrkbo +9926: status Unsatisfiable for COL034-1.p +CLASH, statistics insufficient +9933: Facts: +9933: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +9933: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +9933: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +9933: Goal: +9933: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9933: Order: +9933: nrkbo +9933: Leaf order: +9933: c 1 0 0 +9933: b 1 0 0 +9933: s 1 0 0 +9933: apply 19 2 3 0,2 +9933: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9934: Facts: +9934: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +9934: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +9934: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +9934: Goal: +9934: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9934: Order: +9934: kbo +9934: Leaf order: +9934: c 1 0 0 +9934: b 1 0 0 +9934: s 1 0 0 +9934: apply 19 2 3 0,2 +9934: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9935: Facts: +9935: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +9935: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +9935: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +9935: Goal: +9935: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9935: Order: +9935: lpo +9935: Leaf order: +9935: c 1 0 0 +9935: b 1 0 0 +9935: s 1 0 0 +9935: apply 19 2 3 0,2 +9935: f 3 1 3 0,2,2 +% SZS status Timeout for COL037-1.p +CLASH, statistics insufficient +9973: Facts: +9973: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9973: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +9973: Id : 4, {_}: + apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 + [11, 10, 9] by c_definition ?9 ?10 ?11 +9973: Goal: +9973: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9973: Order: +9973: nrkbo +9973: Leaf order: +9973: c 1 0 0 +9973: m 1 0 0 +9973: b 1 0 0 +9973: apply 15 2 3 0,2 +9973: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9974: Facts: +9974: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9974: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +9974: Id : 4, {_}: + apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 + [11, 10, 9] by c_definition ?9 ?10 ?11 +9974: Goal: +9974: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9974: Order: +9974: kbo +9974: Leaf order: +9974: c 1 0 0 +9974: m 1 0 0 +9974: b 1 0 0 +9974: apply 15 2 3 0,2 +9974: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9975: Facts: +9975: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9975: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +9975: Id : 4, {_}: + apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10 + [11, 10, 9] by c_definition ?9 ?10 ?11 +9975: Goal: +9975: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9975: Order: +9975: lpo +9975: Leaf order: +9975: c 1 0 0 +9975: m 1 0 0 +9975: b 1 0 0 +9975: apply 15 2 3 0,2 +9975: f 3 1 3 0,2,2 +Goal subsumed +Statistics : +Max weight : 54 +Found proof, 2.234152s +% SZS status Unsatisfiable for COL041-1.p +% SZS output start CNFRefutation for COL041-1.p +Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2 +Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2 +Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2 +Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3 +Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL041-1.p +9973: solved COL041-1.p in 1.13607 using nrkbo +9973: status Unsatisfiable for COL041-1.p +CLASH, statistics insufficient +9980: Facts: +9980: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9980: Id : 3, {_}: + apply (apply (apply n ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?9) ?8) ?9 + [9, 8, 7] by n_definition ?7 ?8 ?9 +9980: Goal: +9980: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9980: Order: +9980: nrkbo +9980: Leaf order: +9980: n 1 0 0 +9980: b 1 0 0 +9980: apply 14 2 3 0,2 +9980: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9981: Facts: +9981: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9981: Id : 3, {_}: + apply (apply (apply n ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?9) ?8) ?9 + [9, 8, 7] by n_definition ?7 ?8 ?9 +9981: Goal: +9981: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9981: Order: +9981: kbo +9981: Leaf order: +9981: n 1 0 0 +9981: b 1 0 0 +9981: apply 14 2 3 0,2 +9981: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9982: Facts: +9982: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9982: Id : 3, {_}: + apply (apply (apply n ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?9) ?8) ?9 + [9, 8, 7] by n_definition ?7 ?8 ?9 +9982: Goal: +9982: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +9982: Order: +9982: lpo +9982: Leaf order: +9982: n 1 0 0 +9982: b 1 0 0 +9982: apply 14 2 3 0,2 +9982: f 3 1 3 0,2,2 +Goal subsumed +Statistics : +Max weight : 88 +Found proof, 76.191737s +% SZS status Unsatisfiable for COL044-1.p +% SZS output start CNFRefutation for COL044-1.p +Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13 +Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2 +Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2 +Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2 +Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2 +Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3 +Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3 +Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL044-1.p +9981: solved COL044-1.p in 12.724795 using kbo +9981: status Unsatisfiable for COL044-1.p +CLASH, statistics insufficient +9998: Facts: +9998: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9998: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +9998: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +9998: Goal: +9998: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +9998: Order: +9998: nrkbo +9998: Leaf order: +9998: m 1 0 0 +9998: w 1 0 0 +9998: b 1 0 0 +9998: apply 14 2 3 0,2 +9998: f 3 1 3 0,2,2 +CLASH, statistics insufficient +9999: Facts: +9999: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +9999: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +9999: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +9999: Goal: +9999: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +9999: Order: +9999: kbo +9999: Leaf order: +9999: m 1 0 0 +9999: w 1 0 0 +9999: b 1 0 0 +9999: apply 14 2 3 0,2 +9999: f 3 1 3 0,2,2 +CLASH, statistics insufficient +10000: Facts: +10000: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +10000: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +10000: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +10000: Goal: +10000: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +10000: Order: +10000: lpo +10000: Leaf order: +10000: m 1 0 0 +10000: w 1 0 0 +10000: b 1 0 0 +10000: apply 14 2 3 0,2 +10000: f 3 1 3 0,2,2 +Goal subsumed +Statistics : +Max weight : 54 +Found proof, 12.856628s +% SZS status Unsatisfiable for COL049-1.p +% SZS output start CNFRefutation for COL049-1.p +Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8 +Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2 +Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3 +Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3 +Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2 +Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2 +Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3 +Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1 +% SZS output end CNFRefutation for COL049-1.p +9998: solved COL049-1.p in 6.372397 using nrkbo +9998: status Unsatisfiable for COL049-1.p +CLASH, statistics insufficient +10010: Facts: +10010: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +10010: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +10010: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +10010: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +10010: Goal: +10010: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +10010: Order: +10010: nrkbo +10010: Leaf order: +10010: i 1 0 0 +10010: c 1 0 0 +10010: b 1 0 0 +10010: s 1 0 0 +10010: apply 20 2 3 0,2 +10010: f 3 1 3 0,2,2 +CLASH, statistics insufficient +10011: Facts: +10011: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +10011: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +10011: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +10011: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +10011: Goal: +10011: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +10011: Order: +10011: kbo +10011: Leaf order: +10011: i 1 0 0 +10011: c 1 0 0 +10011: b 1 0 0 +10011: s 1 0 0 +10011: apply 20 2 3 0,2 +10011: f 3 1 3 0,2,2 +CLASH, statistics insufficient +10012: Facts: +10012: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +10012: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +10012: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +10012: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +10012: Goal: +10012: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +10012: Order: +10012: lpo +10012: Leaf order: +10012: i 1 0 0 +10012: c 1 0 0 +10012: b 1 0 0 +10012: s 1 0 0 +10012: apply 20 2 3 0,2 +10012: f 3 1 3 0,2,2 +Goal subsumed +Statistics : +Max weight : 84 +Found proof, 12.629405s +% SZS status Unsatisfiable for COL057-1.p +% SZS output start CNFRefutation for COL057-1.p +Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9 +Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5 +Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3 +Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3 +Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2 +Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3 +Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1 +% SZS output end CNFRefutation for COL057-1.p +10010: solved COL057-1.p in 2.124132 using nrkbo +10010: status Unsatisfiable for COL057-1.p +NO CLASH, using fixed ground order +10025: Facts: +10025: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +10025: Goal: +10025: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +10025: Order: +10025: nrkbo +10025: Leaf order: +10025: inverse 5 1 0 +10025: multiply 10 2 4 0,2 +10025: c 2 0 2 2,2,2 +10025: b 2 0 2 1,2,2 +10025: a 2 0 2 1,2 +NO CLASH, using fixed ground order +10026: Facts: +10026: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +10026: Goal: +10026: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +10026: Order: +10026: kbo +10026: Leaf order: +10026: inverse 5 1 0 +10026: multiply 10 2 4 0,2 +10026: c 2 0 2 2,2,2 +10026: b 2 0 2 1,2,2 +10026: a 2 0 2 1,2 +NO CLASH, using fixed ground order +10027: Facts: +10027: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +10027: Goal: +10027: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +10027: Order: +10027: lpo +10027: Leaf order: +10027: inverse 5 1 0 +10027: multiply 10 2 4 0,2 +10027: c 2 0 2 2,2,2 +10027: b 2 0 2 1,2,2 +10027: a 2 0 2 1,2 +Statistics : +Max weight : 62 +Found proof, 20.319552s +% SZS status Unsatisfiable for GRP014-1.p +% SZS output start CNFRefutation for GRP014-1.p +Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10 +Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2 +Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2 +Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2 +Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2 +Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2 +Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2 +Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3 +Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2 +Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2 +Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2 +Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2 +Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2 +Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2 +Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2 +Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2 +Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2 +Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2 +Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2 +Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3 +Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2 +Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2 +Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3 +Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2 +Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2 +Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2 +Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2 +Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2 +Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3 +Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2 +Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3 +Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2 +Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2 +Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2 +Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2 +Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2 +Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2 +Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2 +Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2 +Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3 +Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2 +Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2 +Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2 +Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2 +Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2 +Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2 +Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2 +Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2 +Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2 +Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2 +Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2 +Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2 +Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2 +Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2 +Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2 +Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2 +Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2 +Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2 +Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2 +Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2 +Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2 +Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2 +Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2 +Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2 +Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2 +Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2 +Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2 +Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2 +Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2 +Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2 +Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2 +Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2 +Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2 +Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2 +Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2 +Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2 +Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2 +Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2 +Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2 +Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2 +Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2 +Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2 +Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2 +Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3 +Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2 +Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2 +Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2 +Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2 +Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2 +Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2 +Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2 +Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2 +Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2 +Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2 +Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2 +Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2 +Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2 +Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3 +Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2 +Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2 +Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2 +Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2 +Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2 +Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2 +Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2 +Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2 +Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2 +Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3 +Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3 +Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2 +Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2 +Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3 +Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2 +Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2 +Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2 +Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2 +Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2 +Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2 +Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2 +Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2 +Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3 +Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity +% SZS output end CNFRefutation for GRP014-1.p +10025: solved GRP014-1.p in 10.216638 using nrkbo +10025: status Unsatisfiable for GRP014-1.p +CLASH, statistics insufficient +10036: Facts: +10036: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10036: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10036: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10036: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10036: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10036: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10036: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10036: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10036: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10036: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10036: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10036: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10036: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10036: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10036: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10036: Id : 17, {_}: + positive_part ?50 =<= least_upper_bound ?50 identity + [50] by lat4_1 ?50 +10036: Id : 18, {_}: + negative_part ?52 =<= greatest_lower_bound ?52 identity + [52] by lat4_2 ?52 +10036: Id : 19, {_}: + least_upper_bound ?54 (greatest_lower_bound ?55 ?56) + =<= + greatest_lower_bound (least_upper_bound ?54 ?55) + (least_upper_bound ?54 ?56) + [56, 55, 54] by lat4_3 ?54 ?55 ?56 +10036: Id : 20, {_}: + greatest_lower_bound ?58 (least_upper_bound ?59 ?60) + =<= + least_upper_bound (greatest_lower_bound ?58 ?59) + (greatest_lower_bound ?58 ?60) + [60, 59, 58] by lat4_4 ?58 ?59 ?60 +10036: Goal: +10036: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +10036: Order: +10036: nrkbo +10036: Leaf order: +10036: least_upper_bound 19 2 0 +10036: greatest_lower_bound 19 2 0 +10036: inverse 1 1 0 +10036: identity 4 0 0 +10036: multiply 19 2 1 0,3 +10036: negative_part 2 1 1 0,2,3 +10036: positive_part 2 1 1 0,1,3 +10036: a 3 0 3 2 +CLASH, statistics insufficient +10037: Facts: +10037: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10037: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10037: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10037: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10037: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10037: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10037: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10037: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10037: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10037: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10037: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10037: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10037: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10037: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10037: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10037: Id : 17, {_}: + positive_part ?50 =<= least_upper_bound ?50 identity + [50] by lat4_1 ?50 +10037: Id : 18, {_}: + negative_part ?52 =<= greatest_lower_bound ?52 identity + [52] by lat4_2 ?52 +10037: Id : 19, {_}: + least_upper_bound ?54 (greatest_lower_bound ?55 ?56) + =<= + greatest_lower_bound (least_upper_bound ?54 ?55) + (least_upper_bound ?54 ?56) + [56, 55, 54] by lat4_3 ?54 ?55 ?56 +10037: Id : 20, {_}: + greatest_lower_bound ?58 (least_upper_bound ?59 ?60) + =<= + least_upper_bound (greatest_lower_bound ?58 ?59) + (greatest_lower_bound ?58 ?60) + [60, 59, 58] by lat4_4 ?58 ?59 ?60 +10037: Goal: +10037: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +10037: Order: +10037: kbo +10037: Leaf order: +10037: least_upper_bound 19 2 0 +10037: greatest_lower_bound 19 2 0 +10037: inverse 1 1 0 +10037: identity 4 0 0 +10037: multiply 19 2 1 0,3 +10037: negative_part 2 1 1 0,2,3 +10037: positive_part 2 1 1 0,1,3 +10037: a 3 0 3 2 +CLASH, statistics insufficient +10038: Facts: +10038: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10038: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10038: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10038: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10038: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10038: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10038: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10038: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10038: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10038: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10038: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10038: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10038: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10038: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10038: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10038: Id : 17, {_}: + positive_part ?50 =>= least_upper_bound ?50 identity + [50] by lat4_1 ?50 +10038: Id : 18, {_}: + negative_part ?52 =>= greatest_lower_bound ?52 identity + [52] by lat4_2 ?52 +10038: Id : 19, {_}: + least_upper_bound ?54 (greatest_lower_bound ?55 ?56) + =<= + greatest_lower_bound (least_upper_bound ?54 ?55) + (least_upper_bound ?54 ?56) + [56, 55, 54] by lat4_3 ?54 ?55 ?56 +10038: Id : 20, {_}: + greatest_lower_bound ?58 (least_upper_bound ?59 ?60) + =>= + least_upper_bound (greatest_lower_bound ?58 ?59) + (greatest_lower_bound ?58 ?60) + [60, 59, 58] by lat4_4 ?58 ?59 ?60 +10038: Goal: +10038: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +10038: Order: +10038: lpo +10038: Leaf order: +10038: least_upper_bound 19 2 0 +10038: greatest_lower_bound 19 2 0 +10038: inverse 1 1 0 +10038: identity 4 0 0 +10038: multiply 19 2 1 0,3 +10038: negative_part 2 1 1 0,2,3 +10038: positive_part 2 1 1 0,1,3 +10038: a 3 0 3 2 +Statistics : +Max weight : 19 +Found proof, 19.804581s +% SZS status Unsatisfiable for GRP167-1.p +% SZS output start CNFRefutation for GRP167-1.p +Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29 +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 134, {_}: multiply ?322 (least_upper_bound ?323 ?324) =<= least_upper_bound (multiply ?322 ?323) (multiply ?322 ?324) [324, 323, 322] by monotony_lub1 ?322 ?323 ?324 +Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32 +Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +Id : 20, {_}: greatest_lower_bound ?58 (least_upper_bound ?59 ?60) =<= least_upper_bound (greatest_lower_bound ?58 ?59) (greatest_lower_bound ?58 ?60) [60, 59, 58] by lat4_4 ?58 ?59 ?60 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52 +Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11 +Id : 237, {_}: multiply (greatest_lower_bound ?514 ?515) ?516 =<= greatest_lower_bound (multiply ?514 ?516) (multiply ?515 ?516) [516, 515, 514] by monotony_glb2 ?514 ?515 ?516 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =>= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71 +Id : 27, {_}: multiply identity ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Super 25 with 3 at 1,2 +Id : 31, {_}: ?76 =<= multiply (inverse ?77) (multiply ?77 ?76) [77, 76] by Demod 27 with 2 at 2 +Id : 242, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= greatest_lower_bound identity (multiply ?533 ?532) [533, 532] by Super 237 with 3 at 1,3 +Id : 278, {_}: greatest_lower_bound identity ?584 =>= negative_part ?584 [584] by Super 5 with 18 at 3 +Id : 15662, {_}: multiply (greatest_lower_bound (inverse ?19569) ?19570) ?19569 =>= negative_part (multiply ?19570 ?19569) [19570, 19569] by Demod 242 with 278 at 3 +Id : 15688, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part (multiply identity ?19646) [19646] by Super 15662 with 18 at 1,2 +Id : 15740, {_}: multiply (negative_part (inverse ?19646)) ?19646 =>= negative_part ?19646 [19646] by Demod 15688 with 2 at 1,3 +Id : 15765, {_}: ?19710 =<= multiply (inverse (negative_part (inverse ?19710))) (negative_part ?19710) [19710] by Super 31 with 15740 at 2,3 +Id : 778, {_}: ?1461 =<= multiply (inverse ?1462) (multiply ?1462 ?1461) [1462, 1461] by Demod 27 with 2 at 2 +Id : 782, {_}: ?1472 =<= multiply (inverse (inverse ?1472)) identity [1472] by Super 778 with 3 at 2,3 +Id : 1371, {_}: multiply (inverse (inverse ?2316)) (least_upper_bound ?2317 identity) =?= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Super 13 with 782 at 2,3 +Id : 1392, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound (multiply (inverse (inverse ?2316)) ?2317) ?2316 [2317, 2316] by Demod 1371 with 17 at 2,2 +Id : 1393, {_}: multiply (inverse (inverse ?2316)) (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1392 with 6 at 3 +Id : 786, {_}: multiply ?1484 ?1485 =<= multiply (inverse (inverse ?1484)) ?1485 [1485, 1484] by Super 778 with 31 at 2,3 +Id : 2137, {_}: ?1472 =<= multiply ?1472 identity [1472] by Demod 782 with 786 at 3 +Id : 2138, {_}: inverse (inverse ?3405) =<= multiply ?3405 identity [3405] by Super 2137 with 786 at 3 +Id : 2189, {_}: inverse (inverse ?3405) =>= ?3405 [3405] by Demod 2138 with 2137 at 3 +Id : 49575, {_}: multiply ?2316 (positive_part ?2317) =<= least_upper_bound ?2316 (multiply (inverse (inverse ?2316)) ?2317) [2317, 2316] by Demod 1393 with 2189 at 1,2 +Id : 49621, {_}: multiply ?54979 (positive_part ?54980) =<= least_upper_bound ?54979 (multiply ?54979 ?54980) [54980, 54979] by Demod 49575 with 2189 at 1,2,3 +Id : 15768, {_}: multiply (negative_part (inverse ?19715)) ?19715 =>= negative_part ?19715 [19715] by Demod 15688 with 2 at 1,3 +Id : 15773, {_}: multiply (negative_part ?19724) (inverse ?19724) =>= negative_part (inverse ?19724) [19724] by Super 15768 with 2189 at 1,1,2 +Id : 49652, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= least_upper_bound (negative_part ?55064) (negative_part (inverse ?55064)) [55064] by Super 49621 with 15773 at 2,3 +Id : 865, {_}: greatest_lower_bound identity (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Super 20 with 278 at 2,3 +Id : 880, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (greatest_lower_bound identity ?1569) (negative_part ?1570) [1570, 1569] by Demod 865 with 278 at 2 +Id : 881, {_}: negative_part (least_upper_bound ?1569 ?1570) =<= least_upper_bound (negative_part ?1569) (negative_part ?1570) [1570, 1569] by Demod 880 with 278 at 1,3 +Id : 49776, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= negative_part (least_upper_bound ?55064 (inverse ?55064)) [55064] by Demod 49652 with 881 at 3 +Id : 15757, {_}: multiply (greatest_lower_bound (negative_part (inverse ?19686)) ?19687) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Super 16 with 15740 at 1,3 +Id : 859, {_}: greatest_lower_bound identity (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Super 7 with 278 at 1,3 +Id : 890, {_}: negative_part (greatest_lower_bound ?1558 ?1559) =>= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 859 with 278 at 2 +Id : 281, {_}: greatest_lower_bound ?591 (greatest_lower_bound ?592 identity) =>= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Super 7 with 18 at 3 +Id : 289, {_}: greatest_lower_bound ?591 (negative_part ?592) =<= negative_part (greatest_lower_bound ?591 ?592) [592, 591] by Demod 281 with 18 at 2,2 +Id : 1628, {_}: greatest_lower_bound ?1558 (negative_part ?1559) =<= greatest_lower_bound (negative_part ?1558) ?1559 [1559, 1558] by Demod 890 with 289 at 2 +Id : 15802, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound (negative_part ?19686) (multiply ?19687 ?19686) [19687, 19686] by Demod 15757 with 1628 at 1,2 +Id : 15803, {_}: multiply (greatest_lower_bound (inverse ?19686) (negative_part ?19687)) ?19686 =>= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19687, 19686] by Demod 15802 with 1628 at 3 +Id : 15650, {_}: multiply (greatest_lower_bound (inverse ?532) ?533) ?532 =>= negative_part (multiply ?533 ?532) [533, 532] by Demod 242 with 278 at 3 +Id : 15804, {_}: negative_part (multiply (negative_part ?19687) ?19686) =<= greatest_lower_bound ?19686 (negative_part (multiply ?19687 ?19686)) [19686, 19687] by Demod 15803 with 15650 at 2 +Id : 49651, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part (inverse ?55062)) (negative_part ?55062) [55062] by Super 49621 with 15740 at 2,3 +Id : 49774, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= least_upper_bound (negative_part ?55062) (negative_part (inverse ?55062)) [55062] by Demod 49651 with 6 at 3 +Id : 49775, {_}: multiply (negative_part (inverse ?55062)) (positive_part ?55062) =>= negative_part (least_upper_bound ?55062 (inverse ?55062)) [55062] by Demod 49774 with 881 at 3 +Id : 49840, {_}: negative_part (multiply (negative_part (negative_part (inverse ?55170))) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Super 15804 with 49775 at 1,2,3 +Id : 268, {_}: greatest_lower_bound ?569 (positive_part ?569) =>= ?569 [569] by Super 12 with 17 at 2,2 +Id : 139, {_}: multiply (inverse ?340) (least_upper_bound ?340 ?341) =>= least_upper_bound identity (multiply (inverse ?340) ?341) [341, 340] by Super 134 with 3 at 1,3 +Id : 264, {_}: least_upper_bound identity ?559 =>= positive_part ?559 [559] by Super 6 with 17 at 3 +Id : 4901, {_}: multiply (inverse ?7380) (least_upper_bound ?7380 ?7381) =>= positive_part (multiply (inverse ?7380) ?7381) [7381, 7380] by Demod 139 with 264 at 3 +Id : 4921, {_}: multiply (inverse ?7441) (positive_part ?7441) =?= positive_part (multiply (inverse ?7441) identity) [7441] by Super 4901 with 17 at 2,2 +Id : 4985, {_}: multiply (inverse ?7525) (positive_part ?7525) =>= positive_part (inverse ?7525) [7525] by Demod 4921 with 2137 at 1,3 +Id : 267, {_}: least_upper_bound ?566 (least_upper_bound ?567 identity) =>= positive_part (least_upper_bound ?566 ?567) [567, 566] by Super 8 with 17 at 3 +Id : 1187, {_}: least_upper_bound ?2080 (positive_part ?2081) =<= positive_part (least_upper_bound ?2080 ?2081) [2081, 2080] by Demod 267 with 17 at 2,2 +Id : 1199, {_}: least_upper_bound ?2117 (positive_part identity) =>= positive_part (positive_part ?2117) [2117] by Super 1187 with 17 at 1,3 +Id : 263, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2 +Id : 1218, {_}: least_upper_bound ?2117 identity =<= positive_part (positive_part ?2117) [2117] by Demod 1199 with 263 at 2,2 +Id : 1219, {_}: positive_part ?2117 =<= positive_part (positive_part ?2117) [2117] by Demod 1218 with 17 at 2 +Id : 4997, {_}: multiply (inverse (positive_part ?7553)) (positive_part ?7553) =>= positive_part (inverse (positive_part ?7553)) [7553] by Super 4985 with 1219 at 2,2 +Id : 5031, {_}: identity =<= positive_part (inverse (positive_part ?7553)) [7553] by Demod 4997 with 3 at 2 +Id : 5129, {_}: greatest_lower_bound (inverse (positive_part ?7677)) identity =>= inverse (positive_part ?7677) [7677] by Super 268 with 5031 at 2,2 +Id : 5176, {_}: greatest_lower_bound identity (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5129 with 5 at 2 +Id : 5177, {_}: negative_part (inverse (positive_part ?7677)) =>= inverse (positive_part ?7677) [7677] by Demod 5176 with 278 at 2 +Id : 5325, {_}: greatest_lower_bound (inverse (positive_part ?7851)) (negative_part ?7852) =>= greatest_lower_bound (inverse (positive_part ?7851)) ?7852 [7852, 7851] by Super 1628 with 5177 at 1,3 +Id : 15685, {_}: multiply (greatest_lower_bound (inverse (positive_part ?19637)) ?19638) (positive_part ?19637) =>= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19638, 19637] by Super 15662 with 5325 at 1,2 +Id : 15737, {_}: negative_part (multiply ?19638 (positive_part ?19637)) =<= negative_part (multiply (negative_part ?19638) (positive_part ?19637)) [19637, 19638] by Demod 15685 with 15650 at 2 +Id : 49928, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =<= greatest_lower_bound (positive_part ?55170) (negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170)))) [55170] by Demod 49840 with 15737 at 2 +Id : 1648, {_}: greatest_lower_bound ?2900 (negative_part ?2901) =<= greatest_lower_bound (negative_part ?2900) ?2901 [2901, 2900] by Demod 890 with 289 at 2 +Id : 863, {_}: negative_part (least_upper_bound identity ?1566) =>= identity [1566] by Super 12 with 278 at 2 +Id : 886, {_}: negative_part (positive_part ?1566) =>= identity [1566] by Demod 863 with 264 at 1,2 +Id : 1653, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= greatest_lower_bound identity ?2915 [2915, 2914] by Super 1648 with 886 at 1,3 +Id : 1710, {_}: greatest_lower_bound (positive_part ?2914) (negative_part ?2915) =>= negative_part ?2915 [2915, 2914] by Demod 1653 with 278 at 3 +Id : 49929, {_}: negative_part (multiply (negative_part (inverse ?55170)) (positive_part ?55170)) =>= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49928 with 1710 at 3 +Id : 49930, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =<= negative_part (negative_part (least_upper_bound ?55170 (inverse ?55170))) [55170] by Demod 49929 with 15737 at 2 +Id : 1014, {_}: greatest_lower_bound ?1717 (positive_part ?1717) =>= ?1717 [1717] by Super 12 with 17 at 2,2 +Id : 858, {_}: least_upper_bound identity (negative_part ?1556) =>= identity [1556] by Super 11 with 278 at 2,2 +Id : 891, {_}: positive_part (negative_part ?1556) =>= identity [1556] by Demod 858 with 264 at 2 +Id : 1019, {_}: greatest_lower_bound (negative_part ?1726) identity =>= negative_part ?1726 [1726] by Super 1014 with 891 at 2,2 +Id : 1039, {_}: greatest_lower_bound identity (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1019 with 5 at 2 +Id : 1040, {_}: negative_part (negative_part ?1726) =>= negative_part ?1726 [1726] by Demod 1039 with 278 at 2 +Id : 49931, {_}: negative_part (multiply (inverse ?55170) (positive_part ?55170)) =>= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49930 with 1040 at 3 +Id : 4960, {_}: multiply (inverse ?7441) (positive_part ?7441) =>= positive_part (inverse ?7441) [7441] by Demod 4921 with 2137 at 1,3 +Id : 49932, {_}: negative_part (positive_part (inverse ?55170)) =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49931 with 4960 at 1,2 +Id : 49933, {_}: identity =<= negative_part (least_upper_bound ?55170 (inverse ?55170)) [55170] by Demod 49932 with 886 at 2 +Id : 53516, {_}: multiply (negative_part ?55064) (positive_part (inverse ?55064)) =>= identity [55064] by Demod 49776 with 49933 at 3 +Id : 53529, {_}: positive_part (inverse ?58317) =<= multiply (inverse (negative_part ?58317)) identity [58317] by Super 31 with 53516 at 2,3 +Id : 53947, {_}: positive_part (inverse ?58761) =>= inverse (negative_part ?58761) [58761] by Demod 53529 with 2137 at 3 +Id : 53952, {_}: positive_part ?58770 =<= inverse (negative_part (inverse ?58770)) [58770] by Super 53947 with 2189 at 1,2 +Id : 54151, {_}: ?19710 =<= multiply (positive_part ?19710) (negative_part ?19710) [19710] by Demod 15765 with 53952 at 1,3 +Id : 54473, {_}: a =?= a [] by Demod 1 with 54151 at 3 +Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4 +% SZS output end CNFRefutation for GRP167-1.p +10037: solved GRP167-1.p in 9.872616 using kbo +10037: status Unsatisfiable for GRP167-1.p +CLASH, statistics insufficient +10051: Facts: +10051: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10051: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10051: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10051: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10051: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10051: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10051: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10051: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10051: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10051: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10051: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10051: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10051: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10051: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10051: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10051: Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +10051: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +10051: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by lat4_3 ?53 ?54 +10051: Id : 20, {_}: + positive_part ?56 =<= least_upper_bound ?56 identity + [56] by lat4_4 ?56 +10051: Id : 21, {_}: + negative_part ?58 =<= greatest_lower_bound ?58 identity + [58] by lat4_5 ?58 +10051: Id : 22, {_}: + least_upper_bound ?60 (greatest_lower_bound ?61 ?62) + =<= + greatest_lower_bound (least_upper_bound ?60 ?61) + (least_upper_bound ?60 ?62) + [62, 61, 60] by lat4_6 ?60 ?61 ?62 +10051: Id : 23, {_}: + greatest_lower_bound ?64 (least_upper_bound ?65 ?66) + =<= + least_upper_bound (greatest_lower_bound ?64 ?65) + (greatest_lower_bound ?64 ?66) + [66, 65, 64] by lat4_7 ?64 ?65 ?66 +10051: Goal: +10051: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +10051: Order: +10051: nrkbo +10051: Leaf order: +10051: least_upper_bound 19 2 0 +10051: greatest_lower_bound 19 2 0 +10051: inverse 7 1 0 +10051: identity 6 0 0 +10051: multiply 21 2 1 0,3 +10051: negative_part 2 1 1 0,2,3 +10051: positive_part 2 1 1 0,1,3 +10051: a 3 0 3 2 +CLASH, statistics insufficient +10052: Facts: +10052: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10052: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10052: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10052: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10052: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10052: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10052: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10052: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10052: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10052: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10052: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10052: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10052: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10052: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10052: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10052: Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +10052: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +10052: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by lat4_3 ?53 ?54 +10052: Id : 20, {_}: + positive_part ?56 =<= least_upper_bound ?56 identity + [56] by lat4_4 ?56 +10052: Id : 21, {_}: + negative_part ?58 =<= greatest_lower_bound ?58 identity + [58] by lat4_5 ?58 +10052: Id : 22, {_}: + least_upper_bound ?60 (greatest_lower_bound ?61 ?62) + =<= + greatest_lower_bound (least_upper_bound ?60 ?61) + (least_upper_bound ?60 ?62) + [62, 61, 60] by lat4_6 ?60 ?61 ?62 +10052: Id : 23, {_}: + greatest_lower_bound ?64 (least_upper_bound ?65 ?66) + =<= + least_upper_bound (greatest_lower_bound ?64 ?65) + (greatest_lower_bound ?64 ?66) + [66, 65, 64] by lat4_7 ?64 ?65 ?66 +10052: Goal: +10052: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +10052: Order: +10052: kbo +10052: Leaf order: +10052: least_upper_bound 19 2 0 +10052: greatest_lower_bound 19 2 0 +10052: inverse 7 1 0 +10052: identity 6 0 0 +10052: multiply 21 2 1 0,3 +10052: negative_part 2 1 1 0,2,3 +10052: positive_part 2 1 1 0,1,3 +10052: a 3 0 3 2 +CLASH, statistics insufficient +10053: Facts: +10053: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10053: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10053: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10053: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10053: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10053: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10053: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10053: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10053: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10053: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10053: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10053: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10053: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10053: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10053: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10053: Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +10053: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +10053: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by lat4_3 ?53 ?54 +10053: Id : 20, {_}: + positive_part ?56 =>= least_upper_bound ?56 identity + [56] by lat4_4 ?56 +10053: Id : 21, {_}: + negative_part ?58 =>= greatest_lower_bound ?58 identity + [58] by lat4_5 ?58 +10053: Id : 22, {_}: + least_upper_bound ?60 (greatest_lower_bound ?61 ?62) + =<= + greatest_lower_bound (least_upper_bound ?60 ?61) + (least_upper_bound ?60 ?62) + [62, 61, 60] by lat4_6 ?60 ?61 ?62 +10053: Id : 23, {_}: + greatest_lower_bound ?64 (least_upper_bound ?65 ?66) + =>= + least_upper_bound (greatest_lower_bound ?64 ?65) + (greatest_lower_bound ?64 ?66) + [66, 65, 64] by lat4_7 ?64 ?65 ?66 +10053: Goal: +10053: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +10053: Order: +10053: lpo +10053: Leaf order: +10053: least_upper_bound 19 2 0 +10053: greatest_lower_bound 19 2 0 +10053: inverse 7 1 0 +10053: identity 6 0 0 +10053: multiply 21 2 1 0,3 +10053: negative_part 2 1 1 0,2,3 +10053: positive_part 2 1 1 0,1,3 +10053: a 3 0 3 2 +Statistics : +Max weight : 15 +Found proof, 6.844655s +% SZS status Unsatisfiable for GRP167-2.p +% SZS output start CNFRefutation for GRP167-2.p +Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54 +Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32 +Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62 +Id : 210, {_}: multiply (least_upper_bound ?453 ?454) ?455 =<= least_upper_bound (multiply ?453 ?455) (multiply ?454 ?455) [455, 454, 453] by monotony_lub2 ?453 ?454 ?455 +Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11 +Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58 +Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 286, {_}: inverse (multiply ?614 ?615) =<= multiply (inverse ?615) (inverse ?614) [615, 614] by lat4_3 ?614 ?615 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =>= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77 +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +Id : 30, {_}: multiply identity ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Super 28 with 3 at 1,2 +Id : 34, {_}: ?82 =<= multiply (inverse ?83) (multiply ?83 ?82) [83, 82] by Demod 30 with 2 at 2 +Id : 288, {_}: inverse (multiply (inverse ?619) ?620) =>= multiply (inverse ?620) ?619 [620, 619] by Super 286 with 18 at 2,3 +Id : 997, {_}: ?1719 =<= multiply (inverse ?1720) (multiply ?1720 ?1719) [1720, 1719] by Demod 30 with 2 at 2 +Id : 1001, {_}: ?1730 =<= multiply (inverse (inverse ?1730)) identity [1730] by Super 997 with 3 at 2,3 +Id : 1026, {_}: ?1730 =<= multiply ?1730 identity [1730] by Demod 1001 with 18 at 1,3 +Id : 1045, {_}: multiply ?1785 (least_upper_bound ?1786 identity) =?= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Super 13 with 1026 at 2,3 +Id : 1078, {_}: multiply ?1785 (positive_part ?1786) =<= least_upper_bound (multiply ?1785 ?1786) ?1785 [1786, 1785] by Demod 1045 with 20 at 2,2 +Id : 5086, {_}: multiply ?7297 (positive_part ?7298) =<= least_upper_bound ?7297 (multiply ?7297 ?7298) [7298, 7297] by Demod 1078 with 6 at 3 +Id : 5090, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound (inverse ?7308) identity [7308] by Super 5086 with 3 at 2,3 +Id : 5133, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= least_upper_bound identity (inverse ?7308) [7308] by Demod 5090 with 6 at 3 +Id : 298, {_}: least_upper_bound identity ?640 =>= positive_part ?640 [640] by Super 6 with 20 at 3 +Id : 5134, {_}: multiply (inverse ?7308) (positive_part ?7308) =>= positive_part (inverse ?7308) [7308] by Demod 5133 with 298 at 3 +Id : 5356, {_}: inverse (positive_part (inverse ?7872)) =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Super 288 with 5134 at 1,2 +Id : 1051, {_}: multiply ?1799 (greatest_lower_bound ?1800 identity) =?= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Super 14 with 1026 at 2,3 +Id : 1072, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound (multiply ?1799 ?1800) ?1799 [1800, 1799] by Demod 1051 with 21 at 2,2 +Id : 4381, {_}: multiply ?6565 (negative_part ?6566) =<= greatest_lower_bound ?6565 (multiply ?6565 ?6566) [6566, 6565] by Demod 1072 with 5 at 3 +Id : 270, {_}: multiply ?567 (inverse ?567) =>= identity [567] by Super 3 with 18 at 1,2 +Id : 4388, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= greatest_lower_bound ?6585 identity [6585] by Super 4381 with 270 at 2,3 +Id : 4428, {_}: multiply ?6585 (negative_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 4388 with 21 at 3 +Id : 1073, {_}: multiply ?1799 (negative_part ?1800) =<= greatest_lower_bound ?1799 (multiply ?1799 ?1800) [1800, 1799] by Demod 1072 with 5 at 3 +Id : 215, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= least_upper_bound identity (multiply ?472 ?471) [472, 471] by Super 210 with 3 at 1,3 +Id : 11818, {_}: multiply (least_upper_bound (inverse ?15728) ?15729) ?15728 =>= positive_part (multiply ?15729 ?15728) [15729, 15728] by Demod 215 with 298 at 3 +Id : 11845, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part (multiply identity ?15810) [15810] by Super 11818 with 20 at 1,2 +Id : 12179, {_}: multiply (positive_part (inverse ?16312)) ?16312 =>= positive_part ?16312 [16312] by Demod 11845 with 2 at 1,3 +Id : 12183, {_}: multiply (positive_part ?16319) (inverse ?16319) =>= positive_part (inverse ?16319) [16319] by Super 12179 with 18 at 1,1,2 +Id : 12264, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= greatest_lower_bound (positive_part ?16391) (positive_part (inverse ?16391)) [16391] by Super 1073 with 12183 at 2,3 +Id : 849, {_}: least_upper_bound identity (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Super 22 with 298 at 2,3 +Id : 877, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (least_upper_bound identity ?1555) (positive_part ?1556) [1556, 1555] by Demod 849 with 298 at 2 +Id : 878, {_}: positive_part (greatest_lower_bound ?1555 ?1556) =<= greatest_lower_bound (positive_part ?1555) (positive_part ?1556) [1556, 1555] by Demod 877 with 298 at 1,3 +Id : 12306, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= positive_part (greatest_lower_bound ?16391 (inverse ?16391)) [16391] by Demod 12264 with 878 at 3 +Id : 853, {_}: least_upper_bound identity (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Super 8 with 298 at 1,3 +Id : 874, {_}: positive_part (least_upper_bound ?1564 ?1565) =>= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 853 with 298 at 2 +Id : 297, {_}: least_upper_bound ?637 (least_upper_bound ?638 identity) =>= positive_part (least_upper_bound ?637 ?638) [638, 637] by Super 8 with 20 at 3 +Id : 307, {_}: least_upper_bound ?637 (positive_part ?638) =<= positive_part (least_upper_bound ?637 ?638) [638, 637] by Demod 297 with 20 at 2,2 +Id : 1518, {_}: least_upper_bound ?1564 (positive_part ?1565) =<= least_upper_bound (positive_part ?1564) ?1565 [1565, 1564] by Demod 874 with 307 at 2 +Id : 309, {_}: least_upper_bound ?657 (negative_part ?657) =>= ?657 [657] by Super 11 with 21 at 2,2 +Id : 4385, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound (inverse ?6576) identity [6576] by Super 4381 with 3 at 2,3 +Id : 4422, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= greatest_lower_bound identity (inverse ?6576) [6576] by Demod 4385 with 5 at 3 +Id : 312, {_}: greatest_lower_bound identity ?665 =>= negative_part ?665 [665] by Super 5 with 21 at 3 +Id : 4454, {_}: multiply (inverse ?6658) (negative_part ?6658) =>= negative_part (inverse ?6658) [6658] by Demod 4422 with 312 at 3 +Id : 1166, {_}: greatest_lower_bound ?1914 (positive_part ?1914) =>= ?1914 [1914] by Super 12 with 20 at 2,2 +Id : 898, {_}: least_upper_bound identity (negative_part ?1605) =>= identity [1605] by Super 11 with 312 at 2,2 +Id : 922, {_}: positive_part (negative_part ?1605) =>= identity [1605] by Demod 898 with 298 at 2 +Id : 1171, {_}: greatest_lower_bound (negative_part ?1923) identity =>= negative_part ?1923 [1923] by Super 1166 with 922 at 2,2 +Id : 1191, {_}: greatest_lower_bound identity (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1171 with 5 at 2 +Id : 1192, {_}: negative_part (negative_part ?1923) =>= negative_part ?1923 [1923] by Demod 1191 with 312 at 2 +Id : 4460, {_}: multiply (inverse (negative_part ?6669)) (negative_part ?6669) =>= negative_part (inverse (negative_part ?6669)) [6669] by Super 4454 with 1192 at 2,2 +Id : 4502, {_}: identity =<= negative_part (inverse (negative_part ?6669)) [6669] by Demod 4460 with 3 at 2 +Id : 4607, {_}: least_upper_bound (inverse (negative_part ?6821)) identity =>= inverse (negative_part ?6821) [6821] by Super 309 with 4502 at 2,2 +Id : 4660, {_}: least_upper_bound identity (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4607 with 6 at 2 +Id : 4661, {_}: positive_part (inverse (negative_part ?6821)) =>= inverse (negative_part ?6821) [6821] by Demod 4660 with 298 at 2 +Id : 4799, {_}: least_upper_bound (inverse (negative_part ?6984)) (positive_part ?6985) =>= least_upper_bound (inverse (negative_part ?6984)) ?6985 [6985, 6984] by Super 1518 with 4661 at 1,3 +Id : 11842, {_}: multiply (least_upper_bound (inverse (negative_part ?15801)) ?15802) (negative_part ?15801) =>= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15802, 15801] by Super 11818 with 4799 at 1,2 +Id : 11803, {_}: multiply (least_upper_bound (inverse ?471) ?472) ?471 =>= positive_part (multiply ?472 ?471) [472, 471] by Demod 215 with 298 at 3 +Id : 11889, {_}: positive_part (multiply ?15802 (negative_part ?15801)) =<= positive_part (multiply (positive_part ?15802) (negative_part ?15801)) [15801, 15802] by Demod 11842 with 11803 at 2 +Id : 11892, {_}: multiply (positive_part (inverse ?15810)) ?15810 =>= positive_part ?15810 [15810] by Demod 11845 with 2 at 1,3 +Id : 12165, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part (inverse ?16276)) (positive_part ?16276) [16276] by Super 1073 with 11892 at 2,3 +Id : 12217, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= greatest_lower_bound (positive_part ?16276) (positive_part (inverse ?16276)) [16276] by Demod 12165 with 5 at 3 +Id : 12218, {_}: multiply (positive_part (inverse ?16276)) (negative_part ?16276) =>= positive_part (greatest_lower_bound ?16276 (inverse ?16276)) [16276] by Demod 12217 with 878 at 3 +Id : 12981, {_}: positive_part (multiply (inverse ?17147) (negative_part ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Super 11889 with 12218 at 1,3 +Id : 4423, {_}: multiply (inverse ?6576) (negative_part ?6576) =>= negative_part (inverse ?6576) [6576] by Demod 4422 with 312 at 3 +Id : 13027, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (positive_part (greatest_lower_bound ?17147 (inverse ?17147))) [17147] by Demod 12981 with 4423 at 1,2 +Id : 1230, {_}: least_upper_bound ?1974 (positive_part ?1975) =<= positive_part (least_upper_bound ?1974 ?1975) [1975, 1974] by Demod 297 with 20 at 2,2 +Id : 1242, {_}: least_upper_bound ?2011 (positive_part identity) =>= positive_part (positive_part ?2011) [2011] by Super 1230 with 20 at 1,3 +Id : 300, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2 +Id : 1261, {_}: least_upper_bound ?2011 identity =<= positive_part (positive_part ?2011) [2011] by Demod 1242 with 300 at 2,2 +Id : 1262, {_}: positive_part ?2011 =<= positive_part (positive_part ?2011) [2011] by Demod 1261 with 20 at 2 +Id : 13028, {_}: positive_part (negative_part (inverse ?17147)) =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13027 with 1262 at 3 +Id : 13029, {_}: identity =<= positive_part (greatest_lower_bound ?17147 (inverse ?17147)) [17147] by Demod 13028 with 922 at 2 +Id : 14199, {_}: multiply (positive_part ?16391) (negative_part (inverse ?16391)) =>= identity [16391] by Demod 12306 with 13029 at 3 +Id : 14209, {_}: negative_part (inverse ?18032) =<= multiply (inverse (positive_part ?18032)) identity [18032] by Super 34 with 14199 at 2,3 +Id : 14275, {_}: negative_part (inverse ?18032) =>= inverse (positive_part ?18032) [18032] by Demod 14209 with 1026 at 3 +Id : 14351, {_}: multiply ?6585 (inverse (positive_part ?6585)) =>= negative_part ?6585 [6585] by Demod 4428 with 14275 at 2,2 +Id : 290, {_}: inverse (multiply ?624 (inverse ?625)) =>= multiply ?625 (inverse ?624) [625, 624] by Super 286 with 18 at 1,3 +Id : 12177, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part (inverse (inverse ?16308)))) [16308] by Super 290 with 11892 at 1,2 +Id : 12203, {_}: inverse (positive_part (inverse ?16308)) =<= multiply ?16308 (inverse (positive_part ?16308)) [16308] by Demod 12177 with 18 at 1,1,2,3 +Id : 14356, {_}: inverse (positive_part (inverse ?6585)) =>= negative_part ?6585 [6585] by Demod 14351 with 12203 at 2 +Id : 14357, {_}: negative_part ?7872 =<= multiply (inverse (positive_part ?7872)) ?7872 [7872] by Demod 5356 with 14356 at 2 +Id : 13168, {_}: multiply (inverse (greatest_lower_bound ?17321 (inverse ?17321))) identity =>= positive_part (inverse (greatest_lower_bound ?17321 (inverse ?17321))) [17321] by Super 5134 with 13029 at 2,2 +Id : 15132, {_}: inverse (greatest_lower_bound ?18904 (inverse ?18904)) =<= positive_part (inverse (greatest_lower_bound ?18904 (inverse ?18904))) [18904] by Demod 13168 with 1026 at 2 +Id : 15140, {_}: inverse (greatest_lower_bound (positive_part (inverse ?18921)) (inverse (positive_part (inverse ?18921)))) =>= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Super 15132 with 14356 at 2,1,1,3 +Id : 899, {_}: greatest_lower_bound identity (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Super 7 with 312 at 1,3 +Id : 921, {_}: negative_part (greatest_lower_bound ?1607 ?1608) =>= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 899 with 312 at 2 +Id : 311, {_}: greatest_lower_bound ?662 (greatest_lower_bound ?663 identity) =>= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Super 7 with 21 at 3 +Id : 321, {_}: greatest_lower_bound ?662 (negative_part ?663) =<= negative_part (greatest_lower_bound ?662 ?663) [663, 662] by Demod 311 with 21 at 2,2 +Id : 1610, {_}: greatest_lower_bound ?2637 (negative_part ?2638) =<= greatest_lower_bound (negative_part ?2637) ?2638 [2638, 2637] by Demod 921 with 321 at 2 +Id : 903, {_}: negative_part (least_upper_bound identity ?1615) =>= identity [1615] by Super 12 with 312 at 2 +Id : 917, {_}: negative_part (positive_part ?1615) =>= identity [1615] by Demod 903 with 298 at 1,2 +Id : 1615, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= greatest_lower_bound identity ?2652 [2652, 2651] by Super 1610 with 917 at 1,3 +Id : 1662, {_}: greatest_lower_bound (positive_part ?2651) (negative_part ?2652) =>= negative_part ?2652 [2652, 2651] by Demod 1615 with 312 at 3 +Id : 4459, {_}: multiply (inverse (positive_part ?6667)) identity =>= negative_part (inverse (positive_part ?6667)) [6667] by Super 4454 with 917 at 2,2 +Id : 4501, {_}: inverse (positive_part ?6667) =<= negative_part (inverse (positive_part ?6667)) [6667] by Demod 4459 with 1026 at 2 +Id : 4523, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= negative_part (inverse (positive_part ?6722)) [6722, 6721] by Super 1662 with 4501 at 2,2 +Id : 4568, {_}: greatest_lower_bound (positive_part ?6721) (inverse (positive_part ?6722)) =>= inverse (positive_part ?6722) [6722, 6721] by Demod 4523 with 4501 at 3 +Id : 15267, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= positive_part (inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921))) [18921] by Demod 15140 with 4568 at 1,2 +Id : 4810, {_}: positive_part (inverse (negative_part ?7011)) =>= inverse (negative_part ?7011) [7011] by Demod 4660 with 298 at 2 +Id : 4822, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (negative_part (greatest_lower_bound ?7038 ?7039)) [7039, 7038] by Super 4810 with 321 at 1,1,2 +Id : 4871, {_}: positive_part (inverse (greatest_lower_bound ?7038 (negative_part ?7039))) =>= inverse (greatest_lower_bound ?7038 (negative_part ?7039)) [7039, 7038] by Demod 4822 with 321 at 1,3 +Id : 15268, {_}: inverse (inverse (positive_part (inverse ?18921))) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15267 with 4871 at 3 +Id : 15269, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (positive_part (inverse ?18921)) (negative_part ?18921)) [18921] by Demod 15268 with 18 at 2 +Id : 15270, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound (negative_part ?18921) (positive_part (inverse ?18921))) [18921] by Demod 15269 with 5 at 1,3 +Id : 1594, {_}: greatest_lower_bound ?1607 (negative_part ?1608) =<= greatest_lower_bound (negative_part ?1607) ?1608 [1608, 1607] by Demod 921 with 321 at 2 +Id : 15271, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 (negative_part (positive_part (inverse ?18921)))) [18921] by Demod 15270 with 1594 at 1,3 +Id : 15272, {_}: positive_part (inverse ?18921) =<= inverse (greatest_lower_bound ?18921 identity) [18921] by Demod 15271 with 917 at 2,1,3 +Id : 15273, {_}: positive_part (inverse ?18921) =>= inverse (negative_part ?18921) [18921] by Demod 15272 with 21 at 1,3 +Id : 15393, {_}: negative_part (inverse ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Super 14357 with 15273 at 1,1,3 +Id : 15435, {_}: inverse (positive_part ?19045) =<= multiply (inverse (inverse (negative_part ?19045))) (inverse ?19045) [19045] by Demod 15393 with 14275 at 2 +Id : 15436, {_}: inverse (positive_part ?19045) =<= inverse (multiply ?19045 (inverse (negative_part ?19045))) [19045] by Demod 15435 with 19 at 3 +Id : 15437, {_}: inverse (positive_part ?19045) =<= multiply (negative_part ?19045) (inverse ?19045) [19045] by Demod 15436 with 290 at 3 +Id : 15800, {_}: inverse ?19405 =<= multiply (inverse (negative_part ?19405)) (inverse (positive_part ?19405)) [19405] by Super 34 with 15437 at 2,3 +Id : 15843, {_}: inverse ?19405 =<= inverse (multiply (positive_part ?19405) (negative_part ?19405)) [19405] by Demod 15800 with 19 at 3 +Id : 20580, {_}: inverse (inverse ?23723) =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Super 18 with 15843 at 1,2 +Id : 20668, {_}: ?23723 =<= multiply (positive_part ?23723) (negative_part ?23723) [23723] by Demod 20580 with 18 at 2 +Id : 20964, {_}: a =?= a [] by Demod 1 with 20668 at 3 +Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4 +% SZS output end CNFRefutation for GRP167-2.p +10052: solved GRP167-2.p in 3.352209 using kbo +10052: status Unsatisfiable for GRP167-2.p +NO CLASH, using fixed ground order +10058: Facts: +10058: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10058: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10058: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10058: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10058: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10058: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10058: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10058: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10058: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10058: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10058: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10058: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10058: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10058: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10058: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10058: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1 +10058: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2 +10058: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3 +10058: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4 +10058: Goal: +10058: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09a +10058: Order: +10058: nrkbo +10058: Leaf order: +10058: least_upper_bound 16 2 0 +10058: inverse 1 1 0 +10058: identity 6 0 0 +10058: greatest_lower_bound 16 2 2 0,2 +10058: multiply 19 2 1 0,2,2 +10058: c 4 0 2 2,2,2 +10058: b 4 0 1 1,2,2 +10058: a 5 0 2 1,2 +NO CLASH, using fixed ground order +10059: Facts: +10059: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10059: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10059: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10059: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10059: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10059: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10059: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +NO CLASH, using fixed ground order +10060: Facts: +10060: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10060: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10060: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10060: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10060: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10060: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10059: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10059: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10059: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10059: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10059: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10059: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10059: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10059: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10059: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1 +10059: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2 +10059: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3 +10059: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4 +10059: Goal: +10059: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09a +10059: Order: +10059: kbo +10059: Leaf order: +10059: least_upper_bound 16 2 0 +10059: inverse 1 1 0 +10059: identity 6 0 0 +10059: greatest_lower_bound 16 2 2 0,2 +10059: multiply 19 2 1 0,2,2 +10059: c 4 0 2 2,2,2 +10059: b 4 0 1 1,2,2 +10059: a 5 0 2 1,2 +10060: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10060: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10060: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10060: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10060: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10060: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10060: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10060: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10060: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10060: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1 +10060: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2 +10060: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3 +10060: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4 +10060: Goal: +10060: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09a +10060: Order: +10060: lpo +10060: Leaf order: +10060: least_upper_bound 16 2 0 +10060: inverse 1 1 0 +10060: identity 6 0 0 +10060: greatest_lower_bound 16 2 2 0,2 +10060: multiply 19 2 1 0,2,2 +10060: c 4 0 2 2,2,2 +10060: b 4 0 1 1,2,2 +10060: a 5 0 2 1,2 +% SZS status Timeout for GRP178-1.p +NO CLASH, using fixed ground order +10102: Facts: +10102: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10102: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10102: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10102: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10102: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10102: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10102: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10102: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10102: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10102: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10102: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10102: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10102: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10102: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10102: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10102: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1 +10102: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2 +10102: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3 +10102: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4 +10102: Goal: +10102: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09b +10102: Order: +10102: nrkbo +10102: Leaf order: +10102: least_upper_bound 13 2 0 +10102: inverse 1 1 0 +10102: identity 9 0 0 +10102: greatest_lower_bound 19 2 2 0,2 +10102: multiply 19 2 1 0,2,2 +10102: c 3 0 2 2,2,2 +10102: b 3 0 1 1,2,2 +10102: a 4 0 2 1,2 +NO CLASH, using fixed ground order +10103: Facts: +10103: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10103: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10103: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10103: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10103: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10103: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10103: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10103: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10103: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10103: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10103: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10103: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10103: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10103: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10103: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10103: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1 +10103: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2 +10103: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3 +10103: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4 +10103: Goal: +10103: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09b +10103: Order: +10103: kbo +10103: Leaf order: +10103: least_upper_bound 13 2 0 +10103: inverse 1 1 0 +10103: identity 9 0 0 +10103: greatest_lower_bound 19 2 2 0,2 +10103: multiply 19 2 1 0,2,2 +10103: c 3 0 2 2,2,2 +10103: b 3 0 1 1,2,2 +10103: a 4 0 2 1,2 +NO CLASH, using fixed ground order +10104: Facts: +10104: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10104: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10104: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10104: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10104: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10104: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10104: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10104: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10104: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10104: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10104: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10104: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10104: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10104: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10104: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10104: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1 +10104: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2 +10104: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3 +10104: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4 +10104: Goal: +10104: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09b +10104: Order: +10104: lpo +10104: Leaf order: +10104: least_upper_bound 13 2 0 +10104: inverse 1 1 0 +10104: identity 9 0 0 +10104: greatest_lower_bound 19 2 2 0,2 +10104: multiply 19 2 1 0,2,2 +10104: c 3 0 2 2,2,2 +10104: b 3 0 1 1,2,2 +10104: a 4 0 2 1,2 +% SZS status Timeout for GRP178-2.p +CLASH, statistics insufficient +10125: Facts: +10125: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10125: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10125: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10125: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10125: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10125: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10125: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10125: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10125: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10125: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10125: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10125: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10125: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10125: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10125: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10125: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_1 +10125: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2 +10125: Id : 19, {_}: + inverse (greatest_lower_bound ?52 ?53) + =<= + least_upper_bound (inverse ?52) (inverse ?53) + [53, 52] by p12x_3 ?52 ?53 +10125: Id : 20, {_}: + inverse (least_upper_bound ?55 ?56) + =<= + greatest_lower_bound (inverse ?55) (inverse ?56) + [56, 55] by p12x_4 ?55 ?56 +10125: Goal: +10125: Id : 1, {_}: a =>= b [] by prove_p12x +10125: Order: +10125: nrkbo +10125: Leaf order: +10125: c 4 0 0 +10125: least_upper_bound 17 2 0 +10125: greatest_lower_bound 17 2 0 +10125: inverse 7 1 0 +10125: multiply 18 2 0 +10125: identity 2 0 0 +10125: b 3 0 1 3 +10125: a 3 0 1 2 +CLASH, statistics insufficient +10126: Facts: +10126: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10126: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10126: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10126: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10126: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10126: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10126: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10126: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10126: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10126: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10126: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10126: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10126: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10126: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10126: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10126: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_1 +10126: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2 +10126: Id : 19, {_}: + inverse (greatest_lower_bound ?52 ?53) + =<= + least_upper_bound (inverse ?52) (inverse ?53) + [53, 52] by p12x_3 ?52 ?53 +10126: Id : 20, {_}: + inverse (least_upper_bound ?55 ?56) + =<= + greatest_lower_bound (inverse ?55) (inverse ?56) + [56, 55] by p12x_4 ?55 ?56 +10126: Goal: +10126: Id : 1, {_}: a =>= b [] by prove_p12x +10126: Order: +10126: kbo +10126: Leaf order: +10126: c 4 0 0 +10126: least_upper_bound 17 2 0 +10126: greatest_lower_bound 17 2 0 +10126: inverse 7 1 0 +10126: multiply 18 2 0 +10126: identity 2 0 0 +10126: b 3 0 1 3 +10126: a 3 0 1 2 +CLASH, statistics insufficient +10127: Facts: +10127: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10127: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10127: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10127: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10127: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10127: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10127: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10127: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10127: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10127: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10127: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10127: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10127: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10127: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10127: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10127: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_1 +10127: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2 +10127: Id : 19, {_}: + inverse (greatest_lower_bound ?52 ?53) + =>= + least_upper_bound (inverse ?52) (inverse ?53) + [53, 52] by p12x_3 ?52 ?53 +10127: Id : 20, {_}: + inverse (least_upper_bound ?55 ?56) + =>= + greatest_lower_bound (inverse ?55) (inverse ?56) + [56, 55] by p12x_4 ?55 ?56 +10127: Goal: +10127: Id : 1, {_}: a =>= b [] by prove_p12x +10127: Order: +10127: lpo +10127: Leaf order: +10127: c 4 0 0 +10127: least_upper_bound 17 2 0 +10127: greatest_lower_bound 17 2 0 +10127: inverse 7 1 0 +10127: multiply 18 2 0 +10127: identity 2 0 0 +10127: b 3 0 1 3 +10127: a 3 0 1 2 +% SZS status Timeout for GRP181-3.p +NO CLASH, using fixed ground order +10150: Facts: +10150: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10150: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10150: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10150: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10150: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10150: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10150: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10150: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10150: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10150: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10150: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10150: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10150: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10150: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10150: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10150: Id : 17, {_}: inverse identity =>= identity [] by p21_1 +10150: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51 +10150: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p21_3 ?53 ?54 +10150: Goal: +10150: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +10150: Order: +10150: nrkbo +10150: Leaf order: +10150: multiply 22 2 2 0,2 +10150: inverse 9 1 2 0,2,2 +10150: greatest_lower_bound 15 2 2 0,1,2,2 +10150: least_upper_bound 15 2 2 0,1,2 +10150: identity 8 0 4 2,1,2 +10150: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +10151: Facts: +10151: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10151: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10151: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10151: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10151: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10151: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10151: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10151: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10151: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10151: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10151: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10151: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10151: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10151: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10151: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10151: Id : 17, {_}: inverse identity =>= identity [] by p21_1 +10151: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51 +10151: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p21_3 ?53 ?54 +10151: Goal: +10151: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +10151: Order: +10151: kbo +10151: Leaf order: +10151: multiply 22 2 2 0,2 +10151: inverse 9 1 2 0,2,2 +10151: greatest_lower_bound 15 2 2 0,1,2,2 +10151: least_upper_bound 15 2 2 0,1,2 +10151: identity 8 0 4 2,1,2 +10151: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +10152: Facts: +10152: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10152: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10152: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10152: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10152: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10152: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10152: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10152: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10152: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10152: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10152: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10152: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10152: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10152: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10152: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10152: Id : 17, {_}: inverse identity =>= identity [] by p21_1 +10152: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51 +10152: Id : 19, {_}: + inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53) + [54, 53] by p21_3 ?53 ?54 +10152: Goal: +10152: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +10152: Order: +10152: lpo +10152: Leaf order: +10152: multiply 22 2 2 0,2 +10152: inverse 9 1 2 0,2,2 +10152: greatest_lower_bound 15 2 2 0,1,2,2 +10152: least_upper_bound 15 2 2 0,1,2 +10152: identity 8 0 4 2,1,2 +10152: a 4 0 4 1,1,2 +% SZS status Timeout for GRP184-2.p +NO CLASH, using fixed ground order +10174: Facts: +10174: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10174: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10174: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10174: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10174: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10174: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10174: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10174: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10174: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10174: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10174: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10174: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10174: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10174: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10174: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10174: Goal: +10174: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +10174: Order: +10174: nrkbo +10174: Leaf order: +10174: greatest_lower_bound 13 2 0 +10174: inverse 1 1 0 +10174: least_upper_bound 19 2 6 0,2 +10174: identity 7 0 5 2,1,2 +10174: multiply 21 2 3 0,1,1,2 +10174: b 3 0 3 2,1,1,2 +10174: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +10175: Facts: +10175: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10175: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10175: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10175: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10175: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10175: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10175: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10175: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10175: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10175: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10175: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10175: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10175: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10175: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10175: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10175: Goal: +10175: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +10175: Order: +10175: kbo +10175: Leaf order: +10175: greatest_lower_bound 13 2 0 +10175: inverse 1 1 0 +10175: least_upper_bound 19 2 6 0,2 +10175: identity 7 0 5 2,1,2 +10175: multiply 21 2 3 0,1,1,2 +10175: b 3 0 3 2,1,1,2 +10175: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +10176: Facts: +10176: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10176: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10176: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10176: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10176: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10176: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10176: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10176: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10176: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10176: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10176: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10176: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10176: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10176: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10176: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10176: Goal: +10176: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +10176: Order: +10176: lpo +10176: Leaf order: +10176: greatest_lower_bound 13 2 0 +10176: inverse 1 1 0 +10176: least_upper_bound 19 2 6 0,2 +10176: identity 7 0 5 2,1,2 +10176: multiply 21 2 3 0,1,1,2 +10176: b 3 0 3 2,1,1,2 +10176: a 3 0 3 1,1,1,2 +Statistics : +Max weight : 21 +Found proof, 4.014671s +% SZS status Unsatisfiable for GRP185-1.p +% SZS output start CNFRefutation for GRP185-1.p +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 67, {_}: least_upper_bound ?151 (least_upper_bound ?152 ?153) =<= least_upper_bound (least_upper_bound ?151 ?152) ?153 [153, 152, 151] by associativity_of_lub ?151 ?152 ?153 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 68, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =<= least_upper_bound (least_upper_bound ?156 ?155) ?157 [157, 156, 155] by Super 67 with 6 at 1,3 +Id : 74, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =?= least_upper_bound ?156 (least_upper_bound ?155 ?157) [157, 156, 155] by Demod 68 with 8 at 3 +Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2 +Id : 562, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2 +Id : 564, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 562 with 3 at 2,3 +Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2 +Id : 570, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 562 with 27 at 2,3 +Id : 855, {_}: ?599 =<= multiply ?599 identity [599] by Demod 564 with 570 at 3 +Id : 65, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3 +Id : 85, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3 +Id : 5149, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) === least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5148 with 74 at 2,2 +Id : 5148, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5147 with 9 at 2,2,2,2 +Id : 5147, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5146 with 2 at 1,2,2,2 +Id : 5146, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5145 with 85 at 2 +Id : 5145, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound identity (least_upper_bound b (least_upper_bound a (multiply a b))) [] by Demod 5144 with 74 at 3 +Id : 5144, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply a b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5143 with 65 at 2,2,2,2 +Id : 5143, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5142 with 855 at 1,2,2,2 +Id : 5142, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5141 with 2 at 1,2,2 +Id : 5141, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound a (multiply a b))) [] by Demod 5140 with 855 at 1,2,2,3 +Id : 5140, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5139 with 2 at 1,2,3 +Id : 5139, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b))))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5138 with 8 at 2,2 +Id : 5138, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (multiply a b))) [] by Demod 5137 with 8 at 2,3 +Id : 5137, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound b (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5136 with 2 at 1,3 +Id : 5136, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5135 with 74 at 2,2 +Id : 5135, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply a b)) [] by Demod 5134 with 74 at 3 +Id : 5134, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5133 with 15 at 2,2,2,2 +Id : 5133, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5132 with 15 at 1,2,2,2 +Id : 5132, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 5131 with 15 at 2,3 +Id : 5131, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 5130 with 15 at 1,3 +Id : 5130, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 237 with 74 at 2 +Id : 237, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 236 with 6 at 1,2,2,2,2 +Id : 236, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 235 with 6 at 1,1,2,2,2 +Id : 235, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 234 with 6 at 1,2,3 +Id : 234, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound a identity) b) [] by Demod 233 with 6 at 1,1,3 +Id : 233, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 232 with 6 at 2,2,2 +Id : 232, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b) [] by Demod 231 with 6 at 3 +Id : 231, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 230 with 13 at 2,2,2 +Id : 230, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 229 with 13 at 3 +Id : 229, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2 +Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a +% SZS output end CNFRefutation for GRP185-1.p +10176: solved GRP185-1.p in 1.916119 using lpo +10176: status Unsatisfiable for GRP185-1.p +NO CLASH, using fixed ground order +10187: Facts: +10187: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10187: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10187: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10187: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10187: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10187: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10187: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10187: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10187: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10187: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10187: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10187: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10187: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10187: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10187: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10187: Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +10187: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +10187: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22a_3 ?53 ?54 +10187: Goal: +10187: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +10187: Order: +10187: nrkbo +10187: Leaf order: +10187: greatest_lower_bound 13 2 0 +10187: inverse 7 1 0 +10187: least_upper_bound 19 2 6 0,2 +10187: identity 9 0 5 2,1,2 +10187: multiply 23 2 3 0,1,1,2 +10187: b 3 0 3 2,1,1,2 +10187: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +10188: Facts: +10188: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10188: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10188: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10188: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10188: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10188: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10188: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10188: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10188: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10188: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10188: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10188: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10188: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10188: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10188: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10188: Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +10188: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +10188: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22a_3 ?53 ?54 +10188: Goal: +10188: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +10188: Order: +10188: kbo +10188: Leaf order: +10188: greatest_lower_bound 13 2 0 +10188: inverse 7 1 0 +10188: least_upper_bound 19 2 6 0,2 +10188: identity 9 0 5 2,1,2 +10188: multiply 23 2 3 0,1,1,2 +10188: b 3 0 3 2,1,1,2 +10188: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +10189: Facts: +10189: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10189: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +10189: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +10189: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +10189: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +10189: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +10189: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +10189: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +10189: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +10189: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +10189: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +10189: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +10189: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +10189: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +10189: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +10189: Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +10189: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +10189: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22a_3 ?53 ?54 +10189: Goal: +10189: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +10189: Order: +10189: lpo +10189: Leaf order: +10189: greatest_lower_bound 13 2 0 +10189: inverse 7 1 0 +10189: least_upper_bound 19 2 6 0,2 +10189: identity 9 0 5 2,1,2 +10189: multiply 23 2 3 0,1,1,2 +10189: b 3 0 3 2,1,1,2 +10189: a 3 0 3 1,1,1,2 +Statistics : +Max weight : 21 +Found proof, 5.587205s +% SZS status Unsatisfiable for GRP185-2.p +% SZS output start CNFRefutation for GRP185-2.p +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +Id : 506, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 782, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3 +Id : 1203, {_}: least_upper_bound ?943 (least_upper_bound ?944 ?943) =>= least_upper_bound ?943 ?944 [944, 943] by Super 782 with 6 at 2,2 +Id : 1211, {_}: least_upper_bound ?966 (least_upper_bound ?967 (least_upper_bound ?968 ?966)) =>= least_upper_bound ?966 (least_upper_bound ?967 ?968) [968, 967, 966] by Super 1203 with 8 at 2,2 +Id : 507, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 506 with 17 at 2,3 +Id : 571, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 507 with 2 at 1,2 +Id : 573, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 571 with 18 at 1,3 +Id : 581, {_}: ?572 =<= multiply ?572 identity [572] by Demod 573 with 18 at 2 +Id : 88, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3 +Id : 3310, {_}: least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) === least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3309 with 88 at 2 +Id : 3309, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3308 with 2 at 1,2,2,2,2 +Id : 3308, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3307 with 581 at 1,2,2,2 +Id : 3307, {_}: least_upper_bound identity (least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3306 with 2 at 1,2,2 +Id : 3306, {_}: least_upper_bound identity (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3305 with 8 at 2,2 +Id : 3305, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3304 with 8 at 2,2 +Id : 3304, {_}: least_upper_bound identity (least_upper_bound (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b)) (multiply a b)) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3303 with 6 at 2,2 +Id : 3303, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound b (multiply a b))) [] by Demod 3302 with 2 at 1,2,2,3 +Id : 3302, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound a (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3301 with 581 at 1,2,3 +Id : 3301, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound identity (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3300 with 2 at 1,3 +Id : 3300, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply identity b))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3299 with 1211 at 2,2 +Id : 3299, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (multiply identity identity) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity b) (multiply a b))) [] by Demod 3298 with 8 at 3 +Id : 3298, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3297 with 15 at 2,2,2,2 +Id : 3297, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3296 with 15 at 1,2,2,2 +Id : 3296, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (least_upper_bound (multiply identity b) (multiply a b)) [] by Demod 3295 with 15 at 2,3 +Id : 3295, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (least_upper_bound (multiply identity identity) (multiply a identity)) (multiply (least_upper_bound identity a) b) [] by Demod 3294 with 15 at 1,3 +Id : 3294, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3293 with 13 at 2,2,2 +Id : 3293, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= least_upper_bound (multiply (least_upper_bound identity a) identity) (multiply (least_upper_bound identity a) b) [] by Demod 3292 with 13 at 3 +Id : 3292, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound identity a) (least_upper_bound identity b))) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 67 with 8 at 2 +Id : 67, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =>= multiply (least_upper_bound identity a) (least_upper_bound identity b) [] by Demod 66 with 6 at 2,3 +Id : 66, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound identity a) (least_upper_bound b identity) [] by Demod 65 with 6 at 1,3 +Id : 65, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound identity b)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 64 with 6 at 2,2,2 +Id : 64, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound identity a) (least_upper_bound b identity)) =<= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 63 with 6 at 1,2,2 +Id : 63, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2 +Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a +% SZS output end CNFRefutation for GRP185-2.p +10189: solved GRP185-2.p in 0.988061 using lpo +10189: status Unsatisfiable for GRP185-2.p +CLASH, statistics insufficient +10194: Facts: +10194: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10194: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10194: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10194: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10194: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10194: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10194: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10194: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10194: Id : 10, {_}: + multiply (multiply ?22 (multiply ?23 ?24)) ?22 + =?= + multiply (multiply ?22 ?23) (multiply ?24 ?22) + [24, 23, 22] by moufang1 ?22 ?23 ?24 +10194: Goal: +10194: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +10194: Order: +10194: nrkbo +10194: Leaf order: +10194: left_inverse 1 1 0 +10194: right_inverse 1 1 0 +10194: right_division 2 2 0 +10194: left_division 2 2 0 +10194: identity 4 0 0 +10194: c 2 0 2 2,1,2 +10194: multiply 20 2 6 0,2 +10194: b 4 0 4 2,1,1,2 +10194: a 2 0 2 1,1,1,2 +CLASH, statistics insufficient +10195: Facts: +10195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10195: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10195: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10195: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10195: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10195: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10195: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10195: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10195: Id : 10, {_}: + multiply (multiply ?22 (multiply ?23 ?24)) ?22 + =>= + multiply (multiply ?22 ?23) (multiply ?24 ?22) + [24, 23, 22] by moufang1 ?22 ?23 ?24 +10195: Goal: +10195: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +10195: Order: +10195: kbo +10195: Leaf order: +10195: left_inverse 1 1 0 +10195: right_inverse 1 1 0 +10195: right_division 2 2 0 +10195: left_division 2 2 0 +10195: identity 4 0 0 +10195: c 2 0 2 2,1,2 +10195: multiply 20 2 6 0,2 +10195: b 4 0 4 2,1,1,2 +10195: a 2 0 2 1,1,1,2 +CLASH, statistics insufficient +10196: Facts: +10196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10196: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10196: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10196: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10196: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10196: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10196: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10196: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10196: Id : 10, {_}: + multiply (multiply ?22 (multiply ?23 ?24)) ?22 + =>= + multiply (multiply ?22 ?23) (multiply ?24 ?22) + [24, 23, 22] by moufang1 ?22 ?23 ?24 +10196: Goal: +10196: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +10196: Order: +10196: lpo +10196: Leaf order: +10196: left_inverse 1 1 0 +10196: right_inverse 1 1 0 +10196: right_division 2 2 0 +10196: left_division 2 2 0 +10196: identity 4 0 0 +10196: c 2 0 2 2,1,2 +10196: multiply 20 2 6 0,2 +10196: b 4 0 4 2,1,1,2 +10196: a 2 0 2 1,1,1,2 +% SZS status Timeout for GRP200-1.p +CLASH, statistics insufficient +10959: Facts: +10959: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10959: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10959: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10959: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10959: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10959: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10959: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10959: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10959: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?24) ?23 + =?= + multiply ?22 (multiply ?23 (multiply ?24 ?23)) + [24, 23, 22] by moufang2 ?22 ?23 ?24 +10959: Goal: +10959: Id : 1, {_}: + multiply (multiply (multiply a b) a) c + =>= + multiply a (multiply b (multiply a c)) + [] by prove_moufang3 +10959: Order: +10959: nrkbo +10959: Leaf order: +10959: left_inverse 1 1 0 +10959: right_inverse 1 1 0 +10959: right_division 2 2 0 +10959: left_division 2 2 0 +10959: identity 4 0 0 +10959: c 2 0 2 2,2 +10959: multiply 20 2 6 0,2 +10959: b 2 0 2 2,1,1,2 +10959: a 4 0 4 1,1,1,2 +CLASH, statistics insufficient +10960: Facts: +10960: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10960: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10960: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10960: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10960: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10960: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10960: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10960: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10960: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?24) ?23 + =>= + multiply ?22 (multiply ?23 (multiply ?24 ?23)) + [24, 23, 22] by moufang2 ?22 ?23 ?24 +10960: Goal: +10960: Id : 1, {_}: + multiply (multiply (multiply a b) a) c + =>= + multiply a (multiply b (multiply a c)) + [] by prove_moufang3 +10960: Order: +10960: kbo +10960: Leaf order: +10960: left_inverse 1 1 0 +10960: right_inverse 1 1 0 +10960: right_division 2 2 0 +10960: left_division 2 2 0 +10960: identity 4 0 0 +10960: c 2 0 2 2,2 +10960: multiply 20 2 6 0,2 +10960: b 2 0 2 2,1,1,2 +10960: a 4 0 4 1,1,1,2 +CLASH, statistics insufficient +10961: Facts: +10961: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10961: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10961: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10961: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10961: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10961: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10961: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10961: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10961: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?24) ?23 + =>= + multiply ?22 (multiply ?23 (multiply ?24 ?23)) + [24, 23, 22] by moufang2 ?22 ?23 ?24 +10961: Goal: +10961: Id : 1, {_}: + multiply (multiply (multiply a b) a) c + =>= + multiply a (multiply b (multiply a c)) + [] by prove_moufang3 +10961: Order: +10961: lpo +10961: Leaf order: +10961: left_inverse 1 1 0 +10961: right_inverse 1 1 0 +10961: right_division 2 2 0 +10961: left_division 2 2 0 +10961: identity 4 0 0 +10961: c 2 0 2 2,2 +10961: multiply 20 2 6 0,2 +10961: b 2 0 2 2,1,1,2 +10961: a 4 0 4 1,1,1,2 +Statistics : +Max weight : 15 +Found proof, 24.390962s +% SZS status Unsatisfiable for GRP201-1.p +% SZS output start CNFRefutation for GRP201-1.p +Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49 +Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18 +Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13 +Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7 +Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20 +Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24 +Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16 +Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121 +Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2 +Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3 +Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2 +Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2 +Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2 +Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2 +Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2 +Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2 +Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2 +Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3 +Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2 +Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3 +Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2 +Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3 +Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2 +Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2 +Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2 +Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2 +Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2 +Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2 +Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2 +Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2 +Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3 +Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2 +Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2 +Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2 +Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2 +Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2 +Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2 +Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2 +Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2 +Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2 +Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2 +Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2 +Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3 +Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2 +Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2 +Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2 +Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3 +Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3 +Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3 +Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2 +Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2 +Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3 +Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2 +Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2 +Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2 +Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2 +Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3 +Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3 +Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2 +Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2 +Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2 +Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3 +Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2 +Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3 +Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3 +Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3 +Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2 +Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3 +Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2 +Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2 +Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3 +% SZS output end CNFRefutation for GRP201-1.p +10960: solved GRP201-1.p in 12.208762 using kbo +10960: status Unsatisfiable for GRP201-1.p +CLASH, statistics insufficient +10977: Facts: +10977: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10977: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10977: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10977: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10977: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10977: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10977: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10977: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10977: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =?= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +10977: Goal: +10977: Id : 1, {_}: + multiply (multiply a (multiply b c)) a + =>= + multiply (multiply a b) (multiply c a) + [] by prove_moufang1 +10977: Order: +10977: nrkbo +10977: Leaf order: +10977: left_inverse 1 1 0 +10977: right_inverse 1 1 0 +10977: right_division 2 2 0 +10977: left_division 2 2 0 +10977: identity 4 0 0 +10977: multiply 20 2 6 0,2 +10977: c 2 0 2 2,2,1,2 +10977: b 2 0 2 1,2,1,2 +10977: a 4 0 4 1,1,2 +CLASH, statistics insufficient +10978: Facts: +10978: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10978: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10978: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10978: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10978: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10978: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10978: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10978: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10978: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +10978: Goal: +10978: Id : 1, {_}: + multiply (multiply a (multiply b c)) a + =>= + multiply (multiply a b) (multiply c a) + [] by prove_moufang1 +10978: Order: +10978: kbo +10978: Leaf order: +10978: left_inverse 1 1 0 +10978: right_inverse 1 1 0 +10978: right_division 2 2 0 +10978: left_division 2 2 0 +10978: identity 4 0 0 +10978: multiply 20 2 6 0,2 +10978: c 2 0 2 2,2,1,2 +10978: b 2 0 2 1,2,1,2 +10978: a 4 0 4 1,1,2 +CLASH, statistics insufficient +10979: Facts: +10979: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +10979: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +10979: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +10979: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +10979: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +10979: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +10979: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +10979: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +10979: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +10979: Goal: +10979: Id : 1, {_}: + multiply (multiply a (multiply b c)) a + =>= + multiply (multiply a b) (multiply c a) + [] by prove_moufang1 +10979: Order: +10979: lpo +10979: Leaf order: +10979: left_inverse 1 1 0 +10979: right_inverse 1 1 0 +10979: right_division 2 2 0 +10979: left_division 2 2 0 +10979: identity 4 0 0 +10979: multiply 20 2 6 0,2 +10979: c 2 0 2 2,2,1,2 +10979: b 2 0 2 1,2,1,2 +10979: a 4 0 4 1,1,2 +Statistics : +Max weight : 20 +Found proof, 29.848585s +% SZS status Unsatisfiable for GRP202-1.p +% SZS output start CNFRefutation for GRP202-1.p +Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128 +Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7 +Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20 +Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10 +Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18 +Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13 +Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16 +Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24 +Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2 +Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2 +Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2 +Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2 +Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2 +Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3 +Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2 +Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3 +Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3 +Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2 +Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2 +Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2 +Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2 +Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2 +Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2 +Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2 +Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2 +Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2 +Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3 +Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2 +Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2 +Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2 +Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2 +Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2 +Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2 +Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2 +Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3 +Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2 +Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3 +Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2 +Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2 +Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2 +Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2 +Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3 +Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3 +Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2 +Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2 +Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3 +Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2 +Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2 +Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3 +Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3 +Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3 +Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3 +Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3 +Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2 +Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3 +Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2 +Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2 +Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2 +Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2 +Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2 +Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3 +Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3 +Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2 +Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2 +Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3 +Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2 +Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3 +Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2 +Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2 +Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3 +Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2 +Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3 +Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2 +Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3 +Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2 +Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3 +Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3 +Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2 +Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2 +Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3 +Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2 +Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3 +Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2 +Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3 +Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3 +Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3 +Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2 +Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3 +Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3 +Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2 +Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3 +Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2 +Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2 +Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3 +Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3 +Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2 +Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2 +Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3 +Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2 +Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2 +Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2 +Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2 +Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2 +Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3 +Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2 +Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3 +Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2 +Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3 +Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2 +Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3 +Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3 +Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2 +Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2 +Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3 +Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2 +Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2 +Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2 +Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3 +Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2 +Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3 +Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2 +Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3 +Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2 +Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2 +Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3 +Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2 +Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3 +Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2 +Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3 +Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2 +Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2 +Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3 +Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3 +Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2 +Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2 +Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2 +Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3 +Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2 +Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2 +Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3 +Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2 +Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3 +Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3 +Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2 +Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2 +Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2 +Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3 +Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2 +Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3 +Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3 +Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3 +Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3 +Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2 +Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1 +% SZS output end CNFRefutation for GRP202-1.p +10978: solved GRP202-1.p in 14.864928 using kbo +10978: status Unsatisfiable for GRP202-1.p +NO CLASH, using fixed ground order +10984: Facts: +10984: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +10984: Goal: +10984: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +10984: Order: +10984: nrkbo +10984: Leaf order: +10984: a2 2 0 2 2,2 +10984: multiply 8 2 2 0,2 +10984: inverse 6 1 1 0,1,1,2 +10984: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +10985: Facts: +10985: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +10985: Goal: +10985: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +10985: Order: +10985: kbo +10985: Leaf order: +10985: a2 2 0 2 2,2 +10985: multiply 8 2 2 0,2 +10985: inverse 6 1 1 0,1,1,2 +10985: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +10986: Facts: +10986: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +10986: Goal: +10986: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +10986: Order: +10986: lpo +10986: Leaf order: +10986: a2 2 0 2 2,2 +10986: multiply 8 2 2 0,2 +10986: inverse 6 1 1 0,1,1,2 +10986: b2 2 0 2 1,1,1,2 +% SZS status Timeout for GRP404-1.p +NO CLASH, using fixed ground order +11033: Facts: +11033: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11033: Goal: +11033: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11033: Order: +11033: nrkbo +11033: Leaf order: +11033: inverse 5 1 0 +11033: c3 2 0 2 2,2 +11033: multiply 10 2 4 0,2 +11033: b3 2 0 2 2,1,2 +11033: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11034: Facts: +11034: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11034: Goal: +11034: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11034: Order: +11034: kbo +11034: Leaf order: +11034: inverse 5 1 0 +11034: c3 2 0 2 2,2 +11034: multiply 10 2 4 0,2 +11034: b3 2 0 2 2,1,2 +11034: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11035: Facts: +11035: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11035: Goal: +11035: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11035: Order: +11035: lpo +11035: Leaf order: +11035: inverse 5 1 0 +11035: c3 2 0 2 2,2 +11035: multiply 10 2 4 0,2 +11035: b3 2 0 2 2,1,2 +11035: a3 2 0 2 1,1,2 +% SZS status Timeout for GRP405-1.p +NO CLASH, using fixed ground order +11052: Facts: +11052: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11052: Goal: +11052: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11052: Order: +11052: nrkbo +11052: Leaf order: +11052: a2 2 0 2 2,2 +11052: multiply 8 2 2 0,2 +11052: inverse 6 1 1 0,1,1,2 +11052: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11053: Facts: +11053: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11053: Goal: +11053: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11053: Order: +11053: kbo +11053: Leaf order: +11053: a2 2 0 2 2,2 +11053: multiply 8 2 2 0,2 +11053: inverse 6 1 1 0,1,1,2 +11053: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11054: Facts: +11054: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11054: Goal: +11054: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11054: Order: +11054: lpo +11054: Leaf order: +11054: a2 2 0 2 2,2 +11054: multiply 8 2 2 0,2 +11054: inverse 6 1 1 0,1,1,2 +11054: b2 2 0 2 1,1,1,2 +% SZS status Timeout for GRP410-1.p +NO CLASH, using fixed ground order +11087: Facts: +11087: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11087: Goal: +11087: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11087: Order: +11087: nrkbo +11087: Leaf order: +11087: inverse 5 1 0 +11087: c3 2 0 2 2,2 +11087: multiply 10 2 4 0,2 +11087: b3 2 0 2 2,1,2 +11087: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11088: Facts: +11088: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11088: Goal: +11088: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11088: Order: +11088: kbo +11088: Leaf order: +11088: inverse 5 1 0 +11088: c3 2 0 2 2,2 +11088: multiply 10 2 4 0,2 +11088: b3 2 0 2 2,1,2 +11088: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11089: Facts: +11089: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11089: Goal: +11089: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11089: Order: +11089: lpo +11089: Leaf order: +11089: inverse 5 1 0 +11089: c3 2 0 2 2,2 +11089: multiply 10 2 4 0,2 +11089: b3 2 0 2 2,1,2 +11089: a3 2 0 2 1,1,2 +% SZS status Timeout for GRP411-1.p +NO CLASH, using fixed ground order +11106: Facts: +11106: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11106: Goal: +11106: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11106: Order: +11106: nrkbo +11106: Leaf order: +11106: a2 2 0 2 2,2 +11106: multiply 8 2 2 0,2 +11106: inverse 8 1 1 0,1,1,2 +11106: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11107: Facts: +11107: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11107: Goal: +11107: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11107: Order: +11107: kbo +11107: Leaf order: +11107: a2 2 0 2 2,2 +11107: multiply 8 2 2 0,2 +11107: inverse 8 1 1 0,1,1,2 +11107: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11108: Facts: +11108: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11108: Goal: +11108: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11108: Order: +11108: lpo +11108: Leaf order: +11108: a2 2 0 2 2,2 +11108: multiply 8 2 2 0,2 +11108: inverse 8 1 1 0,1,1,2 +11108: b2 2 0 2 1,1,1,2 +% SZS status Timeout for GRP419-1.p +NO CLASH, using fixed ground order +11140: Facts: +11140: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11140: Goal: +11140: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11140: Order: +11140: nrkbo +11140: Leaf order: +11140: a2 2 0 2 2,2 +11140: multiply 8 2 2 0,2 +11140: inverse 8 1 1 0,1,1,2 +11140: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11141: Facts: +11141: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11141: Goal: +11141: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11141: Order: +11141: kbo +11141: Leaf order: +11141: a2 2 0 2 2,2 +11141: multiply 8 2 2 0,2 +11141: inverse 8 1 1 0,1,1,2 +11141: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11142: Facts: +11142: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11142: Goal: +11142: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11142: Order: +11142: lpo +11142: Leaf order: +11142: a2 2 0 2 2,2 +11142: multiply 8 2 2 0,2 +11142: inverse 8 1 1 0,1,1,2 +11142: b2 2 0 2 1,1,1,2 +% SZS status Timeout for GRP422-1.p +NO CLASH, using fixed ground order +11162: Facts: +NO CLASH, using fixed ground order +11164: Facts: +11164: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11164: Goal: +11164: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11164: Order: +11164: lpo +11164: Leaf order: +11164: inverse 7 1 0 +11164: c3 2 0 2 2,2 +11164: multiply 10 2 4 0,2 +11164: b3 2 0 2 2,1,2 +11164: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11163: Facts: +11163: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11163: Goal: +11163: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11163: Order: +11163: kbo +11163: Leaf order: +11163: inverse 7 1 0 +11163: c3 2 0 2 2,2 +11163: multiply 10 2 4 0,2 +11163: b3 2 0 2 2,1,2 +11163: a3 2 0 2 1,1,2 +11162: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11162: Goal: +11162: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11162: Order: +11162: nrkbo +11162: Leaf order: +11162: inverse 7 1 0 +11162: c3 2 0 2 2,2 +11162: multiply 10 2 4 0,2 +11162: b3 2 0 2 2,1,2 +11162: a3 2 0 2 1,1,2 +% SZS status Timeout for GRP423-1.p +NO CLASH, using fixed ground order +11197: Facts: +11197: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11197: Goal: +11197: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11197: Order: +11197: kbo +11197: Leaf order: +11197: inverse 5 1 0 +11197: c3 2 0 2 2,2 +11197: multiply 10 2 4 0,2 +11197: b3 2 0 2 2,1,2 +11197: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11198: Facts: +11198: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11198: Goal: +11198: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11198: Order: +11198: lpo +11198: Leaf order: +11198: inverse 5 1 0 +11198: c3 2 0 2 2,2 +11198: multiply 10 2 4 0,2 +11198: b3 2 0 2 2,1,2 +11198: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11196: Facts: +11196: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11196: Goal: +11196: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11196: Order: +11196: nrkbo +11196: Leaf order: +11196: inverse 5 1 0 +11196: c3 2 0 2 2,2 +11196: multiply 10 2 4 0,2 +11196: b3 2 0 2 2,1,2 +11196: a3 2 0 2 1,1,2 +Statistics : +Max weight : 62 +Found proof, 60.632898s +% SZS status Unsatisfiable for GRP429-1.p +% SZS output start CNFRefutation for GRP429-1.p +Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10 +Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2 +Id : 1086, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5854) (multiply (inverse (inverse ?5855)) (multiply (inverse ?5855) ?5856)))) ?5857) (inverse (multiply ?5854 ?5857))) =>= ?5856 [5857, 5856, 5855, 5854] by Super 2 with 5 at 2 +Id : 473, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1916) (multiply (inverse (inverse ?1917)) (multiply (inverse ?1917) ?1918)))) ?1919) (inverse (multiply ?1916 ?1919))) =>= ?1918 [1919, 1918, 1917, 1916] by Super 2 with 5 at 2 +Id : 1106, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?5983) (multiply (inverse (inverse ?5984)) (multiply (inverse ?5984) ?5985)))) ?5986) (inverse (multiply ?5983 ?5986))))) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5986, 5985, 5984, 5983, 5982] by Super 1086 with 473 at 1,2,2,1,1,1,1,2 +Id : 2050, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?13160) (multiply (inverse ?13161) (multiply ?13161 ?13162)))) ?13163) (inverse (multiply ?13160 ?13163))) =>= ?13162 [13163, 13162, 13161, 13160] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2 +Id : 472, {_}: multiply (inverse ?1911) (multiply ?1911 (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912, 1911] by Super 2 with 5 at 2,2 +Id : 1697, {_}: multiply (inverse ?11063) (multiply ?11063 ?11064) =?= multiply (inverse (inverse ?11065)) (multiply (inverse ?11065) ?11064) [11065, 11064, 11063] by Super 472 with 473 at 2,2,2 +Id : 1084, {_}: multiply (inverse ?5842) (multiply ?5842 ?5843) =?= multiply (inverse (inverse ?5844)) (multiply (inverse ?5844) ?5843) [5844, 5843, 5842] by Super 472 with 473 at 2,2,2 +Id : 1735, {_}: multiply (inverse ?11276) (multiply ?11276 ?11277) =?= multiply (inverse ?11278) (multiply ?11278 ?11277) [11278, 11277, 11276] by Super 1697 with 1084 at 3 +Id : 2837, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18056) (multiply ?18056 (multiply ?18057 ?18058)))) ?18059) (inverse (multiply (inverse ?18057) ?18059))) =>= ?18058 [18059, 18058, 18057, 18056] by Super 2050 with 1735 at 1,1,1,1,2 +Id : 2876, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?18341) (multiply ?18341 (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342, 18341] by Super 2837 with 1735 at 2,2,1,1,1,1,2 +Id : 930, {_}: multiply (inverse ?5077) (multiply ?5077 (inverse (multiply (multiply (inverse (multiply (inverse ?5078) ?5079)) ?5080) (inverse (multiply ?5078 ?5080))))) =>= ?5079 [5080, 5079, 5078, 5077] by Super 2 with 5 at 2,2 +Id : 983, {_}: multiply (inverse ?5420) (multiply ?5420 (multiply ?5421 (inverse (multiply (multiply (inverse (multiply (inverse ?5422) ?5423)) ?5424) (inverse (multiply ?5422 ?5424)))))) =>= multiply (inverse (inverse ?5421)) ?5423 [5424, 5423, 5422, 5421, 5420] by Super 930 with 5 at 2,2,2 +Id : 1838, {_}: multiply (inverse ?11737) (multiply ?11737 (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738, 11737] by Super 472 with 1735 at 1,1,1,1,2,2,2 +Id : 2618, {_}: multiply ?16805 (inverse (multiply (multiply (inverse (multiply (inverse ?16806) (multiply ?16806 ?16807))) ?16808) (inverse (multiply (inverse ?16805) ?16808)))) =>= ?16807 [16808, 16807, 16806, 16805] by Super 2 with 1735 at 1,1,1,1,2,2 +Id : 7049, {_}: multiply ?47447 (inverse (multiply (multiply (inverse (multiply (inverse ?47448) (multiply ?47448 ?47449))) (multiply ?47447 ?47450)) (inverse (multiply (inverse ?47451) (multiply ?47451 ?47450))))) =>= ?47449 [47451, 47450, 47449, 47448, 47447] by Super 2618 with 1735 at 1,2,1,2,2 +Id : 7182, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse (multiply (inverse ?48548) (multiply ?48548 (inverse (multiply (multiply (inverse (multiply (inverse ?48549) ?48547)) ?48550) (inverse (multiply ?48549 ?48550))))))))) =>= ?48546 [48550, 48549, 48548, 48547, 48546, 48545] by Super 7049 with 472 at 1,1,2,2 +Id : 7272, {_}: multiply (multiply (inverse ?48545) (multiply ?48545 ?48546)) (inverse (multiply ?48547 (inverse ?48547))) =>= ?48546 [48547, 48546, 48545] by Demod 7182 with 472 at 1,2,1,2,2 +Id : 7322, {_}: multiply (inverse (multiply (inverse ?48938) (multiply ?48938 ?48939))) ?48939 =?= multiply (inverse (multiply (inverse ?48940) (multiply ?48940 ?48941))) ?48941 [48941, 48940, 48939, 48938] by Super 1838 with 7272 at 2,2 +Id : 9244, {_}: multiply (inverse (inverse (multiply (inverse ?63609) (multiply ?63609 (inverse (multiply (multiply (inverse (multiply (inverse ?63610) ?63611)) ?63612) (inverse (multiply ?63610 ?63612)))))))) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63612, 63611, 63610, 63609] by Super 472 with 7322 at 2,2 +Id : 9553, {_}: multiply (inverse (inverse ?63611)) (multiply (inverse (multiply (inverse ?63613) (multiply ?63613 ?63614))) ?63614) =>= ?63611 [63614, 63613, 63611] by Demod 9244 with 472 at 1,1,1,2 +Id : 9607, {_}: multiply (inverse ?66347) (multiply ?66347 (multiply ?66348 (inverse (multiply (multiply (inverse ?66349) ?66350) (inverse (multiply (inverse ?66349) ?66350)))))) =?= multiply (inverse (inverse ?66348)) (multiply (inverse (multiply (inverse ?66351) (multiply ?66351 ?66352))) ?66352) [66352, 66351, 66350, 66349, 66348, 66347] by Super 983 with 9553 at 1,1,1,1,2,2,2,2 +Id : 13028, {_}: multiply (inverse ?88877) (multiply ?88877 (multiply ?88878 (inverse (multiply (multiply (inverse ?88879) ?88880) (inverse (multiply (inverse ?88879) ?88880)))))) =>= ?88878 [88880, 88879, 88878, 88877] by Demod 9607 with 9553 at 3 +Id : 2125, {_}: inverse (multiply (multiply (inverse ?13666) (multiply ?13666 ?13667)) (inverse (multiply ?13668 (multiply (multiply (inverse ?13668) (multiply (inverse ?13669) (multiply ?13669 ?13670))) ?13667)))) =>= ?13670 [13670, 13669, 13668, 13667, 13666] by Super 2050 with 1735 at 1,1,2 +Id : 7292, {_}: inverse (multiply (multiply (inverse ?48720) (multiply ?48720 (inverse (multiply ?48721 (inverse ?48721))))) (inverse (multiply (inverse ?48722) (multiply ?48722 ?48723)))) =>= ?48723 [48723, 48722, 48721, 48720] by Super 2125 with 7272 at 2,1,2,1,2 +Id : 13145, {_}: multiply (inverse ?89741) (multiply ?89741 (multiply ?89742 (inverse (multiply ?89743 (inverse ?89743))))) =>= ?89742 [89743, 89742, 89741] by Super 13028 with 7292 at 2,2,2,2 +Id : 1878, {_}: multiply ?12021 (inverse (multiply (multiply (inverse ?12022) (multiply ?12022 ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12022, 12021] by Super 2 with 1735 at 1,1,2,2 +Id : 13510, {_}: multiply (inverse (inverse ?91449)) (multiply (inverse ?91450) (multiply ?91450 (inverse (multiply ?91451 (inverse ?91451))))) =>= ?91449 [91451, 91450, 91449] by Super 9553 with 13145 at 1,1,2,2 +Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2 +Id : 98, {_}: multiply ?266 (inverse (multiply (multiply (inverse (multiply (inverse ?267) ?268)) ?269) (inverse (multiply ?267 ?269)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?270) (multiply (inverse (inverse ?266)) ?268))) (inverse (multiply (multiply (inverse (multiply (inverse ?271) (multiply (inverse ?270) ?272))) ?273) (inverse (multiply ?271 ?273))))) (inverse ?272)) [273, 272, 271, 270, 269, 268, 267, 266] by Super 2 with 4 at 2,1,1,1,1,2,2 +Id : 13781, {_}: multiply ?92573 (inverse (multiply (multiply (inverse (multiply (inverse ?92574) (multiply (inverse ?92573) (inverse (multiply ?92575 (inverse ?92575)))))) ?92576) (inverse (multiply ?92574 ?92576)))) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92576, 92575, 92574, 92573] by Super 98 with 13510 at 1,1,1,1,3 +Id : 13970, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply (multiply (inverse ?92577) (inverse (multiply (multiply (inverse (multiply (inverse ?92578) (multiply (inverse (inverse ?92577)) ?92579))) ?92580) (inverse (multiply ?92578 ?92580))))) (inverse ?92579)) [92580, 92579, 92578, 92577, 92575] by Demod 13781 with 2 at 2 +Id : 13971, {_}: inverse (multiply ?92575 (inverse ?92575)) =?= inverse (multiply ?92579 (inverse ?92579)) [92579, 92575] by Demod 13970 with 2 at 1,1,3 +Id : 14410, {_}: multiply (inverse (inverse (multiply ?96419 (inverse ?96419)))) (multiply (inverse ?96420) (multiply ?96420 (inverse (multiply ?96421 (inverse ?96421))))) =?= multiply ?96422 (inverse ?96422) [96422, 96421, 96420, 96419] by Super 13510 with 13971 at 1,1,2 +Id : 14473, {_}: multiply ?96419 (inverse ?96419) =?= multiply ?96422 (inverse ?96422) [96422, 96419] by Demod 14410 with 13510 at 2 +Id : 14531, {_}: multiply (multiply (inverse ?96810) (multiply ?96811 (inverse ?96811))) (inverse (multiply ?96812 (inverse ?96812))) =>= inverse ?96810 [96812, 96811, 96810] by Super 7272 with 14473 at 2,1,2 +Id : 15237, {_}: multiply ?101459 (inverse (multiply (multiply (inverse ?101460) (multiply ?101460 (inverse (multiply ?101461 (inverse ?101461))))) (inverse (multiply ?101462 (inverse ?101462))))) =>= inverse (inverse ?101459) [101462, 101461, 101460, 101459] by Super 1878 with 14531 at 2,1,2,1,2,2 +Id : 15353, {_}: multiply ?101459 (inverse (inverse (multiply ?101461 (inverse ?101461)))) =>= inverse (inverse ?101459) [101461, 101459] by Demod 15237 with 7272 at 1,2,2 +Id : 16356, {_}: multiply (inverse (inverse ?111717)) (multiply (inverse (multiply (inverse ?111718) (inverse (inverse ?111718)))) (inverse (inverse (multiply ?111719 (inverse ?111719))))) =>= ?111717 [111719, 111718, 111717] by Super 9553 with 15353 at 2,1,1,2,2 +Id : 18221, {_}: multiply (inverse (inverse ?121427)) (inverse (inverse (inverse (multiply (inverse ?121428) (inverse (inverse ?121428)))))) =>= ?121427 [121428, 121427] by Demod 16356 with 15353 at 2,2 +Id : 16345, {_}: multiply ?111675 (inverse ?111675) =?= inverse (inverse (inverse (multiply ?111676 (inverse ?111676)))) [111676, 111675] by Super 14473 with 15353 at 3 +Id : 18293, {_}: multiply (inverse (inverse ?121732)) (multiply ?121733 (inverse ?121733)) =>= ?121732 [121733, 121732] by Super 18221 with 16345 at 2,2 +Id : 18567, {_}: multiply ?122956 (inverse (multiply ?122957 (inverse ?122957))) =>= inverse (inverse ?122956) [122957, 122956] by Super 7272 with 18293 at 1,2 +Id : 18716, {_}: multiply (inverse ?89741) (multiply ?89741 (inverse (inverse ?89742))) =>= ?89742 [89742, 89741] by Demod 13145 with 18567 at 2,2,2 +Id : 18916, {_}: multiply (inverse (inverse ?124642)) (inverse (inverse (multiply ?124643 (inverse ?124643)))) =>= ?124642 [124643, 124642] by Super 18293 with 18567 at 2,2 +Id : 18985, {_}: inverse (inverse (inverse (inverse ?124642))) =>= ?124642 [124642] by Demod 18916 with 15353 at 2 +Id : 19175, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= inverse (inverse ?124948) [124948, 124947] by Super 18716 with 18985 at 2,2,2 +Id : 19474, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?18342) (multiply ?18342 ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343, 18342] by Demod 2876 with 19175 at 1,1,1,1,2 +Id : 19475, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?18343))))) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19474 with 19175 at 1,1,1,1,1,1,2 +Id : 19512, {_}: inverse (multiply (multiply (inverse ?18343) ?18344) (inverse (multiply (inverse (inverse ?18345)) ?18344))) =>= multiply ?18345 ?18343 [18345, 18344, 18343] by Demod 19475 with 18985 at 1,1,1,2 +Id : 19345, {_}: multiply ?126114 (multiply ?126115 (inverse ?126115)) =>= inverse (inverse ?126114) [126115, 126114] by Super 18293 with 18985 at 1,2 +Id : 19935, {_}: inverse (multiply (multiply (inverse ?128594) (multiply ?128595 (inverse ?128595))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128595, 128594] by Super 19512 with 19345 at 1,2,1,2 +Id : 19990, {_}: inverse (multiply (inverse (inverse (inverse ?128594))) (inverse (inverse (inverse (inverse (inverse ?128596)))))) =>= multiply ?128596 ?128594 [128596, 128594] by Demod 19935 with 19345 at 1,1,2 +Id : 20507, {_}: inverse (multiply (inverse (inverse (inverse ?130153))) (inverse ?130154)) =>= multiply ?130154 ?130153 [130154, 130153] by Demod 19990 with 18985 at 2,1,2 +Id : 20571, {_}: inverse (multiply ?130433 (inverse ?130434)) =>= multiply ?130434 (inverse ?130433) [130434, 130433] by Super 20507 with 18985 at 1,1,2 +Id : 21794, {_}: multiply (multiply (inverse (inverse ?18345)) ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 19512 with 20571 at 2 +Id : 21760, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 21, 22, 20, 19] by Demod 5 with 20571 at 2,2 +Id : 21761, {_}: multiply ?19 (multiply (multiply ?20 ?22) (inverse (multiply (inverse (multiply (inverse ?20) ?21)) ?22))) =?= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 22, 20, 19] by Demod 21760 with 20571 at 3 +Id : 19480, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))))) =>= ?1913 [1914, 1913, 1912] by Demod 472 with 19175 at 2 +Id : 21790, {_}: inverse (inverse (multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)))) =>= ?1913 [1913, 1914, 1912] by Demod 19480 with 20571 at 1,1,2 +Id : 21791, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914) (inverse (multiply ?1912 ?1914))) =>= ?1913 [1914, 1913, 1912] by Demod 21790 with 20571 at 1,2 +Id : 21792, {_}: multiply (multiply ?1912 ?1914) (inverse (multiply (inverse (multiply (inverse ?1912) ?1913)) ?1914)) =>= ?1913 [1913, 1914, 1912] by Demod 21791 with 20571 at 2 +Id : 21810, {_}: multiply ?19 ?21 =<= multiply (multiply ?23 ?24) (inverse (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24)) [24, 23, 21, 19] by Demod 21761 with 21792 at 2,2 +Id : 21811, {_}: multiply ?19 ?21 =<= multiply (inverse (inverse ?19)) ?21 [21, 19] by Demod 21810 with 21792 at 3 +Id : 21822, {_}: multiply (multiply ?18345 ?18344) (inverse (multiply (inverse ?18343) ?18344)) =>= multiply ?18345 ?18343 [18343, 18344, 18345] by Demod 21794 with 21811 at 1,2 +Id : 21949, {_}: multiply (multiply ?139581 (inverse ?139582)) (multiply ?139582 (inverse (inverse ?139583))) =>= multiply ?139581 ?139583 [139583, 139582, 139581] by Super 21822 with 20571 at 2,2 +Id : 19491, {_}: multiply ?12021 (inverse (multiply (inverse (inverse ?12023)) (inverse (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023))))) =>= ?12025 [12025, 12024, 12023, 12021] by Demod 1878 with 19175 at 1,1,2,2 +Id : 21735, {_}: multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse (inverse (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 19491 with 20571 at 2,2 +Id : 3075, {_}: multiply (inverse ?19377) (multiply ?19377 (multiply ?19378 (inverse (multiply (multiply (inverse (multiply (inverse ?19379) ?19380)) ?19381) (inverse (multiply ?19379 ?19381)))))) =>= multiply (inverse (inverse ?19378)) ?19380 [19381, 19380, 19379, 19378, 19377] by Super 930 with 5 at 2,2,2 +Id : 1191, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?5982) (multiply (inverse ?5985) (multiply ?5985 ?5987)))) ?5988) (inverse (multiply ?5982 ?5988))) =>= ?5987 [5988, 5987, 5985, 5982] by Demod 1106 with 473 at 1,1,2,1,1,1,1,2 +Id : 3153, {_}: multiply (inverse ?20008) (multiply ?20008 (multiply ?20009 ?20010)) =?= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009, 20008] by Super 3075 with 1191 at 2,2,2,2 +Id : 19484, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (multiply (inverse ?20011) (multiply ?20011 ?20010)) [20011, 20010, 20009] by Demod 3153 with 19175 at 2 +Id : 19485, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply (inverse (inverse ?20009)) (inverse (inverse ?20010)) [20010, 20009] by Demod 19484 with 19175 at 2,3 +Id : 21818, {_}: inverse (inverse (multiply ?20009 ?20010)) =<= multiply ?20009 (inverse (inverse ?20010)) [20010, 20009] by Demod 19485 with 21811 at 3 +Id : 21880, {_}: multiply ?12021 (inverse (inverse (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21735 with 21818 at 2,2 +Id : 21881, {_}: inverse (inverse (multiply ?12021 (multiply (multiply ?12024 (multiply (multiply (inverse ?12024) (multiply (inverse ?12021) ?12025)) ?12023)) (inverse ?12023)))) =>= ?12025 [12023, 12025, 12024, 12021] by Demod 21880 with 21818 at 2 +Id : 1840, {_}: multiply (inverse ?11749) (multiply ?11749 (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750, 11749] by Super 472 with 1735 at 1,1,2,2,2 +Id : 19489, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?11750) (multiply ?11750 ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751, 11750] by Demod 1840 with 19175 at 2 +Id : 19490, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))))) =>= ?11753 [11753, 11752, 11751] by Demod 19489 with 19175 at 1,1,1,1,2 +Id : 21784, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))))) =>= ?11753 [11751, 11753, 11752] by Demod 19490 with 20571 at 1,1,2 +Id : 21785, {_}: inverse (multiply (inverse (inverse ?11751)) (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21784 with 20571 at 1,2 +Id : 21786, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse (inverse (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21785 with 20571 at 2 +Id : 21834, {_}: inverse (inverse (multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751))) =>= ?11753 [11751, 11753, 11752] by Demod 21786 with 21818 at 2 +Id : 21842, {_}: inverse (multiply ?11751 (inverse (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)))) =>= ?11753 [11753, 11752, 11751] by Demod 21834 with 20571 at 1,2 +Id : 21843, {_}: multiply (multiply ?11752 (multiply (multiply (inverse ?11752) ?11753) ?11751)) (inverse ?11751) =>= ?11753 [11751, 11753, 11752] by Demod 21842 with 20571 at 2 +Id : 21882, {_}: inverse (inverse (multiply ?12021 (multiply (inverse ?12021) ?12025))) =>= ?12025 [12025, 12021] by Demod 21881 with 21843 at 2,1,1,2 +Id : 1876, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (multiply (inverse ?12012) (multiply ?12012 ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12012, 12011] by Super 2 with 1735 at 1,1,1,1,2,2 +Id : 19478, {_}: multiply ?12011 (inverse (multiply (multiply (inverse (inverse (inverse ?12013))) ?12014) (inverse (multiply (inverse ?12011) ?12014)))) =>= ?12013 [12014, 12013, 12011] by Demod 1876 with 19175 at 1,1,1,1,2,2 +Id : 21793, {_}: multiply ?12011 (multiply (multiply (inverse ?12011) ?12014) (inverse (multiply (inverse (inverse (inverse ?12013))) ?12014))) =>= ?12013 [12013, 12014, 12011] by Demod 19478 with 20571 at 2,2 +Id : 19486, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?11738) (multiply ?11738 ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739, 11738] by Demod 1838 with 19175 at 2 +Id : 19487, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 19486 with 19175 at 1,1,1,1,1,1,2 +Id : 21787, {_}: inverse (inverse (multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)))) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 19487 with 20571 at 1,1,2 +Id : 21788, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?11739))) ?11740) (inverse (multiply ?11741 ?11740))) =>= multiply ?11741 ?11739 [11741, 11740, 11739] by Demod 21787 with 20571 at 1,2 +Id : 21789, {_}: multiply (multiply ?11741 ?11740) (inverse (multiply (inverse (inverse (inverse ?11739))) ?11740)) =>= multiply ?11741 ?11739 [11739, 11740, 11741] by Demod 21788 with 20571 at 2 +Id : 21802, {_}: multiply ?12011 (multiply (inverse ?12011) ?12013) =>= ?12013 [12013, 12011] by Demod 21793 with 21789 at 2,2 +Id : 21883, {_}: inverse (inverse ?12025) =>= ?12025 [12025] by Demod 21882 with 21802 at 1,1,2 +Id : 22088, {_}: multiply (multiply ?140028 (inverse ?140029)) (multiply ?140029 ?140030) =>= multiply ?140028 ?140030 [140030, 140029, 140028] by Demod 21949 with 21883 at 2,2,2 +Id : 21892, {_}: multiply (inverse ?124947) (multiply ?124947 ?124948) =>= ?124948 [124948, 124947] by Demod 19175 with 21883 at 3 +Id : 22102, {_}: multiply (multiply ?140094 (inverse (inverse ?140095))) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Super 22088 with 21892 at 2,2 +Id : 22180, {_}: multiply (multiply ?140094 ?140095) ?140096 =>= multiply ?140094 (multiply ?140095 ?140096) [140096, 140095, 140094] by Demod 22102 with 21883 at 2,1,2 +Id : 22441, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 22180 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP429-1.p +11197: solved GRP429-1.p in 30.365897 using kbo +11197: status Unsatisfiable for GRP429-1.p +NO CLASH, using fixed ground order +11215: Facts: +11215: Id : 2, {_}: + inverse + (multiply ?2 + (multiply ?3 + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?5 (multiply ?2 ?3)))))) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11215: Goal: +11215: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11215: Order: +11215: nrkbo +11215: Leaf order: +11215: inverse 3 1 0 +11215: c3 2 0 2 2,2 +11215: multiply 10 2 4 0,2 +11215: b3 2 0 2 2,1,2 +11215: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11216: Facts: +11216: Id : 2, {_}: + inverse + (multiply ?2 + (multiply ?3 + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?5 (multiply ?2 ?3)))))) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11216: Goal: +11216: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11216: Order: +11216: kbo +11216: Leaf order: +11216: inverse 3 1 0 +11216: c3 2 0 2 2,2 +11216: multiply 10 2 4 0,2 +11216: b3 2 0 2 2,1,2 +11216: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11217: Facts: +11217: Id : 2, {_}: + inverse + (multiply ?2 + (multiply ?3 + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?5 (multiply ?2 ?3)))))) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11217: Goal: +11217: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11217: Order: +11217: lpo +11217: Leaf order: +11217: inverse 3 1 0 +11217: c3 2 0 2 2,2 +11217: multiply 10 2 4 0,2 +11217: b3 2 0 2 2,1,2 +11217: a3 2 0 2 1,1,2 +% SZS status Timeout for GRP444-1.p +NO CLASH, using fixed ground order +11235: Facts: +NO CLASH, using fixed ground order +11236: Facts: +11236: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11236: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +11236: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +11236: Goal: +11236: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11236: Order: +11236: kbo +11236: Leaf order: +11236: divide 13 2 0 +11236: a2 2 0 2 2,2 +11236: multiply 3 2 2 0,2 +11236: inverse 2 1 1 0,1,1,2 +11236: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11237: Facts: +11237: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11237: Id : 3, {_}: + multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +11237: Id : 4, {_}: + inverse ?10 =?= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +11237: Goal: +11237: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11237: Order: +11237: lpo +11237: Leaf order: +11237: divide 13 2 0 +11237: a2 2 0 2 2,2 +11237: multiply 3 2 2 0,2 +11237: inverse 2 1 1 0,1,1,2 +11237: b2 2 0 2 1,1,1,2 +11235: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +11235: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +11235: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +11235: Goal: +11235: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11235: Order: +11235: nrkbo +11235: Leaf order: +11235: divide 13 2 0 +11235: a2 2 0 2 2,2 +11235: multiply 3 2 2 0,2 +11235: inverse 2 1 1 0,1,1,2 +11235: b2 2 0 2 1,1,1,2 +Statistics : +Max weight : 38 +Found proof, 1.775197s +% SZS status Unsatisfiable for GRP452-1.p +% SZS output start CNFRefutation for GRP452-1.p +Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15 +Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91 +Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11 +Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8 +Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3 +Id : 122, {_}: multiply (divide ?250 ?250) ?251 =>= inverse (inverse ?251) [251, 250] by Super 29 with 4 at 3 +Id : 128, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= inverse (inverse ?269) [269, 268] by Super 122 with 29 at 1,2 +Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2 +Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3 +Id : 481, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2 +Id : 482, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 481 with 4 at 1,2,1,1,1,2 +Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3 +Id : 483, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 482 with 36 at 2,1,1,1,2 +Id : 484, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 483 with 29 at 1,1,1,2 +Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2 +Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2 +Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3 +Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3 +Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3 +Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3 +Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3 +Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3 +Id : 896, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3 +Id : 911, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 896 with 36 at 2,1,1,3 +Id : 944, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 911 with 4 at 1,1,2 +Id : 978, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 911 with 4 at 1,1,2 +Id : 989, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =?= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 978 with 32 at 1,1,3 +Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3 +Id : 1018, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 989 with 223 at 2 +Id : 1036, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1018 at 2,3 +Id : 1074, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1036 with 29 at 3 +Id : 1107, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 944 with 1074 at 1,1,3 +Id : 1180, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1107 with 29 at 2 +Id : 1223, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 944 with 1180 at 1,1,3 +Id : 1540, {_}: multiply (inverse (inverse (inverse (inverse ?3274)))) ?3275 =<= inverse (inverse (inverse (inverse (multiply ?3274 ?3275)))) [3275, 3274] by Demod 1223 with 29 at 2 +Id : 10, {_}: divide (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) (divide (divide ?37 ?37) ?36) =>= ?35 [37, 36, 35, 34] by Super 2 with 3 at 2,2,2,1,2 +Id : 24, {_}: multiply (divide (divide ?34 ?34) (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 10 with 3 at 2 +Id : 793, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (divide (divide ?34 ?34) ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 24 with 4 at 1,2 +Id : 794, {_}: multiply (inverse (divide ?34 (divide ?35 (multiply (inverse ?34) ?36)))) ?36 =>= ?35 [36, 35, 34] by Demod 793 with 4 at 1,2,2,1,1,2 +Id : 1550, {_}: multiply (inverse (inverse (inverse (inverse (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))))))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Super 1540 with 794 at 1,1,1,1,3 +Id : 1600, {_}: multiply (inverse (divide ?3307 (divide ?3308 (multiply (inverse ?3307) ?3309)))) ?3309 =>= inverse (inverse (inverse (inverse ?3308))) [3309, 3308, 3307] by Demod 1550 with 1018 at 1,2 +Id : 1601, {_}: ?3308 =<= inverse (inverse (inverse (inverse ?3308))) [3308] by Demod 1600 with 794 at 2 +Id : 1634, {_}: multiply ?3404 (inverse (inverse (inverse ?3405))) =>= divide ?3404 ?3405 [3405, 3404] by Super 29 with 1601 at 2,3 +Id : 1707, {_}: divide (inverse (inverse ?3544)) (inverse (inverse ?3545)) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Super 944 with 1634 at 1,1,3 +Id : 1741, {_}: multiply (inverse (inverse ?3544)) (inverse ?3545) =>= inverse (inverse (divide ?3544 ?3545)) [3545, 3544] by Demod 1707 with 29 at 2 +Id : 1807, {_}: divide (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) (inverse ?3667) =>= inverse (inverse ?3666) [3667, 3666] by Super 484 with 1741 at 1,1,1,2 +Id : 1849, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3666 ?3667))))) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1807 with 29 at 2 +Id : 1850, {_}: multiply (divide ?3666 ?3667) ?3667 =>= inverse (inverse ?3666) [3667, 3666] by Demod 1849 with 1601 at 1,2 +Id : 1880, {_}: inverse (inverse ?3792) =<= divide (divide ?3792 (inverse (inverse (inverse ?3793)))) ?3793 [3793, 3792] by Super 1634 with 1850 at 2 +Id : 2688, {_}: inverse (inverse ?5905) =<= divide (multiply ?5905 (inverse (inverse ?5906))) ?5906 [5906, 5905] by Demod 1880 with 29 at 1,3 +Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2 +Id : 2714, {_}: inverse (inverse (inverse (inverse (divide ?5996 ?5996)))) =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Super 2688 with 224 at 1,3 +Id : 2767, {_}: divide ?5996 ?5996 =?= divide (inverse (inverse (inverse (inverse ?5997)))) ?5997 [5997, 5996] by Demod 2714 with 1601 at 2 +Id : 2768, {_}: divide ?5996 ?5996 =?= divide ?5997 ?5997 [5997, 5996] by Demod 2767 with 1601 at 1,3 +Id : 2830, {_}: divide (inverse (divide ?6176 (divide (inverse ?6177) (divide (inverse ?6176) ?6178)))) ?6178 =?= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6178, 6177, 6176] by Super 145 with 2768 at 2,1,3 +Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2 +Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2 +Id : 2905, {_}: inverse ?6177 =<= inverse (divide ?6177 (divide ?6179 ?6179)) [6179, 6177] by Demod 2830 with 31 at 2 +Id : 2962, {_}: divide ?6532 (divide ?6533 ?6533) =?= inverse (inverse (inverse (inverse ?6532))) [6533, 6532] by Super 1601 with 2905 at 1,1,1,3 +Id : 3014, {_}: divide ?6532 (divide ?6533 ?6533) =>= ?6532 [6533, 6532] by Demod 2962 with 1601 at 3 +Id : 3088, {_}: divide (inverse (divide ?6789 ?6790)) (divide ?6791 ?6791) =>= inverse (inverse (multiply ?6790 (inverse ?6789))) [6791, 6790, 6789] by Super 250 with 3014 at 2,1,1,3 +Id : 3148, {_}: inverse (divide ?6789 ?6790) =<= inverse (inverse (multiply ?6790 (inverse ?6789))) [6790, 6789] by Demod 3088 with 3014 at 2 +Id : 3149, {_}: inverse (divide ?6789 ?6790) =<= divide (inverse (inverse ?6790)) ?6789 [6790, 6789] by Demod 3148 with 944 at 3 +Id : 3377, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 484 with 3149 at 2 +Id : 3423, {_}: inverse (divide ?7500 ?7501) =<= divide (inverse (inverse ?7501)) ?7500 [7501, 7500] by Demod 3148 with 944 at 3 +Id : 3441, {_}: inverse (divide ?7566 (inverse (inverse ?7567))) =>= divide ?7567 ?7566 [7567, 7566] by Super 3423 with 1601 at 1,3 +Id : 3536, {_}: inverse (multiply ?7566 (inverse ?7567)) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3441 with 29 at 1,2 +Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3 +Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3 +Id : 3378, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3149 at 3 +Id : 3383, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3378 with 29 at 1,3 +Id : 3089, {_}: multiply ?6793 (divide ?6794 ?6794) =>= inverse (inverse ?6793) [6794, 6793] by Super 1850 with 3014 at 1,2 +Id : 3760, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3383 with 3089 at 1,3 +Id : 3763, {_}: multiply ?3404 (inverse ?3405) =>= divide ?3404 ?3405 [3405, 3404] by Demod 1634 with 3760 at 2,2 +Id : 3764, {_}: inverse (divide ?7566 ?7567) =>= divide ?7567 ?7566 [7567, 7566] by Demod 3536 with 3763 at 1,2 +Id : 3776, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3377 with 3764 at 2 +Id : 1886, {_}: multiply (divide ?3813 ?3814) ?3814 =>= inverse (inverse ?3813) [3814, 3813] by Demod 1849 with 1601 at 1,2 +Id : 1895, {_}: multiply (multiply ?3842 ?3843) (inverse ?3843) =>= inverse (inverse ?3842) [3843, 3842] by Super 1886 with 29 at 1,2 +Id : 3766, {_}: divide (multiply ?3842 ?3843) ?3843 =>= inverse (inverse ?3842) [3843, 3842] by Demod 1895 with 3763 at 2 +Id : 3800, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3776 with 3766 at 2 +Id : 3806, {_}: multiply (multiply (inverse ?268) ?268) ?269 =>= ?269 [269, 268] by Demod 128 with 3800 at 3 +Id : 3889, {_}: a2 =?= a2 [] by Demod 1 with 3806 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP452-1.p +11236: solved GRP452-1.p in 0.984061 using kbo +11236: status Unsatisfiable for GRP452-1.p +NO CLASH, using fixed ground order +11242: Facts: +11242: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11242: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11242: Goal: +11242: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11242: Order: +11242: nrkbo +11242: Leaf order: +11242: divide 7 2 0 +11242: b1 2 0 2 1,1,3 +11242: multiply 3 2 2 0,2 +11242: inverse 4 1 2 0,1,2 +11242: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11243: Facts: +11243: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11243: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11243: Goal: +11243: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11243: Order: +11243: kbo +11243: Leaf order: +11243: divide 7 2 0 +11243: b1 2 0 2 1,1,3 +11243: multiply 3 2 2 0,2 +11243: inverse 4 1 2 0,1,2 +11243: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11244: Facts: +11244: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11244: Id : 3, {_}: + multiply ?7 ?8 =?= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11244: Goal: +11244: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11244: Order: +11244: lpo +11244: Leaf order: +11244: divide 7 2 0 +11244: b1 2 0 2 1,1,3 +11244: multiply 3 2 2 0,2 +11244: inverse 4 1 2 0,1,2 +11244: a1 2 0 2 1,1,2 +% SZS status Timeout for GRP469-1.p +NO CLASH, using fixed ground order +11271: Facts: +11271: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11271: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11271: Goal: +11271: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11271: Order: +11271: nrkbo +11271: Leaf order: +11271: divide 7 2 0 +11271: a2 2 0 2 2,2 +11271: multiply 3 2 2 0,2 +11271: inverse 3 1 1 0,1,1,2 +11271: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11272: Facts: +11272: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11272: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11272: Goal: +11272: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11272: Order: +11272: kbo +11272: Leaf order: +11272: divide 7 2 0 +11272: a2 2 0 2 2,2 +11272: multiply 3 2 2 0,2 +11272: inverse 3 1 1 0,1,1,2 +11272: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11273: Facts: +11273: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11273: Id : 3, {_}: + multiply ?7 ?8 =?= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11273: Goal: +11273: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11273: Order: +11273: lpo +11273: Leaf order: +11273: divide 7 2 0 +11273: a2 2 0 2 2,2 +11273: multiply 3 2 2 0,2 +11273: inverse 3 1 1 0,1,1,2 +11273: b2 2 0 2 1,1,1,2 +Statistics : +Max weight : 55 +Found proof, 64.719986s +% SZS status Unsatisfiable for GRP470-1.p +% SZS output start CNFRefutation for GRP470-1.p +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2 +Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2 +Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2 +Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2 +Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2 +Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3 +Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3 +Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2 +Id : 7613, {_}: ?38021 =<= multiply (multiply (divide (inverse ?38022) ?38023) (divide (multiply ?38023 ?38022) (divide ?38024 ?38021))) ?38024 [38024, 38023, 38022, 38021] by Super 7101 with 3 at 1,2,1,3 +Id : 7678, {_}: ?38552 =<= multiply (multiply (multiply (inverse ?38553) ?38554) (divide (multiply (inverse ?38554) ?38553) (divide ?38555 ?38552))) ?38555 [38555, 38554, 38553, 38552] by Super 7613 with 3 at 1,1,3 +Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2 +Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2 +Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2 +Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2 +Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2 +Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3 +Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2 +Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3 +Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3 +Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2 +Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2 +Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3 +Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3 +Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2 +Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3 +Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3 +Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3 +Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2 +Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3 +Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3 +Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3 +Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3 +Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3 +Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2 +Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3 +Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3 +Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3 +Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3 +Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3 +Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3 +Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3 +Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3 +Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3 +Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3 +Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2 +Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2 +Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2 +Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3 +Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3 +Id : 12991, {_}: inverse (inverse (divide (divide ?67798 ?67799) (multiply ?67800 (multiply (inverse ?67801) ?67802)))) =>= multiply ?67798 (multiply (inverse ?67799) (inverse (multiply (divide ?67800 ?67801) ?67802))) [67802, 67801, 67800, 67799, 67798] by Super 12770 with 12807 at 1,1,2 +Id : 15565, {_}: inverse (inverse (divide (divide ?82879 ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883)))) =>= multiply ?82879 (divide (inverse ?82880) (multiply ?82881 (multiply (inverse ?82882) ?82883))) [82883, 82882, 82881, 82880, 82879] by Demod 12991 with 12807 at 2,3 +Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2 +Id : 15584, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =<= multiply ?83055 (divide (inverse ?83056) (multiply (multiply (divide ?83058 ?83059) (divide (divide ?83059 ?83058) (divide (multiply (inverse ?83060) ?83061) ?83057))) (multiply (inverse ?83060) ?83061))) [83061, 83060, 83059, 83058, 83057, 83056, 83055] by Super 15565 with 6973 at 2,1,1,2 +Id : 15659, {_}: inverse (inverse (divide (divide ?83055 ?83056) ?83057)) =>= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15584 with 6973 at 2,2,3 +Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3 +Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =>= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2 +Id : 13083, {_}: inverse (inverse (divide (multiply ?68472 ?68473) (multiply ?68474 (multiply (inverse ?68475) ?68476)))) =>= multiply ?68472 (multiply (inverse (inverse ?68473)) (inverse (multiply (divide ?68474 ?68475) ?68476))) [68476, 68475, 68474, 68473, 68472] by Super 12858 with 12807 at 1,1,2 +Id : 14137, {_}: inverse (inverse (divide (multiply ?73757 ?73758) (multiply ?73759 (multiply (inverse ?73760) ?73761)))) =>= multiply ?73757 (divide (inverse (inverse ?73758)) (multiply ?73759 (multiply (inverse ?73760) ?73761))) [73761, 73760, 73759, 73758, 73757] by Demod 13083 with 12807 at 2,3 +Id : 14155, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =<= multiply ?73925 (divide (inverse (inverse ?73926)) (multiply (multiply (divide ?73928 ?73929) (divide (divide ?73929 ?73928) (divide (multiply (inverse ?73930) ?73931) ?73927))) (multiply (inverse ?73930) ?73931))) [73931, 73930, 73929, 73928, 73927, 73926, 73925] by Super 14137 with 6973 at 2,1,1,2 +Id : 14212, {_}: inverse (inverse (divide (multiply ?73925 ?73926) ?73927)) =>= multiply ?73925 (divide (inverse (inverse ?73926)) ?73927) [73927, 73926, 73925] by Demod 14155 with 6973 at 2,2,3 +Id : 15715, {_}: multiply ?83687 (inverse (divide (divide ?83688 ?83689) ?83690)) =>= divide ?83687 (multiply ?83688 (divide (inverse ?83689) ?83690)) [83690, 83689, 83688, 83687] by Super 3 with 15659 at 2,3 +Id : 15912, {_}: divide (divide ?84886 (divide (inverse ?84887) ?84888)) (divide ?84889 ?84890) =<= divide (multiply ?84886 ?84888) (multiply ?84889 (divide (inverse ?84890) ?84887)) [84890, 84889, 84888, 84887, 84886] by Super 9552 with 15715 at 3 +Id : 16736, {_}: inverse (inverse (divide (divide ?88411 (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415))) =>= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Super 14212 with 15912 at 1,1,2 +Id : 16823, {_}: multiply ?88411 (divide (inverse (divide (inverse ?88412) ?88413)) (divide ?88414 ?88415)) =<= multiply ?88411 (divide (inverse (inverse ?88413)) (multiply ?88414 (divide (inverse ?88415) ?88412))) [88415, 88414, 88413, 88412, 88411] by Demod 16736 with 15659 at 2 +Id : 19503, {_}: inverse (divide (inverse (inverse ?101466)) (multiply ?101467 (divide (inverse ?101468) ?101469))) =<= multiply (multiply (divide (inverse ?101470) ?101471) (divide (multiply ?101471 ?101470) (multiply ?101472 (divide (inverse (divide (inverse ?101469) ?101466)) (divide ?101467 ?101468))))) ?101472 [101472, 101471, 101470, 101469, 101468, 101467, 101466] by Super 7337 with 16823 at 2,2,1,3 +Id : 20509, {_}: inverse (divide (inverse (inverse ?107024)) (multiply ?107025 (divide (inverse ?107026) ?107027))) =>= inverse (divide (inverse (divide (inverse ?107027) ?107024)) (divide ?107025 ?107026)) [107027, 107026, 107025, 107024] by Demod 19503 with 7337 at 3 +Id : 15122, {_}: multiply ?80264 (inverse (divide (multiply ?80265 ?80266) ?80267)) =<= divide ?80264 (multiply ?80265 (divide (inverse (inverse ?80266)) ?80267)) [80267, 80266, 80265, 80264] by Super 3 with 14212 at 2,3 +Id : 20594, {_}: inverse (multiply (inverse (inverse ?107698)) (inverse (divide (multiply ?107699 ?107700) ?107701))) =>= inverse (divide (inverse (divide (inverse ?107701) ?107698)) (divide ?107699 (inverse ?107700))) [107701, 107700, 107699, 107698] by Super 20509 with 15122 at 1,2 +Id : 20893, {_}: inverse (multiply (inverse (inverse ?108369)) (inverse (divide (multiply ?108370 ?108371) ?108372))) =>= inverse (divide (inverse (divide (inverse ?108372) ?108369)) (multiply ?108370 ?108371)) [108372, 108371, 108370, 108369] by Demod 20594 with 3 at 2,1,3 +Id : 20903, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =<= inverse (divide (inverse (divide (inverse ?108449) ?108447)) (multiply (multiply (divide ?108450 ?108451) (divide (divide ?108451 ?108450) (divide ?108452 ?108448))) ?108452)) [108452, 108451, 108450, 108449, 108448, 108447] by Super 20893 with 6973 at 1,1,2,1,2 +Id : 21279, {_}: inverse (multiply (inverse (inverse ?109423)) (inverse (divide ?109424 ?109425))) =>= inverse (divide (inverse (divide (inverse ?109425) ?109423)) ?109424) [109425, 109424, 109423] by Demod 20903 with 6973 at 2,1,3 +Id : 21354, {_}: inverse (multiply (multiply ?109942 (divide (inverse ?109943) ?109944)) (inverse (divide ?109945 ?109946))) =>= inverse (divide (inverse (divide (inverse ?109946) (divide (divide ?109942 ?109943) ?109944))) ?109945) [109946, 109945, 109944, 109943, 109942] by Super 21279 with 15659 at 1,1,2 +Id : 25671, {_}: inverse (divide (divide ?128948 (divide (inverse ?128949) (divide (inverse ?128950) ?128951))) ?128952) =<= inverse (divide (inverse (divide (inverse ?128949) (divide (divide ?128948 ?128950) ?128951))) ?128952) [128952, 128951, 128950, 128949, 128948] by Demod 21354 with 9552 at 1,2 +Id : 25729, {_}: inverse (divide (divide ?129446 (divide (inverse (divide ?129447 (divide (divide ?129448 (divide (divide ?129449 ?129450) ?129447)) (divide ?129450 ?129449)))) (divide (inverse ?129451) ?129452))) ?129453) =>= inverse (divide (inverse (divide ?129448 (divide (divide ?129446 ?129451) ?129452))) ?129453) [129453, 129452, 129451, 129450, 129449, 129448, 129447, 129446] by Super 25671 with 53 at 1,1,1,1,3 +Id : 26075, {_}: inverse (divide (divide ?131096 (divide ?131097 (divide (inverse ?131098) ?131099))) ?131100) =<= inverse (divide (inverse (divide ?131097 (divide (divide ?131096 ?131098) ?131099))) ?131100) [131100, 131099, 131098, 131097, 131096] by Demod 25729 with 53 at 1,2,1,1,2 +Id : 26111, {_}: inverse (divide (divide ?131425 (divide ?131426 (divide (inverse (inverse ?131427)) ?131428))) ?131429) =>= inverse (divide (inverse (divide ?131426 (divide (multiply ?131425 ?131427) ?131428))) ?131429) [131429, 131428, 131427, 131426, 131425] by Super 26075 with 3 at 1,2,1,1,1,3 +Id : 30666, {_}: inverse (inverse (divide (inverse (divide ?153822 (divide (multiply ?153823 ?153824) ?153825))) ?153826)) =>= multiply ?153823 (divide (inverse (divide ?153822 (divide (inverse (inverse ?153824)) ?153825))) ?153826) [153826, 153825, 153824, 153823, 153822] by Super 15659 with 26111 at 1,2 +Id : 30731, {_}: inverse (inverse (multiply ?154370 ?154371)) =<= multiply ?154370 (divide (inverse (divide ?154372 (divide (inverse (inverse ?154371)) (divide ?154373 ?154374)))) (divide (divide ?154374 ?154373) ?154372)) [154374, 154373, 154372, 154371, 154370] by Super 30666 with 2 at 1,1,2 +Id : 31025, {_}: inverse (inverse (multiply ?155310 ?155311)) =>= multiply ?155310 (inverse (inverse ?155311)) [155311, 155310] by Demod 30731 with 2 at 2,3 +Id : 7367, {_}: inverse ?36880 =<= multiply (multiply (multiply ?36881 ?36882) (divide (divide (inverse ?36882) ?36881) (multiply ?36883 ?36880))) ?36883 [36883, 36882, 36881, 36880] by Super 7303 with 3 at 1,1,3 +Id : 15740, {_}: inverse (inverse (divide (divide ?83867 ?83868) ?83869)) =>= multiply ?83867 (divide (inverse ?83868) ?83869) [83869, 83868, 83867] by Demod 15584 with 6973 at 2,2,3 +Id : 15787, {_}: inverse (inverse (multiply (multiply ?84179 ?84180) (inverse (multiply ?84181 ?84182)))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Super 15740 with 9554 at 1,1,2 +Id : 15809, {_}: multiply ?84179 (multiply (inverse (inverse ?84180)) (inverse (multiply ?84181 ?84182))) =>= multiply ?84179 (divide (inverse (divide (inverse (inverse ?84182)) ?84180)) ?84181) [84182, 84181, 84180, 84179] by Demod 15787 with 12858 at 2 +Id : 16238, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =<= multiply (multiply (multiply ?86043 ?86044) (divide (divide (inverse ?86044) ?86043) (multiply ?86045 (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041)))) ?86045 [86045, 86044, 86043, 86042, 86041, 86040] by Super 7367 with 15809 at 2,2,1,3 +Id : 16326, {_}: inverse (multiply (inverse (inverse ?86040)) (inverse (multiply ?86041 ?86042))) =>= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86042, 86041, 86040] by Demod 16238 with 7367 at 3 +Id : 31064, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?155519)) ?155520)) ?155521)) =>= multiply (inverse (inverse ?155520)) (inverse (inverse (inverse (multiply ?155521 ?155519)))) [155521, 155520, 155519] by Super 31025 with 16326 at 1,2 +Id : 30884, {_}: inverse (inverse (multiply ?154370 ?154371)) =>= multiply ?154370 (inverse (inverse ?154371)) [154371, 154370] by Demod 30731 with 2 at 2,3 +Id : 32647, {_}: inverse (inverse (divide (inverse (divide (inverse (inverse ?161221)) ?161222)) ?161223)) =>= multiply (inverse (inverse ?161222)) (inverse (multiply ?161223 (inverse (inverse ?161221)))) [161223, 161222, 161221] by Demod 31064 with 30884 at 1,2,3 +Id : 32648, {_}: inverse (inverse (divide (inverse (divide (inverse ?161225) ?161226)) ?161227)) =<= multiply (inverse (inverse ?161226)) (inverse (multiply ?161227 (inverse (inverse (divide ?161228 (divide (divide ?161225 (divide (divide ?161229 ?161230) ?161228)) (divide ?161230 ?161229))))))) [161230, 161229, 161228, 161227, 161226, 161225] by Super 32647 with 53 at 1,1,1,1,1,1,2 +Id : 33188, {_}: inverse (inverse (divide (inverse (divide (inverse ?162681) ?162682)) ?162683)) =>= multiply (inverse (inverse ?162682)) (inverse (multiply ?162683 (inverse ?162681))) [162683, 162682, 162681] by Demod 32648 with 53 at 1,2,1,2,3 +Id : 33189, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =<= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 (inverse (divide ?162688 (divide (divide ?162685 (divide (divide ?162689 ?162690) ?162688)) (divide ?162690 ?162689)))))) [162690, 162689, 162688, 162687, 162686, 162685] by Super 33188 with 53 at 1,1,1,1,1,2 +Id : 33732, {_}: inverse (inverse (divide (inverse (divide ?164373 ?164374)) ?164375)) =>= multiply (inverse (inverse ?164374)) (inverse (multiply ?164375 ?164373)) [164375, 164374, 164373] by Demod 33189 with 53 at 2,1,2,3 +Id : 33815, {_}: inverse (inverse (multiply (inverse (divide ?164946 ?164947)) ?164948)) =<= multiply (inverse (inverse ?164947)) (inverse (multiply (inverse ?164948) ?164946)) [164948, 164947, 164946] by Super 33732 with 3 at 1,1,2 +Id : 34748, {_}: multiply (inverse (divide ?166758 ?166759)) (inverse (inverse ?166760)) =<= multiply (inverse (inverse ?166759)) (inverse (multiply (inverse ?166760) ?166758)) [166760, 166759, 166758] by Demod 33815 with 30884 at 2 +Id : 34749, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse (inverse (divide ?166764 (divide (divide ?166765 (divide (divide ?166766 ?166767) ?166764)) (divide ?166767 ?166766))))) =>= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166767, 166766, 166765, 166764, 166763, 166762] by Super 34748 with 53 at 1,1,2,3 +Id : 35052, {_}: multiply (inverse (divide ?166762 ?166763)) (inverse ?166765) =<= multiply (inverse (inverse ?166763)) (inverse (multiply ?166765 ?166762)) [166765, 166763, 166762] by Demod 34749 with 53 at 1,2,2 +Id : 35278, {_}: multiply (inverse (divide ?167869 ?167870)) (inverse (divide ?167871 ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Super 12807 with 35052 at 2 +Id : 33419, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (inverse ?162686)) (inverse (multiply ?162687 ?162685)) [162687, 162686, 162685] by Demod 33189 with 53 at 2,1,2,3 +Id : 35198, {_}: inverse (inverse (divide (inverse (divide ?162685 ?162686)) ?162687)) =>= multiply (inverse (divide ?162685 ?162686)) (inverse ?162687) [162687, 162686, 162685] by Demod 33419 with 35052 at 3 +Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2 +Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2 +Id : 38131, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =<= multiply (inverse (divide (inverse (divide ?178376 (divide ?178374 (multiply (divide ?178377 ?178378) (divide ?178378 (divide ?178379 (multiply (divide (divide ?178380 ?178381) ?178382) (divide ?178382 (divide ?178377 (divide ?178381 ?178380)))))))))) (divide ?178379 ?178376))) (inverse ?178375) [178382, 178381, 178380, 178379, 178378, 178377, 178376, 178375, 178374] by Super 35198 with 38 at 1,1,1,1,2 +Id : 38834, {_}: inverse (inverse (divide (inverse ?178374) ?178375)) =>= multiply (inverse ?178374) (inverse ?178375) [178375, 178374] by Demod 38131 with 38 at 1,1,3 +Id : 39627, {_}: multiply ?187316 (inverse (divide (inverse ?187317) ?187318)) =>= divide ?187316 (multiply (inverse ?187317) (inverse ?187318)) [187318, 187317, 187316] by Super 3 with 38834 at 2,3 +Id : 39628, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =<= divide ?187320 (multiply (inverse (divide ?187323 (divide (divide ?187321 (divide (divide ?187324 ?187325) ?187323)) (divide ?187325 ?187324)))) (inverse ?187322)) [187325, 187324, 187323, 187322, 187321, 187320] by Super 39627 with 53 at 1,1,2,2 +Id : 39950, {_}: multiply ?187320 (inverse (divide ?187321 ?187322)) =>= divide ?187320 (multiply ?187321 (inverse ?187322)) [187322, 187321, 187320] by Demod 39628 with 53 at 1,2,3 +Id : 45468, {_}: divide (inverse (divide ?167869 ?167870)) (multiply ?167871 (inverse ?167872)) =<= divide (inverse (inverse ?167870)) (multiply ?167871 (multiply (inverse ?167872) ?167869)) [167872, 167871, 167870, 167869] by Demod 35278 with 39950 at 2 +Id : 45552, {_}: divide (inverse ?204144) (multiply (divide ?204145 ?204146) (divide (divide ?204146 ?204145) (divide ?204144 (divide (inverse (divide ?204147 ?204148)) (multiply ?204149 (inverse ?204150)))))) =>= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204150, 204149, 204148, 204147, 204146, 204145, 204144] by Super 362 with 45468 at 2,2,2,2,2 +Id : 45856, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= divide (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse (inverse ?204148)) [204148, 204147, 204150, 204149] by Demod 45552 with 362 at 2 +Id : 45857, {_}: divide (multiply ?204149 (inverse ?204150)) (inverse (divide ?204147 ?204148)) =<= multiply (multiply ?204149 (multiply (inverse ?204150) ?204147)) (inverse ?204148) [204148, 204147, 204150, 204149] by Demod 45856 with 3 at 3 +Id : 46240, {_}: multiply (multiply ?206273 (inverse ?206274)) (divide ?206275 ?206276) =<= multiply (multiply ?206273 (multiply (inverse ?206274) ?206275)) (inverse ?206276) [206276, 206275, 206274, 206273] by Demod 45857 with 3 at 2 +Id : 30915, {_}: multiply (multiply ?67174 ?67175) (inverse (inverse ?67176)) =?= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 30884 at 2 +Id : 46333, {_}: multiply (multiply ?207013 (inverse (inverse ?207014))) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Super 46240 with 30915 at 1,3 +Id : 1890, {_}: divide (inverse (divide (divide ?8674 ?8675) ?8676)) ?8677 =<= inverse (divide (inverse (divide ?8678 ?8677)) (divide ?8676 (divide ?8678 (divide ?8675 ?8674)))) [8678, 8677, 8676, 8675, 8674] by Super 7 with 1266 at 2,2 +Id : 1908, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide ?8836 ?8835)) (divide ?8834 (divide ?8836 (multiply ?8833 ?8832)))) [8836, 8835, 8834, 8833, 8832] by Super 1890 with 3 at 2,2,2,1,3 +Id : 61, {_}: divide (inverse (divide ?349 ?350)) (divide (divide ?351 (divide ?352 ?353)) ?349) =>= inverse (divide ?351 (divide ?350 (divide ?353 ?352))) [353, 352, 351, 350, 349] by Super 4 with 2 at 2,1,1,2 +Id : 65, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide ?384 (divide ?383 (divide (inverse ?386) ?385))) [386, 385, 384, 383, 382] by Super 61 with 3 at 2,1,2,2 +Id : 16676, {_}: divide (inverse ?87869) (multiply (divide ?87870 ?87871) (divide (divide ?87871 ?87870) (divide ?87869 (divide (divide ?87872 (divide (inverse ?87873) ?87874)) (divide ?87875 ?87876))))) =>= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87876, 87875, 87874, 87873, 87872, 87871, 87870, 87869] by Super 362 with 15912 at 2,2,2,2,2 +Id : 16850, {_}: divide (divide ?87875 ?87876) (divide ?87872 (divide (inverse ?87873) ?87874)) =<= divide (multiply ?87875 (divide (inverse ?87876) ?87873)) (multiply ?87872 ?87874) [87874, 87873, 87872, 87876, 87875] by Demod 16676 with 362 at 2 +Id : 17219, {_}: inverse (inverse (divide (divide ?91192 ?91193) (divide ?91194 (divide (inverse ?91195) ?91196)))) =>= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Super 14212 with 16850 at 1,1,2 +Id : 17309, {_}: multiply ?91192 (divide (inverse ?91193) (divide ?91194 (divide (inverse ?91195) ?91196))) =<= multiply ?91192 (divide (inverse (inverse (divide (inverse ?91193) ?91195))) (multiply ?91194 ?91196)) [91196, 91195, 91194, 91193, 91192] by Demod 17219 with 15659 at 2 +Id : 22082, {_}: inverse (divide (inverse (inverse (divide (inverse ?112093) ?112094))) (multiply ?112095 ?112096)) =<= multiply (multiply (divide (inverse ?112097) ?112098) (divide (multiply ?112098 ?112097) (multiply ?112099 (divide (inverse ?112093) (divide ?112095 (divide (inverse ?112094) ?112096)))))) ?112099 [112099, 112098, 112097, 112096, 112095, 112094, 112093] by Super 7337 with 17309 at 2,2,1,3 +Id : 22476, {_}: inverse (divide (inverse (inverse (divide (inverse ?113967) ?113968))) (multiply ?113969 ?113970)) =>= inverse (divide (inverse ?113967) (divide ?113969 (divide (inverse ?113968) ?113970))) [113970, 113969, 113968, 113967] by Demod 22082 with 7337 at 3 +Id : 22508, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =<= inverse (divide (inverse (divide ?114208 (divide (divide ?114204 (divide (divide ?114209 ?114210) ?114208)) (divide ?114210 ?114209)))) (divide ?114206 (divide (inverse ?114205) ?114207))) [114210, 114209, 114208, 114207, 114206, 114205, 114204] by Super 22476 with 53 at 1,1,1,1,1,2 +Id : 22780, {_}: inverse (divide (inverse (inverse (divide ?114204 ?114205))) (multiply ?114206 ?114207)) =>= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22508 with 53 at 1,1,3 +Id : 40158, {_}: inverse (inverse (divide ?188657 ?188658)) =<= multiply (multiply (multiply ?188659 ?188660) (divide (divide (inverse ?188660) ?188659) (divide ?188661 (multiply ?188657 (inverse ?188658))))) ?188661 [188661, 188660, 188659, 188658, 188657] by Super 7367 with 39950 at 2,2,1,3 +Id : 7191, {_}: ?36095 =<= multiply (multiply (multiply ?36096 ?36097) (divide (divide (inverse ?36097) ?36096) (divide ?36098 ?36095))) ?36098 [36098, 36097, 36096, 36095] by Super 7101 with 3 at 1,1,3 +Id : 40350, {_}: inverse (inverse (divide ?188657 ?188658)) =>= multiply ?188657 (inverse ?188658) [188658, 188657] by Demod 40158 with 7191 at 3 +Id : 40577, {_}: inverse (divide (multiply ?114204 (inverse ?114205)) (multiply ?114206 ?114207)) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114207, 114206, 114205, 114204] by Demod 22780 with 40350 at 1,1,2 +Id : 40645, {_}: divide (divide ?189801 (divide (multiply ?189802 (inverse ?189803)) ?189804)) ?189805 =<= multiply (multiply ?189801 ?189804) (inverse (multiply ?189805 (divide ?189802 ?189803))) [189805, 189804, 189803, 189802, 189801] by Super 9554 with 40350 at 1,2,1,2 +Id : 30968, {_}: multiply ?154958 (inverse (multiply ?154959 ?154960)) =<= divide ?154958 (multiply ?154959 (inverse (inverse ?154960))) [154960, 154959, 154958] by Super 3 with 30884 at 2,3 +Id : 40629, {_}: multiply ?189704 (inverse (multiply ?189705 (divide ?189706 ?189707))) =>= divide ?189704 (multiply ?189705 (multiply ?189706 (inverse ?189707))) [189707, 189706, 189705, 189704] by Super 30968 with 40350 at 2,2,3 +Id : 62131, {_}: divide (divide ?257834 (divide (multiply ?257835 (inverse ?257836)) ?257837)) ?257838 =<= divide (multiply ?257834 ?257837) (multiply ?257838 (multiply ?257835 (inverse ?257836))) [257838, 257837, 257836, 257835, 257834] by Demod 40645 with 40629 at 3 +Id : 62178, {_}: divide (divide ?258249 (divide (multiply (multiply (divide ?258250 ?258251) (divide (divide ?258251 ?258250) (divide (inverse ?258252) ?258253))) (inverse ?258252)) ?258254)) ?258255 =>= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258252, 258251, 258250, 258249] by Super 62131 with 6973 at 2,2,3 +Id : 62493, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =<= divide (multiply ?258249 ?258254) (multiply ?258255 ?258253) [258255, 258254, 258253, 258249] by Demod 62178 with 6973 at 1,2,1,2 +Id : 62632, {_}: inverse (divide (divide ?114204 (divide ?114207 (inverse ?114205))) ?114206) =?= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 40577 with 62493 at 1,2 +Id : 62637, {_}: inverse (divide (divide ?114204 (multiply ?114207 ?114205)) ?114206) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114206, 114205, 114207, 114204] by Demod 62632 with 3 at 2,1,1,2 +Id : 62641, {_}: divide (inverse (divide ?382 ?383)) (divide (divide ?384 (multiply ?385 ?386)) ?382) =>= inverse (divide (divide ?384 (multiply ?385 ?386)) ?383) [386, 385, 384, 383, 382] by Demod 65 with 62637 at 3 +Id : 19, {_}: divide (inverse ?90) (divide (divide ?91 ?92) (inverse (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93)))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Super 2 with 15 at 1,1,2 +Id : 40, {_}: divide (inverse ?90) (multiply (divide ?91 ?92) (divide (divide ?92 ?91) (divide ?90 (multiply (divide (divide ?93 ?94) ?95) (divide ?95 (divide ?96 (divide ?94 ?93))))))) =>= ?96 [96, 95, 94, 93, 92, 91, 90] by Demod 19 with 3 at 2,2 +Id : 89822, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =?= inverse (divide (divide (inverse ?333800) (multiply (divide ?333801 ?333802) (divide (divide ?333802 ?333801) (divide ?333800 (multiply (divide (divide ?333803 ?333804) ?333805) (divide ?333805 (divide ?333799 (divide ?333804 ?333803)))))))) ?333798) [333805, 333804, 333803, 333802, 333801, 333800, 333799, 333798, 333797] by Super 62641 with 40 at 1,2,2 +Id : 90396, {_}: divide (inverse (divide ?333797 ?333798)) (divide ?333799 ?333797) =>= inverse (divide ?333799 ?333798) [333799, 333798, 333797] by Demod 89822 with 40 at 1,1,3 +Id : 101099, {_}: inverse (divide (divide ?31 (divide ?32 ?33)) ?30) =?= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [30, 33, 32, 31] by Demod 7 with 90396 at 2 +Id : 101112, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (divide (inverse (divide ?8836 ?8835)) (divide (multiply ?8833 ?8832) ?8836)) ?8834) [8836, 8835, 8834, 8833, 8832] by Demod 1908 with 101099 at 3 +Id : 101118, {_}: divide (inverse (divide (divide (inverse ?8832) ?8833) ?8834)) ?8835 =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8835, 8834, 8833, 8832] by Demod 101112 with 90396 at 1,1,3 +Id : 101316, {_}: divide (inverse (divide (divide (inverse ?356253) ?356254) (divide ?356255 (multiply ?356254 ?356253)))) ?356256 =>= inverse (inverse (divide ?356255 ?356256)) [356256, 356255, 356254, 356253] by Super 101118 with 90396 at 1,3 +Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2 +Id : 101095, {_}: inverse (divide (divide (inverse ?56) ?55) (divide ?54 (multiply ?55 ?56))) =>= ?54 [54, 55, 56] by Demod 12 with 90396 at 2 +Id : 101519, {_}: divide ?356255 ?356256 =<= inverse (inverse (divide ?356255 ?356256)) [356256, 356255] by Demod 101316 with 101095 at 1,2 +Id : 101520, {_}: divide ?356255 ?356256 =<= multiply ?356255 (inverse ?356256) [356256, 356255] by Demod 101519 with 40350 at 3 +Id : 102152, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= multiply (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) (inverse ?207016) [207016, 207015, 207014, 207013] by Demod 46333 with 101520 at 1,2 +Id : 102153, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =<= divide (multiply (multiply ?207013 ?207014) (inverse (inverse ?207015))) ?207016 [207016, 207015, 207014, 207013] by Demod 102152 with 101520 at 3 +Id : 102154, {_}: multiply (divide ?207013 (inverse ?207014)) (divide ?207015 ?207016) =>= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102153 with 101520 at 1,3 +Id : 102308, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =<= divide (divide (multiply ?207013 ?207014) (inverse ?207015)) ?207016 [207016, 207015, 207014, 207013] by Demod 102154 with 3 at 1,2 +Id : 102309, {_}: multiply (multiply ?207013 ?207014) (divide ?207015 ?207016) =>= divide (multiply (multiply ?207013 ?207014) ?207015) ?207016 [207016, 207015, 207014, 207013] by Demod 102308 with 3 at 1,3 +Id : 102310, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38554) (multiply (inverse ?38554) ?38553)) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 7678 with 102309 at 1,3 +Id : 52549, {_}: multiply (multiply ?225200 (inverse (inverse ?225201))) (divide ?225202 ?225203) =<= multiply (multiply (multiply ?225200 ?225201) (inverse (inverse ?225202))) (inverse ?225203) [225203, 225202, 225201, 225200] by Super 46240 with 30915 at 1,3 +Id : 52684, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (divide ?226213 (inverse ?226214)) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Super 52549 with 30915 at 3 +Id : 53235, {_}: multiply (multiply ?226211 (inverse (inverse ?226212))) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 52684 with 3 at 2,2 +Id : 102165, {_}: multiply (divide ?226211 (inverse ?226212)) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 53235 with 101520 at 1,2 +Id : 102295, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply ?226211 ?226212) (multiply (inverse (inverse (inverse (inverse ?226213)))) ?226214) [226214, 226213, 226212, 226211] by Demod 102165 with 3 at 1,2 +Id : 30916, {_}: multiply (divide ?66357 ?66358) (inverse (inverse ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12770 with 30884 at 2 +Id : 9965, {_}: divide (divide ?51846 (divide (inverse (inverse ?51847)) ?51848)) ?51849 =>= multiply (multiply ?51846 ?51848) (inverse (multiply ?51849 ?51847)) [51849, 51848, 51847, 51846] by Super 9472 with 7237 at 1,1,3 +Id : 9976, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (multiply ?51938 (inverse ?51940)) (inverse (multiply ?51941 ?51939)) [51941, 51940, 51939, 51938] by Super 9965 with 3 at 2,1,2 +Id : 40724, {_}: inverse (inverse (divide ?190294 ?190295)) =>= multiply ?190294 (inverse ?190295) [190295, 190294] by Demod 40158 with 7191 at 3 +Id : 40043, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= divide (multiply ?49359 ?49361) (multiply ?49362 (inverse ?49360)) [49362, 49361, 49360, 49359] by Demod 9552 with 39950 at 3 +Id : 40771, {_}: inverse (inverse (divide (divide ?190577 (divide (inverse ?190578) ?190579)) ?190580)) =>= multiply (multiply ?190577 ?190579) (inverse (multiply ?190580 (inverse ?190578))) [190580, 190579, 190578, 190577] by Super 40724 with 40043 at 1,1,2 +Id : 42949, {_}: multiply (divide ?196696 (divide (inverse ?196697) ?196698)) (inverse ?196699) =<= multiply (multiply ?196696 ?196698) (inverse (multiply ?196699 (inverse ?196697))) [196699, 196698, 196697, 196696] by Demod 40771 with 40350 at 2 +Id : 42950, {_}: multiply (divide ?196701 (divide (inverse (divide ?196702 (divide (divide ?196703 (divide (divide ?196704 ?196705) ?196702)) (divide ?196705 ?196704)))) ?196706)) (inverse ?196707) =>= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196705, 196704, 196703, 196702, 196701] by Super 42949 with 53 at 2,1,2,3 +Id : 43226, {_}: multiply (divide ?196701 (divide ?196703 ?196706)) (inverse ?196707) =<= multiply (multiply ?196701 ?196706) (inverse (multiply ?196707 ?196703)) [196707, 196706, 196703, 196701] by Demod 42950 with 53 at 1,2,1,2 +Id : 43404, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =<= multiply (divide ?51938 (divide ?51939 (inverse ?51940))) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 9976 with 43226 at 3 +Id : 43406, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= multiply (divide ?51938 (multiply ?51939 ?51940)) (inverse ?51941) [51941, 51940, 51939, 51938] by Demod 43404 with 3 at 2,1,3 +Id : 62671, {_}: divide (divide (divide ?259262 (divide ?259263 ?259264)) (inverse (inverse ?259265))) ?259266 =>= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Super 43406 with 62493 at 1,2 +Id : 63074, {_}: divide (multiply (divide ?259262 (divide ?259263 ?259264)) (inverse ?259265)) ?259266 =<= multiply (divide (multiply ?259262 ?259264) (multiply ?259265 ?259263)) (inverse ?259266) [259266, 259265, 259264, 259263, 259262] by Demod 62671 with 3 at 1,2 +Id : 84448, {_}: divide (multiply (divide ?320603 (divide ?320604 ?320605)) (inverse ?320606)) ?320607 =<= multiply (divide (divide ?320603 (divide ?320604 ?320605)) ?320606) (inverse ?320607) [320607, 320606, 320605, 320604, 320603] by Demod 63074 with 62493 at 1,3 +Id : 84555, {_}: divide (multiply (divide (inverse (divide ?321565 (divide ?321566 (multiply (divide (divide ?321567 ?321568) ?321569) (divide ?321569 (divide ?321570 (divide ?321568 ?321567))))))) (divide ?321570 ?321565)) (inverse ?321571)) ?321572 =>= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321570, 321569, 321568, 321567, 321566, 321565] by Super 84448 with 15 at 1,1,3 +Id : 85061, {_}: divide (multiply ?321566 (inverse ?321571)) ?321572 =<= multiply (divide ?321566 ?321571) (inverse ?321572) [321572, 321571, 321566] by Demod 84555 with 15 at 1,1,2 +Id : 85186, {_}: divide (multiply ?66357 (inverse ?66358)) (inverse ?66359) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 30916 with 85061 at 2 +Id : 85229, {_}: multiply (multiply ?66357 (inverse ?66358)) ?66359 =?= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85186 with 3 at 2 +Id : 102180, {_}: multiply (divide ?66357 ?66358) ?66359 =<= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 85229 with 101520 at 1,2 +Id : 102296, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse (inverse (inverse ?226213)))) ?226214 [226214, 226213, 226212, 226211] by Demod 102295 with 102180 at 3 +Id : 102297, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (multiply (multiply ?226211 ?226212) (inverse (inverse ?226213))) ?226214 [226214, 226213, 226212, 226211] by Demod 102296 with 3 at 1,3 +Id : 102298, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =<= multiply (divide (multiply ?226211 ?226212) (inverse ?226213)) ?226214 [226214, 226213, 226212, 226211] by Demod 102297 with 101520 at 1,3 +Id : 102299, {_}: multiply (multiply ?226211 ?226212) (multiply ?226213 ?226214) =?= multiply (multiply (multiply ?226211 ?226212) ?226213) ?226214 [226214, 226213, 226212, 226211] by Demod 102298 with 3 at 1,3 +Id : 102317, {_}: ?38552 =<= multiply (divide (multiply (multiply (multiply (inverse ?38553) ?38554) (inverse ?38554)) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102310 with 102299 at 1,1,3 +Id : 102318, {_}: ?38552 =<= multiply (divide (multiply (divide (multiply (inverse ?38553) ?38554) ?38554) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38554, 38553, 38552] by Demod 102317 with 101520 at 1,1,1,3 +Id : 2791, {_}: divide (divide (inverse (multiply ?13892 ?13893)) (divide (divide (inverse ?13894) ?13895) ?13892)) (multiply ?13895 ?13894) =>= inverse ?13893 [13895, 13894, 13893, 13892] by Super 2771 with 3 at 2,2 +Id : 89847, {_}: divide (inverse ?334058) (multiply (divide ?334059 ?334060) (divide (divide ?334060 ?334059) (divide ?334058 (multiply (divide (divide ?334061 ?334062) ?334063) (divide ?334063 (divide ?334064 (divide ?334062 ?334061))))))) =>= ?334064 [334064, 334063, 334062, 334061, 334060, 334059, 334058] by Demod 19 with 3 at 2,2 +Id : 43403, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (divide ?49369 (divide ?49370 ?49371)) (inverse ?49372) [49372, 49371, 49370, 49369] by Demod 9554 with 43226 at 3 +Id : 85181, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (multiply ?49369 (inverse (divide ?49370 ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 43403 with 85061 at 3 +Id : 85235, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= divide (divide ?49369 (multiply ?49370 (inverse ?49371))) ?49372 [49372, 49371, 49370, 49369] by Demod 85181 with 39950 at 1,3 +Id : 89956, {_}: divide (inverse ?335244) (multiply (divide ?335245 ?335246) (divide (divide ?335246 ?335245) (divide ?335244 (multiply (divide (divide ?335247 ?335248) ?335249) (divide ?335249 (divide (divide ?335250 (multiply ?335251 (inverse ?335252))) (divide ?335248 ?335247))))))) =>= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250, 335249, 335248, 335247, 335246, 335245, 335244] by Super 89847 with 85235 at 2,2,2,2,2,2,2 +Id : 90764, {_}: divide ?335250 (multiply ?335251 (inverse ?335252)) =<= divide ?335250 (divide (inverse (inverse ?335251)) ?335252) [335252, 335251, 335250] by Demod 89956 with 40 at 2 +Id : 92959, {_}: divide (inverse (inverse ?344076)) ?344077 =<= multiply (multiply (multiply (inverse ?344078) ?344079) (divide (multiply (inverse ?344079) ?344078) (divide ?344080 (multiply ?344076 (inverse ?344077))))) ?344080 [344080, 344079, 344078, 344077, 344076] by Super 7678 with 90764 at 2,2,1,3 +Id : 93432, {_}: divide (inverse (inverse ?344076)) ?344077 =>= multiply ?344076 (inverse ?344077) [344077, 344076] by Demod 92959 with 7678 at 3 +Id : 94198, {_}: multiply (inverse (inverse ?346092)) (inverse (multiply ?346093 ?346094)) =?= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346094, 346093, 346092] by Super 30968 with 93432 at 3 +Id : 95063, {_}: multiply (inverse (divide ?346094 ?346092)) (inverse ?346093) =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 94198 with 35052 at 2 +Id : 102213, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= multiply ?346092 (inverse (multiply ?346093 (inverse (inverse ?346094)))) [346093, 346092, 346094] by Demod 95063 with 101520 at 2 +Id : 102214, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =<= divide ?346092 (multiply ?346093 (inverse (inverse ?346094))) [346093, 346092, 346094] by Demod 102213 with 101520 at 3 +Id : 102215, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =?= divide ?346092 (divide ?346093 (inverse ?346094)) [346093, 346092, 346094] by Demod 102214 with 101520 at 2,3 +Id : 102222, {_}: divide (inverse (divide ?346094 ?346092)) ?346093 =>= divide ?346092 (multiply ?346093 ?346094) [346093, 346092, 346094] by Demod 102215 with 3 at 2,3 +Id : 102235, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide (inverse (divide (multiply ?8833 ?8832) ?8835)) ?8834) [8833, 8832, 8835, 8834] by Demod 101118 with 102222 at 2 +Id : 102236, {_}: divide ?8834 (multiply ?8835 (divide (inverse ?8832) ?8833)) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102235 with 102222 at 1,3 +Id : 35199, {_}: inverse (multiply (inverse (divide ?86042 ?86040)) (inverse ?86041)) =<= inverse (divide (inverse (divide (inverse (inverse ?86042)) ?86040)) ?86041) [86041, 86040, 86042] by Demod 16326 with 35052 at 1,2 +Id : 40695, {_}: inverse (multiply (inverse (divide (divide ?190115 ?190116) ?190117)) (inverse ?190118)) =>= inverse (divide (inverse (divide (multiply ?190115 (inverse ?190116)) ?190117)) ?190118) [190118, 190117, 190116, 190115] by Super 35199 with 40350 at 1,1,1,1,3 +Id : 46674, {_}: inverse (inverse (divide (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) ?207383)) =>= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Super 30884 with 40695 at 1,2 +Id : 47015, {_}: multiply (inverse (divide (multiply ?207380 (inverse ?207381)) ?207382)) (inverse ?207383) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207383, 207382, 207381, 207380] by Demod 46674 with 40350 at 2 +Id : 31439, {_}: multiply ?157170 (inverse (multiply ?157171 ?157172)) =<= divide ?157170 (multiply ?157171 (inverse (inverse ?157172))) [157172, 157171, 157170] by Super 3 with 30884 at 2,3 +Id : 31475, {_}: multiply ?157430 (inverse (multiply ?157431 (multiply ?157432 ?157433))) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Super 31439 with 30884 at 2,2,3 +Id : 45490, {_}: multiply (inverse (inverse ?203652)) (inverse (multiply ?203653 (multiply (inverse ?203654) ?203655))) =>= divide (inverse (divide (inverse (inverse ?203655)) ?203652)) (multiply ?203653 (inverse ?203654)) [203655, 203654, 203653, 203652] by Super 31475 with 45468 at 3 +Id : 71413, {_}: multiply (inverse (divide (multiply (inverse ?287029) ?287030) ?287031)) (inverse ?287032) =<= divide (inverse (divide (inverse (inverse ?287030)) ?287031)) (multiply ?287032 (inverse ?287029)) [287032, 287031, 287030, 287029] by Demod 45490 with 35052 at 2 +Id : 71414, {_}: multiply (inverse (divide (multiply (inverse (divide ?287034 (divide (divide ?287035 (divide (divide ?287036 ?287037) ?287034)) (divide ?287037 ?287036)))) ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287037, 287036, 287035, 287034] by Super 71413 with 53 at 2,2,3 +Id : 72001, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =<= divide (inverse (divide (inverse (inverse ?287038)) ?287039)) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 71414 with 53 at 1,1,1,1,2 +Id : 94096, {_}: multiply (inverse (divide (multiply ?287035 ?287038) ?287039)) (inverse ?287040) =>= divide (inverse (multiply ?287038 (inverse ?287039))) (multiply ?287040 ?287035) [287040, 287039, 287038, 287035] by Demod 72001 with 93432 at 1,1,3 +Id : 94118, {_}: divide (inverse (multiply (inverse ?207381) (inverse ?207382))) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 47015 with 94096 at 2 +Id : 102205, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= multiply (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse (inverse ?207383))) [207380, 207383, 207382, 207381] by Demod 94118 with 101520 at 1,1,2 +Id : 102206, {_}: divide (inverse (divide (inverse ?207381) ?207382)) (multiply ?207383 ?207380) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207380, 207383, 207382, 207381] by Demod 102205 with 101520 at 3 +Id : 102244, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide (inverse (divide (divide ?207380 ?207381) ?207382)) (inverse (inverse ?207383)) [207381, 207380, 207383, 207382] by Demod 102206 with 102222 at 2 +Id : 102245, {_}: divide ?207382 (multiply (multiply ?207383 ?207380) (inverse ?207381)) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102244 with 102222 at 3 +Id : 102246, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply (inverse (inverse ?207383)) (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102245 with 101520 at 2,2 +Id : 85182, {_}: divide (divide ?51938 (multiply (inverse (inverse ?51939)) ?51940)) ?51941 =>= divide (multiply ?51938 (inverse (multiply ?51939 ?51940))) ?51941 [51941, 51940, 51939, 51938] by Demod 43406 with 85061 at 3 +Id : 89950, {_}: divide (inverse ?335180) (multiply (divide ?335181 ?335182) (divide (divide ?335182 ?335181) (divide ?335180 (multiply (divide (divide ?335183 ?335184) ?335185) (divide ?335185 (divide (multiply ?335186 (inverse (multiply ?335187 ?335188))) (divide ?335184 ?335183))))))) =>= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186, 335185, 335184, 335183, 335182, 335181, 335180] by Super 89847 with 85182 at 2,2,2,2,2,2,2 +Id : 90760, {_}: multiply ?335186 (inverse (multiply ?335187 ?335188)) =<= divide ?335186 (multiply (inverse (inverse ?335187)) ?335188) [335188, 335187, 335186] by Demod 89950 with 40 at 2 +Id : 94126, {_}: multiply (inverse (inverse ?345644)) (inverse (multiply ?345645 ?345646)) =?= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345646, 345645, 345644] by Super 90760 with 93432 at 3 +Id : 95228, {_}: multiply (inverse (divide ?345646 ?345644)) (inverse ?345645) =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 94126 with 35052 at 2 +Id : 102219, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= multiply ?345644 (inverse (multiply (inverse (inverse ?345645)) ?345646)) [345645, 345644, 345646] by Demod 95228 with 101520 at 2 +Id : 102220, {_}: divide (inverse (divide ?345646 ?345644)) ?345645 =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345645, 345644, 345646] by Demod 102219 with 101520 at 3 +Id : 102238, {_}: divide ?345644 (multiply ?345645 ?345646) =<= divide ?345644 (multiply (inverse (inverse ?345645)) ?345646) [345646, 345645, 345644] by Demod 102220 with 102222 at 2 +Id : 102247, {_}: divide ?207382 (divide (multiply ?207383 ?207380) ?207381) =<= divide ?207382 (multiply ?207383 (divide ?207380 ?207381)) [207381, 207380, 207383, 207382] by Demod 102246 with 102238 at 3 +Id : 102262, {_}: divide ?8834 (divide (multiply ?8835 (inverse ?8832)) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102236 with 102247 at 2 +Id : 102264, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =<= inverse (divide ?8835 (multiply ?8834 (multiply ?8833 ?8832))) [8833, 8832, 8835, 8834] by Demod 102262 with 101520 at 1,2,2 +Id : 101098, {_}: inverse (divide (divide ?5 ?4) (divide ?3 (divide ?4 ?5))) =>= ?3 [3, 4, 5] by Demod 2 with 90396 at 2 +Id : 102493, {_}: divide (divide (inverse (divide (inverse ?357684) ?357685)) (multiply (divide ?357686 ?357687) ?357684)) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357687, 357686, 357685, 357684] by Super 2814 with 101520 at 1,1,1,2 +Id : 102761, {_}: divide (divide ?357685 (multiply (multiply (divide ?357686 ?357687) ?357684) (inverse ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102493 with 102222 at 1,2 +Id : 102131, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (multiply ?157432 (inverse (inverse ?157433)))) [157433, 157432, 157431, 157430] by Demod 31475 with 101520 at 2 +Id : 102132, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (multiply ?157431 (divide ?157432 (inverse ?157433))) [157433, 157432, 157431, 157430] by Demod 102131 with 101520 at 2,2,3 +Id : 102348, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =<= divide ?157430 (divide (multiply ?157431 ?157432) (inverse ?157433)) [157433, 157432, 157431, 157430] by Demod 102132 with 102247 at 3 +Id : 102349, {_}: divide ?157430 (multiply ?157431 (multiply ?157432 ?157433)) =?= divide ?157430 (multiply (multiply ?157431 ?157432) ?157433) [157433, 157432, 157431, 157430] by Demod 102348 with 3 at 2,3 +Id : 102762, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (multiply ?357684 (inverse ?357684)))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102761 with 102349 at 1,2 +Id : 102763, {_}: divide (divide ?357685 (multiply (divide ?357686 ?357687) (divide ?357684 ?357684))) (divide ?357687 ?357686) =>= inverse (inverse ?357685) [357684, 357687, 357686, 357685] by Demod 102762 with 101520 at 2,2,1,2 +Id : 41245, {_}: multiply ?191831 (inverse (multiply ?191832 (divide ?191833 ?191834))) =>= divide ?191831 (multiply ?191832 (multiply ?191833 (inverse ?191834))) [191834, 191833, 191832, 191831] by Super 30968 with 40350 at 2,2,3 +Id : 40574, {_}: multiply (divide ?83055 ?83056) (inverse ?83057) =?= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 15659 with 40350 at 2 +Id : 41328, {_}: multiply ?192465 (divide (inverse ?192466) (multiply ?192467 (divide ?192468 ?192469))) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Super 41245 with 40574 at 2 +Id : 85188, {_}: divide (multiply ?83055 (inverse ?83056)) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 40574 with 85061 at 2 +Id : 85202, {_}: divide (multiply ?192465 (inverse ?192466)) (multiply ?192467 (divide ?192468 ?192469)) =>= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192469, 192468, 192467, 192466, 192465] by Demod 41328 with 85188 at 2 +Id : 85220, {_}: divide (divide ?192465 (divide (divide ?192468 ?192469) (inverse ?192466))) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85202 with 62493 at 2 +Id : 85221, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =<= divide (divide ?192465 ?192466) (multiply ?192467 (multiply ?192468 (inverse ?192469))) [192467, 192466, 192469, 192468, 192465] by Demod 85220 with 3 at 2,1,2 +Id : 102178, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (multiply ?192467 (divide ?192468 ?192469)) [192467, 192466, 192469, 192468, 192465] by Demod 85221 with 101520 at 2,2,3 +Id : 102288, {_}: divide (divide ?192465 (multiply (divide ?192468 ?192469) ?192466)) ?192467 =?= divide (divide ?192465 ?192466) (divide (multiply ?192467 ?192468) ?192469) [192467, 192466, 192469, 192468, 192465] by Demod 102178 with 102247 at 3 +Id : 102764, {_}: divide (divide ?357685 (divide ?357684 ?357684)) (divide (multiply (divide ?357687 ?357686) ?357686) ?357687) =>= inverse (inverse ?357685) [357686, 357687, 357684, 357685] by Demod 102763 with 102288 at 2 +Id : 101094, {_}: divide (inverse (divide (divide ?5777 ?5778) ?5776)) (divide ?5778 ?5777) =>= ?5776 [5776, 5778, 5777] by Demod 1266 with 90396 at 1,2 +Id : 102237, {_}: divide ?5776 (multiply (divide ?5778 ?5777) (divide ?5777 ?5778)) =>= ?5776 [5777, 5778, 5776] by Demod 101094 with 102222 at 2 +Id : 102251, {_}: divide ?5776 (divide (multiply (divide ?5778 ?5777) ?5777) ?5778) =>= ?5776 [5777, 5778, 5776] by Demod 102237 with 102247 at 2 +Id : 102765, {_}: divide ?357685 (divide ?357684 ?357684) =>= inverse (inverse ?357685) [357684, 357685] by Demod 102764 with 102251 at 2 +Id : 102313, {_}: inverse ?36880 =<= multiply (divide (multiply (multiply ?36881 ?36882) (divide (inverse ?36882) ?36881)) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 7367 with 102309 at 1,3 +Id : 102314, {_}: inverse ?36880 =<= multiply (divide (divide (multiply (multiply ?36881 ?36882) (inverse ?36882)) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102313 with 102309 at 1,1,3 +Id : 102315, {_}: inverse ?36880 =<= multiply (divide (divide (divide (multiply ?36881 ?36882) ?36882) ?36881) (multiply ?36883 ?36880)) ?36883 [36883, 36882, 36881, 36880] by Demod 102314 with 101520 at 1,1,1,3 +Id : 102533, {_}: inverse (inverse ?357905) =<= multiply (divide (divide (divide (multiply ?357906 ?357907) ?357907) ?357906) (divide ?357908 ?357905)) ?357908 [357908, 357907, 357906, 357905] by Super 102315 with 101520 at 2,1,3 +Id : 102311, {_}: ?36095 =<= multiply (divide (multiply (multiply ?36096 ?36097) (divide (inverse ?36097) ?36096)) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 7191 with 102309 at 1,3 +Id : 102312, {_}: ?36095 =<= multiply (divide (divide (multiply (multiply ?36096 ?36097) (inverse ?36097)) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102311 with 102309 at 1,1,3 +Id : 102316, {_}: ?36095 =<= multiply (divide (divide (divide (multiply ?36096 ?36097) ?36097) ?36096) (divide ?36098 ?36095)) ?36098 [36098, 36097, 36096, 36095] by Demod 102312 with 101520 at 1,1,1,3 +Id : 102664, {_}: inverse (inverse ?357905) =>= ?357905 [357905] by Demod 102533 with 102316 at 3 +Id : 103069, {_}: divide ?357685 (divide ?357684 ?357684) =>= ?357685 [357684, 357685] by Demod 102765 with 102664 at 3 +Id : 103199, {_}: inverse (divide ?359423 ?359424) =>= divide ?359424 ?359423 [359424, 359423] by Super 101098 with 103069 at 1,2 +Id : 103718, {_}: divide ?8834 (divide (divide ?8835 ?8832) ?8833) =?= divide (multiply ?8834 (multiply ?8833 ?8832)) ?8835 [8833, 8832, 8835, 8834] by Demod 102264 with 103199 at 3 +Id : 103734, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (inverse ?13894)) (multiply ?13895 ?13894) =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 2791 with 103718 at 1,2 +Id : 40697, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (multiply ?190126 (inverse ?190127)) (inverse (multiply ?190128 ?190125)) [190128, 190127, 190126, 190125] by Super 35052 with 40350 at 1,3 +Id : 40823, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (divide ?190126 (multiply (inverse (inverse ?190125)) ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 40697 with 9976 at 3 +Id : 43409, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= multiply (divide ?190126 (multiply ?190125 ?190127)) (inverse ?190128) [190128, 190127, 190126, 190125] by Demod 40823 with 43406 at 3 +Id : 85192, {_}: multiply (inverse (divide ?190125 (divide ?190126 ?190127))) (inverse ?190128) =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 43409 with 85061 at 3 +Id : 102170, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (multiply ?190126 (inverse (multiply ?190125 ?190127))) ?190128 [190128, 190127, 190126, 190125] by Demod 85192 with 101520 at 2 +Id : 102171, {_}: divide (inverse (divide ?190125 (divide ?190126 ?190127))) ?190128 =>= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190128, 190127, 190126, 190125] by Demod 102170 with 101520 at 1,3 +Id : 102293, {_}: divide (divide ?190126 ?190127) (multiply ?190128 ?190125) =?= divide (divide ?190126 (multiply ?190125 ?190127)) ?190128 [190125, 190128, 190127, 190126] by Demod 102171 with 102222 at 2 +Id : 103736, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) (multiply ?13892 ?13895)) (multiply ?13894 (inverse ?13894))) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103734 with 102293 at 2 +Id : 103737, {_}: divide (divide (divide (inverse (multiply ?13892 ?13893)) (divide (inverse ?13894) (multiply ?13892 ?13895))) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103736 with 62493 at 1,2 +Id : 40061, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (multiply ?188029 (inverse ?188030))) [188032, 188031, 188030, 188029, 188028] by Super 40043 with 39950 at 2,3 +Id : 102158, {_}: divide (divide ?188028 (divide (inverse (divide ?188029 ?188030)) ?188031)) ?188032 =>= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188031, 188030, 188029, 188028] by Demod 40061 with 101520 at 2,2,3 +Id : 102302, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =<= divide (multiply ?188028 ?188031) (divide ?188032 (divide ?188029 ?188030)) [188032, 188029, 188031, 188030, 188028] by Demod 102158 with 102222 at 2,1,2 +Id : 103711, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =<= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30] by Demod 101099 with 103199 at 2 +Id : 103712, {_}: divide ?30 (divide ?31 (divide ?32 ?33)) =?= divide (divide ?30 (divide ?33 ?32)) ?31 [33, 32, 31, 30] by Demod 103711 with 103199 at 3 +Id : 103741, {_}: divide (divide ?188028 (divide ?188030 (multiply ?188031 ?188029))) ?188032 =?= divide (divide (multiply ?188028 ?188031) (divide ?188030 ?188029)) ?188032 [188032, 188029, 188031, 188030, 188028] by Demod 102302 with 103712 at 3 +Id : 103744, {_}: divide (divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide (inverse ?13894) ?13895)) ?13894) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103737 with 103741 at 1,2 +Id : 103708, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= inverse (divide ?114204 (divide ?114206 (divide (inverse ?114205) ?114207))) [114205, 114207, 114204, 114206] by Demod 62637 with 103199 at 2 +Id : 103709, {_}: divide ?114206 (divide ?114204 (multiply ?114207 ?114205)) =<= divide (divide ?114206 (divide (inverse ?114205) ?114207)) ?114204 [114205, 114207, 114204, 114206] by Demod 103708 with 103199 at 3 +Id : 103749, {_}: divide (divide (multiply (inverse (multiply ?13892 ?13893)) ?13892) (divide ?13894 (multiply ?13895 ?13894))) ?13895 =>= inverse ?13893 [13895, 13894, 13893, 13892] by Demod 103744 with 103709 at 1,2 +Id : 103750, {_}: divide (divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) (divide ?13894 ?13894)) ?13895 =>= inverse ?13893 [13894, 13895, 13893, 13892] by Demod 103749 with 103741 at 2 +Id : 103751, {_}: divide (multiply (multiply (inverse (multiply ?13892 ?13893)) ?13892) ?13895) ?13895 =>= inverse ?13893 [13895, 13893, 13892] by Demod 103750 with 103069 at 1,2 +Id : 2811, {_}: divide (divide (inverse (multiply ?14050 ?14051)) (divide (multiply ?14052 ?14053) ?14050)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Super 2771 with 3 at 1,2,1,2 +Id : 103699, {_}: divide (divide ?346092 ?346094) ?346093 =?= divide ?346092 (multiply ?346093 ?346094) [346093, 346094, 346092] by Demod 102222 with 103199 at 1,2 +Id : 103754, {_}: divide (divide ?258249 (divide ?258253 ?258254)) ?258255 =?= divide (divide (multiply ?258249 ?258254) ?258253) ?258255 [258255, 258254, 258253, 258249] by Demod 62493 with 103699 at 3 +Id : 103756, {_}: divide (divide (multiply (inverse (multiply ?14050 ?14051)) ?14050) (multiply ?14052 ?14053)) (divide (inverse ?14053) ?14052) =>= inverse ?14051 [14053, 14052, 14051, 14050] by Demod 2811 with 103754 at 2 +Id : 103714, {_}: divide (divide ?54 (multiply ?55 ?56)) (divide (inverse ?56) ?55) =>= ?54 [56, 55, 54] by Demod 101095 with 103199 at 2 +Id : 103765, {_}: multiply (inverse (multiply ?14050 ?14051)) ?14050 =>= inverse ?14051 [14051, 14050] by Demod 103756 with 103714 at 2 +Id : 103766, {_}: divide (multiply (inverse ?13893) ?13895) ?13895 =>= inverse ?13893 [13895, 13893] by Demod 103751 with 103765 at 1,1,2 +Id : 103767, {_}: ?38552 =<= multiply (divide (multiply (inverse ?38553) ?38553) (divide ?38555 ?38552)) ?38555 [38555, 38553, 38552] by Demod 102318 with 103766 at 1,1,1,3 +Id : 103801, {_}: multiply ?360754 (divide ?360755 ?360756) =>= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Super 3 with 103199 at 2,3 +Id : 102172, {_}: divide (divide ?83055 ?83056) ?83057 =<= multiply ?83055 (divide (inverse ?83056) ?83057) [83057, 83056, 83055] by Demod 85188 with 101520 at 1,2 +Id : 102958, {_}: divide (divide ?358448 (inverse ?358449)) ?358450 =>= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Super 102172 with 102664 at 1,2,3 +Id : 103012, {_}: divide (multiply ?358448 ?358449) ?358450 =<= multiply ?358448 (divide ?358449 ?358450) [358450, 358449, 358448] by Demod 102958 with 3 at 1,2 +Id : 104738, {_}: divide (multiply ?360754 ?360755) ?360756 =?= divide ?360754 (divide ?360756 ?360755) [360756, 360755, 360754] by Demod 103801 with 103012 at 2 +Id : 104742, {_}: ?38552 =<= multiply (divide (multiply (multiply (inverse ?38553) ?38553) ?38552) ?38555) ?38555 [38555, 38553, 38552] by Demod 103767 with 104738 at 1,3 +Id : 102256, {_}: divide (inverse ?35) (divide (multiply (divide ?36 ?37) (divide ?37 ?36)) (divide ?35 (divide ?38 ?39))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 362 with 102247 at 2 +Id : 102304, {_}: divide (inverse ?35) (divide (divide (divide ?36 ?37) (divide ?39 (multiply (divide ?37 ?36) ?38))) ?35) =>= divide ?39 ?38 [38, 39, 37, 36, 35] by Demod 102256 with 102302 at 2,2 +Id : 103730, {_}: divide (multiply (inverse ?35) (multiply ?35 (divide ?39 (multiply (divide ?37 ?36) ?38)))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 102304 with 103718 at 2 +Id : 104003, {_}: divide (multiply (inverse ?35) (divide (multiply ?35 ?39) (multiply (divide ?37 ?36) ?38))) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 103730 with 103012 at 2,1,2 +Id : 104004, {_}: divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) (multiply (divide ?37 ?36) ?38)) (divide ?36 ?37) =>= divide ?39 ?38 [38, 36, 37, 39, 35] by Demod 104003 with 103012 at 1,2 +Id : 104036, {_}: divide (divide (divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38) (divide ?37 ?36)) (divide ?36 ?37) =>= divide ?39 ?38 [36, 37, 38, 39, 35] by Demod 104004 with 103699 at 1,2 +Id : 103700, {_}: divide (divide ?3 (divide ?4 ?5)) (divide ?5 ?4) =>= ?3 [5, 4, 3] by Demod 101098 with 103199 at 2 +Id : 104037, {_}: divide (multiply (inverse ?35) (multiply ?35 ?39)) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104036 with 103700 at 2 +Id : 21134, {_}: inverse (multiply (inverse (inverse ?108447)) (inverse (divide ?108448 ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 20903 with 6973 at 2,1,3 +Id : 40046, {_}: inverse (divide (inverse (inverse ?108447)) (multiply ?108448 (inverse ?108449))) =>= inverse (divide (inverse (divide (inverse ?108449) ?108447)) ?108448) [108449, 108448, 108447] by Demod 21134 with 39950 at 1,2 +Id : 40707, {_}: inverse (divide (multiply ?190184 (inverse ?190185)) (multiply ?190186 (inverse ?190187))) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190187, 190186, 190185, 190184] by Super 40046 with 40350 at 1,1,2 +Id : 40813, {_}: inverse (divide (divide ?190184 (divide (inverse ?190187) (inverse ?190185))) ?190186) =<= inverse (divide (inverse (divide (inverse ?190187) (divide ?190184 ?190185))) ?190186) [190186, 190185, 190187, 190184] by Demod 40707 with 40043 at 1,2 +Id : 47405, {_}: inverse (divide (divide ?210380 (multiply (inverse ?210381) ?210382)) ?210383) =<= inverse (divide (inverse (divide (inverse ?210381) (divide ?210380 ?210382))) ?210383) [210383, 210382, 210381, 210380] by Demod 40813 with 3 at 2,1,1,2 +Id : 47459, {_}: inverse (divide (divide ?210809 (multiply (inverse (divide ?210810 (divide (divide ?210811 (divide (divide ?210812 ?210813) ?210810)) (divide ?210813 ?210812)))) ?210814)) ?210815) =>= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210813, 210812, 210811, 210810, 210809] by Super 47405 with 53 at 1,1,1,1,3 +Id : 48148, {_}: inverse (divide (divide ?212886 (multiply ?212887 ?212888)) ?212889) =<= inverse (divide (inverse (divide ?212887 (divide ?212886 ?212888))) ?212889) [212889, 212888, 212887, 212886] by Demod 47459 with 53 at 1,2,1,1,2 +Id : 48271, {_}: inverse (divide (divide ?213823 (multiply ?213824 ?213825)) (inverse ?213826)) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Super 48148 with 3 at 1,3 +Id : 48613, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =<= inverse (multiply (inverse (divide ?213824 (divide ?213823 ?213825))) ?213826) [213826, 213825, 213824, 213823] by Demod 48271 with 3 at 1,2 +Id : 103705, {_}: inverse (multiply (divide ?213823 (multiply ?213824 ?213825)) ?213826) =?= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213826, 213825, 213824, 213823] by Demod 48613 with 103199 at 1,1,3 +Id : 106200, {_}: divide (multiply ?367270 ?367271) ?367271 =>= ?367270 [367271, 367270] by Super 103069 with 104738 at 2 +Id : 106204, {_}: divide (inverse ?367290) ?367291 =<= inverse (multiply ?367291 ?367290) [367291, 367290] by Super 106200 with 103765 at 1,2 +Id : 106549, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =<= inverse (multiply (divide (divide ?213823 ?213825) ?213824) ?213826) [213825, 213824, 213823, 213826] by Demod 103705 with 106204 at 2 +Id : 106550, {_}: divide (inverse ?213826) (divide ?213823 (multiply ?213824 ?213825)) =?= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213824, 213823, 213826] by Demod 106549 with 106204 at 3 +Id : 47859, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =<= inverse (divide (inverse (divide ?210811 (divide ?210809 ?210814))) ?210815) [210815, 210814, 210811, 210809] by Demod 47459 with 53 at 1,2,1,1,2 +Id : 102230, {_}: inverse (divide (divide ?210809 (multiply ?210811 ?210814)) ?210815) =?= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210815, 210814, 210811, 210809] by Demod 47859 with 102222 at 1,3 +Id : 103696, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =<= inverse (divide (divide ?210809 ?210814) (multiply ?210815 ?210811)) [210814, 210811, 210809, 210815] by Demod 102230 with 103199 at 2 +Id : 103697, {_}: divide ?210815 (divide ?210809 (multiply ?210811 ?210814)) =?= divide (multiply ?210815 ?210811) (divide ?210809 ?210814) [210814, 210811, 210809, 210815] by Demod 103696 with 103199 at 3 +Id : 106566, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =<= divide (inverse ?213826) (divide (divide ?213823 ?213825) ?213824) [213825, 213823, 213824, 213826] by Demod 106550 with 103697 at 2 +Id : 106567, {_}: divide (multiply (inverse ?213826) ?213824) (divide ?213823 ?213825) =?= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213825, 213823, 213824, 213826] by Demod 106566 with 103718 at 3 +Id : 106568, {_}: divide (multiply (multiply (inverse ?213826) ?213824) ?213825) ?213823 =<= divide (multiply (inverse ?213826) (multiply ?213824 ?213825)) ?213823 [213823, 213825, 213824, 213826] by Demod 106567 with 104738 at 2 +Id : 106569, {_}: divide (multiply (multiply (inverse ?35) ?35) ?39) ?38 =>= divide ?39 ?38 [38, 39, 35] by Demod 104037 with 106568 at 2 +Id : 106570, {_}: ?38552 =<= multiply (divide ?38552 ?38555) ?38555 [38555, 38552] by Demod 104742 with 106569 at 1,3 +Id : 104876, {_}: divide (multiply ?363468 ?363469) ?363469 =>= ?363468 [363469, 363468] by Super 103069 with 104738 at 2 +Id : 106173, {_}: inverse ?367130 =<= divide ?367131 (multiply ?367130 ?367131) [367131, 367130] by Super 103199 with 104876 at 1,2 +Id : 106805, {_}: ?367778 =<= multiply (inverse ?367779) (multiply ?367779 ?367778) [367779, 367778] by Super 106570 with 106173 at 1,3 +Id : 106633, {_}: multiply ?367594 (multiply ?367595 ?367596) =<= divide ?367594 (divide (inverse ?367596) ?367595) [367596, 367595, 367594] by Super 3 with 106204 at 2,3 +Id : 104940, {_}: multiply (multiply ?363900 ?363901) ?363902 =<= divide ?363900 (divide (inverse ?363902) ?363901) [363902, 363901, 363900] by Super 3 with 104738 at 3 +Id : 108764, {_}: multiply ?367594 (multiply ?367595 ?367596) =?= multiply (multiply ?367594 ?367595) ?367596 [367596, 367595, 367594] by Demod 106633 with 104940 at 3 +Id : 109130, {_}: ?367778 =<= multiply (multiply (inverse ?367779) ?367779) ?367778 [367779, 367778] by Demod 106805 with 108764 at 3 +Id : 109444, {_}: a2 === a2 [] by Demod 1 with 109130 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP470-1.p +11271: solved GRP470-1.p in 32.33802 using nrkbo +11271: status Unsatisfiable for GRP470-1.p +NO CLASH, using fixed ground order +11326: Facts: +11326: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11326: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11326: Goal: +11326: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11326: Order: +11326: nrkbo +11326: Leaf order: +11326: inverse 2 1 0 +11326: divide 7 2 0 +11326: c3 2 0 2 2,2 +11326: multiply 5 2 4 0,2 +11326: b3 2 0 2 2,1,2 +11326: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11327: Facts: +11327: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11327: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11327: Goal: +11327: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11327: Order: +11327: kbo +11327: Leaf order: +11327: inverse 2 1 0 +11327: divide 7 2 0 +11327: c3 2 0 2 2,2 +11327: multiply 5 2 4 0,2 +11327: b3 2 0 2 2,1,2 +11327: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11328: Facts: +11328: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11328: Id : 3, {_}: + multiply ?7 ?8 =>= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11328: Goal: +11328: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11328: Order: +11328: lpo +11328: Leaf order: +11328: inverse 2 1 0 +11328: divide 7 2 0 +11328: c3 2 0 2 2,2 +11328: multiply 5 2 4 0,2 +11328: b3 2 0 2 2,1,2 +11328: a3 2 0 2 1,1,2 +Statistics : +Max weight : 52 +Found proof, 38.615883s +% SZS status Unsatisfiable for GRP471-1.p +% SZS output start CNFRefutation for GRP471-1.p +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 2, {_}: divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) (divide (divide ?5 ?4) ?2) =>= ?3 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide ?10 (divide ?11 (divide ?12 ?13)))) (divide (divide ?13 ?12) ?10) =>= ?11 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 8, {_}: divide (inverse ?35) (divide (divide ?36 ?37) (inverse (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39))))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Super 4 with 2 at 1,1,2 +Id : 377, {_}: divide (inverse ?1785) (multiply (divide ?1786 ?1787) (divide (divide ?1787 ?1786) (divide ?1785 (divide ?1788 ?1789)))) =>= divide ?1789 ?1788 [1789, 1788, 1787, 1786, 1785] by Demod 8 with 3 at 2,2 +Id : 362, {_}: divide (inverse ?35) (multiply (divide ?36 ?37) (divide (divide ?37 ?36) (divide ?35 (divide ?38 ?39)))) =>= divide ?39 ?38 [39, 38, 37, 36, 35] by Demod 8 with 3 at 2,2 +Id : 385, {_}: divide (inverse ?1855) (multiply (divide ?1856 ?1857) (divide (divide ?1857 ?1856) (divide ?1855 (divide ?1858 ?1859)))) =?= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1859, 1858, 1857, 1856, 1855] by Super 377 with 362 at 2,2,2,2,2 +Id : 436, {_}: divide ?1859 ?1858 =<= divide (multiply (divide ?1860 ?1861) (divide (divide ?1861 ?1860) (divide ?1862 (divide ?1859 ?1858)))) (inverse ?1862) [1862, 1861, 1860, 1858, 1859] by Demod 385 with 362 at 2 +Id : 6830, {_}: divide ?34177 ?34178 =<= multiply (multiply (divide ?34179 ?34180) (divide (divide ?34180 ?34179) (divide ?34181 (divide ?34177 ?34178)))) ?34181 [34181, 34180, 34179, 34178, 34177] by Demod 436 with 3 at 3 +Id : 5, {_}: divide (inverse (divide ?15 (divide ?16 (divide (divide (divide ?17 ?18) ?19) (inverse (divide ?19 (divide ?20 (divide ?18 ?17)))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 1,2,2 +Id : 15, {_}: divide (inverse (divide ?15 (divide ?16 (multiply (divide (divide ?17 ?18) ?19) (divide ?19 (divide ?20 (divide ?18 ?17))))))) (divide ?20 ?15) =>= ?16 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 2,2,1,1,2 +Id : 18, {_}: divide (inverse (divide ?82 ?83)) (divide (divide ?84 ?85) ?82) =?= inverse (divide ?84 (divide ?83 (multiply (divide (divide ?86 ?87) ?88) (divide ?88 (divide ?85 (divide ?87 ?86)))))) [88, 87, 86, 85, 84, 83, 82] by Super 2 with 15 at 2,1,1,2 +Id : 1723, {_}: divide (divide (inverse (divide ?8026 ?8027)) (divide (divide ?8028 ?8029) ?8026)) (divide ?8029 ?8028) =>= ?8027 [8029, 8028, 8027, 8026] by Super 15 with 18 at 1,2 +Id : 1779, {_}: divide (divide (inverse (multiply ?8457 ?8458)) (divide (divide ?8459 ?8460) ?8457)) (divide ?8460 ?8459) =>= inverse ?8458 [8460, 8459, 8458, 8457] by Super 1723 with 3 at 1,1,1,2 +Id : 6854, {_}: divide (divide (inverse (multiply ?34395 ?34396)) (divide (divide ?34397 ?34398) ?34395)) (divide ?34398 ?34397) =?= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34398, 34397, 34396, 34395] by Super 6830 with 1779 at 2,2,2,1,3 +Id : 7005, {_}: inverse ?34396 =<= multiply (multiply (divide ?34399 ?34400) (divide (divide ?34400 ?34399) (divide ?34401 (inverse ?34396)))) ?34401 [34401, 34400, 34399, 34396] by Demod 6854 with 1779 at 2 +Id : 7303, {_}: inverse ?36376 =<= multiply (multiply (divide ?36377 ?36378) (divide (divide ?36378 ?36377) (multiply ?36379 ?36376))) ?36379 [36379, 36378, 36377, 36376] by Demod 7005 with 3 at 2,2,1,3 +Id : 7337, {_}: inverse ?36648 =<= multiply (multiply (divide (inverse ?36649) ?36650) (divide (multiply ?36650 ?36649) (multiply ?36651 ?36648))) ?36651 [36651, 36650, 36649, 36648] by Super 7303 with 3 at 1,2,1,3 +Id : 6831, {_}: divide (inverse (divide ?34183 (divide ?34184 (divide ?34185 ?34186)))) (divide (divide ?34186 ?34185) ?34183) =?= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34186, 34185, 34184, 34183] by Super 6830 with 2 at 2,2,2,1,3 +Id : 7101, {_}: ?35399 =<= multiply (multiply (divide ?35400 ?35401) (divide (divide ?35401 ?35400) (divide ?35402 ?35399))) ?35402 [35402, 35401, 35400, 35399] by Demod 6831 with 2 at 2 +Id : 2771, {_}: divide (divide (inverse (multiply ?13734 ?13735)) (divide (divide ?13736 ?13737) ?13734)) (divide ?13737 ?13736) =>= inverse ?13735 [13737, 13736, 13735, 13734] by Super 1723 with 3 at 1,1,1,2 +Id : 2814, {_}: divide (divide (inverse (multiply (inverse ?14067) ?14068)) (multiply (divide ?14069 ?14070) ?14067)) (divide ?14070 ?14069) =>= inverse ?14068 [14070, 14069, 14068, 14067] by Super 2771 with 3 at 2,1,2 +Id : 7163, {_}: ?35873 =<= multiply (multiply (divide (multiply (divide ?35873 ?35874) ?35875) (inverse (multiply (inverse ?35875) ?35876))) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Super 7101 with 2814 at 2,1,3 +Id : 7239, {_}: ?35873 =<= multiply (multiply (multiply (multiply (divide ?35873 ?35874) ?35875) (multiply (inverse ?35875) ?35876)) (inverse ?35876)) ?35874 [35876, 35875, 35874, 35873] by Demod 7163 with 3 at 1,1,3 +Id : 1759, {_}: divide (divide (inverse (divide ?8306 ?8307)) (divide (multiply ?8308 ?8309) ?8306)) (divide (inverse ?8309) ?8308) =>= ?8307 [8309, 8308, 8307, 8306] by Super 1723 with 3 at 1,2,1,2 +Id : 7159, {_}: ?35853 =<= multiply (multiply (divide (divide (multiply ?35853 ?35854) ?35855) (inverse (divide ?35855 ?35856))) ?35856) (inverse ?35854) [35856, 35855, 35854, 35853] by Super 7101 with 1759 at 2,1,3 +Id : 7892, {_}: ?39681 =<= multiply (multiply (multiply (divide (multiply ?39681 ?39682) ?39683) (divide ?39683 ?39684)) ?39684) (inverse ?39682) [39684, 39683, 39682, 39681] by Demod 7159 with 3 at 1,1,3 +Id : 9472, {_}: ?48735 =<= multiply (multiply (multiply (multiply (multiply ?48735 ?48736) ?48737) (divide (inverse ?48737) ?48738)) ?48738) (inverse ?48736) [48738, 48737, 48736, 48735] by Super 7892 with 3 at 1,1,1,3 +Id : 1266, {_}: divide (divide (inverse (divide ?5775 ?5776)) (divide (divide ?5777 ?5778) ?5775)) (divide ?5778 ?5777) =>= ?5776 [5778, 5777, 5776, 5775] by Super 15 with 18 at 1,2 +Id : 7158, {_}: ?35848 =<= multiply (multiply (divide (divide (divide ?35848 ?35849) ?35850) (inverse (divide ?35850 ?35851))) ?35851) ?35849 [35851, 35850, 35849, 35848] by Super 7101 with 1266 at 2,1,3 +Id : 7234, {_}: ?35848 =<= multiply (multiply (multiply (divide (divide ?35848 ?35849) ?35850) (divide ?35850 ?35851)) ?35851) ?35849 [35851, 35850, 35849, 35848] by Demod 7158 with 3 at 1,1,3 +Id : 9552, {_}: divide (divide ?49359 (divide (inverse ?49360) ?49361)) ?49362 =<= multiply (multiply ?49359 ?49361) (inverse (divide ?49362 ?49360)) [49362, 49361, 49360, 49359] by Super 9472 with 7234 at 1,1,3 +Id : 9555, {_}: multiply (divide ?49374 (divide (inverse (inverse ?49375)) ?49376)) ?49377 =<= multiply (multiply ?49374 ?49376) (inverse (multiply (inverse ?49377) ?49375)) [49377, 49376, 49375, 49374] by Super 9472 with 7239 at 1,1,3 +Id : 10048, {_}: divide (divide (multiply ?52036 ?52037) (divide (inverse ?52038) (inverse (multiply (inverse ?52039) ?52040)))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Super 9552 with 9555 at 1,3 +Id : 10181, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= multiply (multiply (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) ?52039) (inverse (divide ?52041 ?52038)) [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10048 with 3 at 2,1,2 +Id : 10182, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (divide (divide ?52036 (divide (inverse (inverse ?52040)) ?52037)) (divide (inverse ?52038) ?52039)) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10181 with 9552 at 3 +Id : 7161, {_}: ?35863 =<= multiply (multiply (divide (divide (divide ?35863 ?35864) ?35865) (inverse (multiply ?35865 ?35866))) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Super 7101 with 1779 at 2,1,3 +Id : 7237, {_}: ?35863 =<= multiply (multiply (multiply (divide (divide ?35863 ?35864) ?35865) (multiply ?35865 ?35866)) (inverse ?35866)) ?35864 [35866, 35865, 35864, 35863] by Demod 7161 with 3 at 1,1,3 +Id : 9554, {_}: divide (divide ?49369 (divide (inverse (inverse ?49370)) ?49371)) ?49372 =>= multiply (multiply ?49369 ?49371) (inverse (multiply ?49372 ?49370)) [49372, 49371, 49370, 49369] by Super 9472 with 7237 at 1,1,3 +Id : 10183, {_}: divide (divide (multiply ?52036 ?52037) (multiply (inverse ?52038) (multiply (inverse ?52039) ?52040))) ?52041 =<= divide (multiply (multiply ?52036 ?52037) (inverse (multiply (divide (inverse ?52038) ?52039) ?52040))) ?52041 [52041, 52040, 52039, 52038, 52037, 52036] by Demod 10182 with 9554 at 1,3 +Id : 12174, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =<= multiply (multiply (multiply (multiply (divide (divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033))) ?64034) ?64035) (multiply (inverse ?64035) ?64036)) (inverse ?64036)) ?64034 [64036, 64035, 64034, 64033, 64032, 64031, 64030, 64029] by Super 7239 with 10183 at 1,1,1,1,3 +Id : 12258, {_}: multiply (multiply ?64029 ?64030) (inverse (multiply (divide (inverse ?64031) ?64032) ?64033)) =>= divide (multiply ?64029 ?64030) (multiply (inverse ?64031) (multiply (inverse ?64032) ?64033)) [64033, 64032, 64031, 64030, 64029] by Demod 12174 with 7239 at 3 +Id : 12491, {_}: inverse (inverse (multiply (divide (inverse ?65291) ?65292) ?65293)) =<= multiply (multiply (divide (inverse ?65294) ?65295) (divide (multiply ?65295 ?65294) (divide (multiply ?65296 ?65297) (multiply (inverse ?65291) (multiply (inverse ?65292) ?65293))))) (multiply ?65296 ?65297) [65297, 65296, 65295, 65294, 65293, 65292, 65291] by Super 7337 with 12258 at 2,2,1,3 +Id : 7157, {_}: ?35843 =<= multiply (multiply (divide (inverse ?35844) ?35845) (divide (multiply ?35845 ?35844) (divide ?35846 ?35843))) ?35846 [35846, 35845, 35844, 35843] by Super 7101 with 3 at 1,2,1,3 +Id : 12726, {_}: inverse (inverse (multiply (divide (inverse ?66353) ?66354) ?66355)) =>= multiply (inverse ?66353) (multiply (inverse ?66354) ?66355) [66355, 66354, 66353] by Demod 12491 with 7157 at 3 +Id : 7, {_}: divide (inverse (divide ?29 ?30)) (divide (divide ?31 (divide ?32 ?33)) ?29) =>= inverse (divide ?31 (divide ?30 (divide ?33 ?32))) [33, 32, 31, 30, 29] by Super 4 with 2 at 2,1,1,2 +Id : 53, {_}: inverse (divide ?279 (divide (divide ?280 (divide (divide ?281 ?282) ?279)) (divide ?282 ?281))) =>= ?280 [282, 281, 280, 279] by Super 2 with 7 at 2 +Id : 12727, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =<= multiply (inverse (divide ?66360 (divide (divide ?66357 (divide (divide ?66361 ?66362) ?66360)) (divide ?66362 ?66361)))) (multiply (inverse ?66358) ?66359) [66362, 66361, 66360, 66359, 66358, 66357] by Super 12726 with 53 at 1,1,1,1,2 +Id : 12825, {_}: inverse (inverse (multiply (divide ?66943 ?66944) ?66945)) =>= multiply ?66943 (multiply (inverse ?66944) ?66945) [66945, 66944, 66943] by Demod 12727 with 53 at 1,3 +Id : 12858, {_}: inverse (inverse (multiply (multiply ?67174 ?67175) ?67176)) =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Super 12825 with 3 at 1,1,1,2 +Id : 12, {_}: divide (inverse (divide ?53 (divide ?54 (multiply ?55 ?56)))) (divide (divide (inverse ?56) ?55) ?53) =>= ?54 [56, 55, 54, 53] by Super 2 with 3 at 2,2,1,1,2 +Id : 17, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (divide (divide ?76 ?77) (inverse (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78)))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Super 2 with 15 at 2,2,1,1,2 +Id : 66361, {_}: divide (inverse (divide ?259836 (divide ?259837 ?259838))) (divide (multiply (divide ?259839 ?259840) (divide ?259840 (divide ?259838 (multiply (divide (divide ?259841 ?259842) ?259843) (divide ?259843 (divide ?259839 (divide ?259842 ?259841))))))) ?259836) =>= ?259837 [259843, 259842, 259841, 259840, 259839, 259838, 259837, 259836] by Demod 17 with 3 at 1,2,2 +Id : 12770, {_}: inverse (inverse (multiply (divide ?66357 ?66358) ?66359)) =>= multiply ?66357 (multiply (inverse ?66358) ?66359) [66359, 66358, 66357] by Demod 12727 with 53 at 1,3 +Id : 12807, {_}: multiply ?66813 (inverse (multiply (divide ?66814 ?66815) ?66816)) =>= divide ?66813 (multiply ?66814 (multiply (inverse ?66815) ?66816)) [66816, 66815, 66814, 66813] by Super 3 with 12770 at 2,3 +Id : 13153, {_}: inverse (inverse (multiply (multiply ?68629 ?68630) (inverse (multiply (divide ?68631 ?68632) ?68633)))) =<= multiply ?68629 (divide (inverse (inverse ?68630)) (multiply ?68631 (multiply (inverse ?68632) ?68633))) [68633, 68632, 68631, 68630, 68629] by Super 12858 with 12807 at 2,3 +Id : 15503, {_}: inverse (inverse (divide (multiply ?81665 ?81666) (multiply ?81667 (multiply (inverse ?81668) ?81669)))) =<= multiply ?81665 (divide (inverse (inverse ?81666)) (multiply ?81667 (multiply (inverse ?81668) ?81669))) [81669, 81668, 81667, 81666, 81665] by Demod 13153 with 12807 at 1,1,2 +Id : 6973, {_}: ?34184 =<= multiply (multiply (divide ?34187 ?34188) (divide (divide ?34188 ?34187) (divide ?34189 ?34184))) ?34189 [34189, 34188, 34187, 34184] by Demod 6831 with 2 at 2 +Id : 15524, {_}: inverse (inverse (divide (multiply ?81857 ?81858) (multiply (multiply (divide ?81859 ?81860) (divide (divide ?81860 ?81859) (divide (multiply (inverse ?81861) ?81862) ?81863))) (multiply (inverse ?81861) ?81862)))) =>= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81862, 81861, 81860, 81859, 81858, 81857] by Super 15503 with 6973 at 2,2,3 +Id : 15656, {_}: inverse (inverse (divide (multiply ?81857 ?81858) ?81863)) =<= multiply ?81857 (divide (inverse (inverse ?81858)) ?81863) [81863, 81858, 81857] by Demod 15524 with 6973 at 2,1,1,2 +Id : 23797, {_}: divide (divide ?119374 (divide (inverse ?119375) (divide (inverse (inverse ?119376)) ?119377))) ?119378 =<= multiply (inverse (inverse (divide (multiply ?119374 ?119376) ?119377))) (inverse (divide ?119378 ?119375)) [119378, 119377, 119376, 119375, 119374] by Super 9552 with 15656 at 1,3 +Id : 23859, {_}: divide (divide (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) (divide (inverse ?119934) (divide (inverse (inverse ?119932)) ?119935))) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Super 23797 with 7157 at 1,1,1,1,3 +Id : 13062, {_}: inverse (inverse (divide (divide ?67961 ?67962) (multiply ?67963 (multiply (inverse ?67964) ?67965)))) =>= multiply ?67961 (multiply (inverse ?67962) (inverse (multiply (divide ?67963 ?67964) ?67965))) [67965, 67964, 67963, 67962, 67961] by Super 12770 with 12807 at 1,1,2 +Id : 16664, {_}: inverse (inverse (divide (divide ?87645 ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649)))) =>= multiply ?87645 (divide (inverse ?87646) (multiply ?87647 (multiply (inverse ?87648) ?87649))) [87649, 87648, 87647, 87646, 87645] by Demod 13062 with 12807 at 2,3 +Id : 16690, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =<= multiply ?87882 (divide (inverse ?87883) (multiply (multiply (divide ?87885 ?87886) (divide (divide ?87886 ?87885) (divide (multiply (inverse ?87887) ?87888) ?87884))) (multiply (inverse ?87887) ?87888))) [87888, 87887, 87886, 87885, 87884, 87883, 87882] by Super 16664 with 6973 at 2,1,1,2 +Id : 16778, {_}: inverse (inverse (divide (divide ?87882 ?87883) ?87884)) =>= multiply ?87882 (divide (inverse ?87883) ?87884) [87884, 87883, 87882] by Demod 16690 with 6973 at 2,2,3 +Id : 16836, {_}: multiply ?88530 (inverse (divide (divide ?88531 ?88532) ?88533)) =>= divide ?88530 (multiply ?88531 (divide (inverse ?88532) ?88533)) [88533, 88532, 88531, 88530] by Super 3 with 16778 at 2,3 +Id : 16941, {_}: divide (divide ?89130 (divide (inverse ?89131) ?89132)) (divide ?89133 ?89134) =<= divide (multiply ?89130 ?89132) (multiply ?89133 (divide (inverse ?89134) ?89131)) [89134, 89133, 89132, 89131, 89130] by Super 9552 with 16836 at 3 +Id : 17721, {_}: divide (inverse ?92223) (multiply (divide ?92224 ?92225) (divide (divide ?92225 ?92224) (divide ?92223 (divide (divide ?92226 (divide (inverse ?92227) ?92228)) (divide ?92229 ?92230))))) =>= divide (multiply ?92229 (divide (inverse ?92230) ?92227)) (multiply ?92226 ?92228) [92230, 92229, 92228, 92227, 92226, 92225, 92224, 92223] by Super 362 with 16941 at 2,2,2,2,2 +Id : 18088, {_}: divide (divide ?94725 ?94726) (divide ?94727 (divide (inverse ?94728) ?94729)) =<= divide (multiply ?94725 (divide (inverse ?94726) ?94728)) (multiply ?94727 ?94729) [94729, 94728, 94727, 94726, 94725] by Demod 17721 with 362 at 2 +Id : 18882, {_}: divide (divide ?99448 ?99449) (divide ?99450 (divide (inverse (inverse ?99451)) ?99452)) =>= divide (multiply ?99448 (multiply (inverse ?99449) ?99451)) (multiply ?99450 ?99452) [99452, 99451, 99450, 99449, 99448] by Super 18088 with 3 at 2,1,3 +Id : 18956, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =?= divide (multiply ?100120 (multiply (inverse (inverse ?100121)) ?100123)) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Super 18882 with 3 at 1,2 +Id : 19253, {_}: divide (multiply ?100120 ?100121) (divide ?100122 (divide (inverse (inverse ?100123)) ?100124)) =>= divide (inverse (inverse (multiply (multiply ?100120 ?100121) ?100123))) (multiply ?100122 ?100124) [100124, 100123, 100122, 100121, 100120] by Demod 18956 with 12858 at 1,3 +Id : 24073, {_}: divide (divide (inverse (inverse (multiply (multiply (divide (inverse ?119930) ?119931) (divide (multiply ?119931 ?119930) (divide ?119932 ?119933))) ?119932))) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933, 119932, 119931, 119930] by Demod 23859 with 19253 at 1,2 +Id : 24074, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =<= multiply (inverse (inverse (divide ?119933 ?119935))) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24073 with 7157 at 1,1,1,1,2 +Id : 18174, {_}: divide (divide ?95484 (inverse ?95485)) (divide ?95486 (divide (inverse ?95487) ?95488)) =>= divide (inverse (inverse (divide (multiply ?95484 ?95485) ?95487))) (multiply ?95486 ?95488) [95488, 95487, 95486, 95485, 95484] by Super 18088 with 15656 at 1,3 +Id : 20071, {_}: divide (multiply ?105383 ?105384) (divide ?105385 (divide (inverse ?105386) ?105387)) =<= divide (inverse (inverse (divide (multiply ?105383 ?105384) ?105386))) (multiply ?105385 ?105387) [105387, 105386, 105385, 105384, 105383] by Demod 18174 with 3 at 1,2 +Id : 20108, {_}: divide (multiply (multiply (divide ?105694 ?105695) (divide (divide ?105695 ?105694) (divide ?105696 ?105697))) ?105696) (divide ?105698 (divide (inverse ?105699) ?105700)) =>= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697, 105696, 105695, 105694] by Super 20071 with 6973 at 1,1,1,1,3 +Id : 20428, {_}: divide ?105697 (divide ?105698 (divide (inverse ?105699) ?105700)) =<= divide (inverse (inverse (divide ?105697 ?105699))) (multiply ?105698 ?105700) [105700, 105699, 105698, 105697] by Demod 20108 with 6973 at 1,2 +Id : 20476, {_}: inverse (inverse (divide (divide ?106039 (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043)) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Super 16778 with 20428 at 1,1,1,2 +Id : 20938, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= multiply (inverse (inverse (divide ?106039 ?106041))) (divide (inverse (multiply ?106040 ?106042)) ?106043) [106043, 106042, 106041, 106040, 106039] by Demod 20476 with 16778 at 2 +Id : 24149, {_}: inverse (inverse (multiply (multiply ?120312 (divide ?120313 ?120314)) (inverse (divide ?120315 ?120316)))) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120316, 120315, 120314, 120313, 120312] by Super 12858 with 24074 at 2,3 +Id : 24438, {_}: inverse (inverse (divide (divide ?120312 (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315)) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24149 with 9552 at 1,1,2 +Id : 24439, {_}: multiply ?120312 (divide (inverse (divide (inverse ?120316) (divide ?120313 ?120314))) ?120315) =<= multiply ?120312 (divide (divide (inverse (inverse ?120313)) (multiply (inverse ?120316) ?120314)) ?120315) [120315, 120314, 120313, 120316, 120312] by Demod 24438 with 16778 at 2 +Id : 33216, {_}: inverse (divide (divide (inverse (inverse ?156723)) (multiply (inverse ?156724) ?156725)) ?156726) =<= multiply (multiply (divide (inverse ?156727) ?156728) (divide (multiply ?156728 ?156727) (multiply ?156729 (divide (inverse (divide (inverse ?156724) (divide ?156723 ?156725))) ?156726)))) ?156729 [156729, 156728, 156727, 156726, 156725, 156724, 156723] by Super 7337 with 24439 at 2,2,1,3 +Id : 33721, {_}: inverse (divide (divide (inverse (inverse ?158945)) (multiply (inverse ?158946) ?158947)) ?158948) =>= inverse (divide (inverse (divide (inverse ?158946) (divide ?158945 ?158947))) ?158948) [158948, 158947, 158946, 158945] by Demod 33216 with 7337 at 3 +Id : 33722, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =<= inverse (divide (inverse (divide (inverse (divide ?158954 (divide (divide ?158951 (divide (divide ?158955 ?158956) ?158954)) (divide ?158956 ?158955)))) (divide ?158950 ?158952))) ?158953) [158956, 158955, 158954, 158953, 158952, 158951, 158950] by Super 33721 with 53 at 1,2,1,1,2 +Id : 34010, {_}: inverse (divide (divide (inverse (inverse ?158950)) (multiply ?158951 ?158952)) ?158953) =>= inverse (divide (inverse (divide ?158951 (divide ?158950 ?158952))) ?158953) [158953, 158952, 158951, 158950] by Demod 33722 with 53 at 1,1,1,1,3 +Id : 34077, {_}: inverse (inverse (divide (inverse (divide ?159790 (divide ?159791 ?159792))) ?159793)) =<= multiply (inverse (inverse ?159791)) (divide (inverse (multiply ?159790 ?159792)) ?159793) [159793, 159792, 159791, 159790] by Super 16778 with 34010 at 1,2 +Id : 34441, {_}: multiply ?106039 (divide (inverse (divide ?106040 (divide (inverse ?106041) ?106042))) ?106043) =<= inverse (inverse (divide (inverse (divide ?106040 (divide (divide ?106039 ?106041) ?106042))) ?106043)) [106043, 106042, 106041, 106040, 106039] by Demod 20938 with 34077 at 3 +Id : 16, {_}: divide (inverse (divide ?64 (divide ?65 (divide (divide ?66 ?67) (inverse (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69))))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Super 2 with 15 at 1,2,2 +Id : 38, {_}: divide (inverse (divide ?64 (divide ?65 (multiply (divide ?66 ?67) (divide ?67 (divide ?68 (multiply (divide (divide ?69 ?70) ?71) (divide ?71 (divide ?66 (divide ?70 ?69)))))))))) (divide ?68 ?64) =>= ?65 [71, 70, 69, 68, 67, 66, 65, 64] by Demod 16 with 3 at 2,2,1,1,2 +Id : 43649, {_}: multiply ?191130 (divide (inverse (divide ?191131 (divide (inverse ?191132) (multiply (divide ?191133 ?191134) (divide ?191134 (divide ?191135 (multiply (divide (divide ?191136 ?191137) ?191138) (divide ?191138 (divide ?191133 (divide ?191137 ?191136)))))))))) (divide ?191135 ?191131)) =>= inverse (inverse (divide ?191130 ?191132)) [191138, 191137, 191136, 191135, 191134, 191133, 191132, 191131, 191130] by Super 34441 with 38 at 1,1,3 +Id : 44429, {_}: multiply ?191130 (inverse ?191132) =<= inverse (inverse (divide ?191130 ?191132)) [191132, 191130] by Demod 43649 with 38 at 2,2 +Id : 44886, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= multiply (multiply ?119933 (inverse ?119935)) (inverse (divide ?119936 ?119934)) [119936, 119935, 119934, 119933] by Demod 24074 with 44429 at 1,3 +Id : 44891, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (divide (inverse ?119934) (inverse ?119935))) ?119936 [119936, 119935, 119934, 119933] by Demod 44886 with 9552 at 3 +Id : 44892, {_}: divide (divide (inverse (inverse ?119933)) (multiply (inverse ?119934) ?119935)) ?119936 =>= divide (divide ?119933 (multiply (inverse ?119934) ?119935)) ?119936 [119936, 119935, 119934, 119933] by Demod 44891 with 3 at 2,1,3 +Id : 66804, {_}: divide (inverse (divide ?265003 (divide (divide ?265004 (multiply (inverse ?265005) ?265006)) ?265007))) (divide (multiply (divide ?265008 ?265009) (divide ?265009 (divide ?265007 (multiply (divide (divide ?265010 ?265011) ?265012) (divide ?265012 (divide ?265008 (divide ?265011 ?265010))))))) ?265003) =>= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265012, 265011, 265010, 265009, 265008, 265007, 265006, 265005, 265004, 265003] by Super 66361 with 44892 at 2,1,1,2 +Id : 39, {_}: divide (inverse (divide ?73 (divide ?74 ?75))) (divide (multiply (divide ?76 ?77) (divide ?77 (divide ?75 (multiply (divide (divide ?78 ?79) ?80) (divide ?80 (divide ?76 (divide ?79 ?78))))))) ?73) =>= ?74 [80, 79, 78, 77, 76, 75, 74, 73] by Demod 17 with 3 at 1,2,2 +Id : 67572, {_}: divide ?265004 (multiply (inverse ?265005) ?265006) =<= divide (inverse (inverse ?265004)) (multiply (inverse ?265005) ?265006) [265006, 265005, 265004] by Demod 66804 with 39 at 2 +Id : 67796, {_}: divide (inverse (divide ?266802 (divide ?266803 (multiply (inverse ?266804) ?266805)))) (divide (divide (inverse ?266805) (inverse ?266804)) ?266802) =>= inverse (inverse ?266803) [266805, 266804, 266803, 266802] by Super 12 with 67572 at 2,1,1,2 +Id : 68093, {_}: ?266803 =<= inverse (inverse ?266803) [266803] by Demod 67796 with 12 at 2 +Id : 68404, {_}: multiply (multiply ?67174 ?67175) ?67176 =<= multiply ?67174 (multiply (inverse (inverse ?67175)) ?67176) [67176, 67175, 67174] by Demod 12858 with 68093 at 2 +Id : 68405, {_}: multiply (multiply ?67174 ?67175) ?67176 =?= multiply ?67174 (multiply ?67175 ?67176) [67176, 67175, 67174] by Demod 68404 with 68093 at 1,2,3 +Id : 68861, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 68405 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP471-1.p +11326: solved GRP471-1.p in 19.353208 using nrkbo +11326: status Unsatisfiable for GRP471-1.p +NO CLASH, using fixed ground order +11333: Facts: +11333: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11333: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11333: Goal: +11333: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11333: Order: +11333: nrkbo +11333: Leaf order: +11333: divide 7 2 0 +11333: b1 2 0 2 1,1,3 +11333: multiply 3 2 2 0,2 +11333: inverse 4 1 2 0,1,2 +11333: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11334: Facts: +11334: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11334: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11334: Goal: +11334: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11334: Order: +11334: kbo +11334: Leaf order: +11334: divide 7 2 0 +11334: b1 2 0 2 1,1,3 +11334: multiply 3 2 2 0,2 +11334: inverse 4 1 2 0,1,2 +11334: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11335: Facts: +11335: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11335: Id : 3, {_}: + multiply ?7 ?8 =?= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11335: Goal: +11335: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11335: Order: +11335: lpo +11335: Leaf order: +11335: divide 7 2 0 +11335: b1 2 0 2 1,1,3 +11335: multiply 3 2 2 0,2 +11335: inverse 4 1 2 0,1,2 +11335: a1 2 0 2 1,1,2 +% SZS status Timeout for GRP475-1.p +NO CLASH, using fixed ground order +11373: Facts: +11373: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11373: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11373: Goal: +11373: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11373: Order: +11373: nrkbo +11373: Leaf order: +11373: divide 7 2 0 +11373: a2 2 0 2 2,2 +11373: multiply 3 2 2 0,2 +11373: inverse 3 1 1 0,1,1,2 +11373: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11374: Facts: +11374: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11374: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11374: Goal: +11374: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11374: Order: +11374: kbo +11374: Leaf order: +11374: divide 7 2 0 +11374: a2 2 0 2 2,2 +11374: multiply 3 2 2 0,2 +11374: inverse 3 1 1 0,1,1,2 +11374: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11375: Facts: +11375: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11375: Id : 3, {_}: + multiply ?7 ?8 =?= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11375: Goal: +11375: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11375: Order: +11375: lpo +11375: Leaf order: +11375: divide 7 2 0 +11375: a2 2 0 2 2,2 +11375: multiply 3 2 2 0,2 +11375: inverse 3 1 1 0,1,1,2 +11375: b2 2 0 2 1,1,1,2 +Statistics : +Max weight : 49 +Found proof, 60.308770s +% SZS status Unsatisfiable for GRP476-1.p +% SZS output start CNFRefutation for GRP476-1.p +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2 +Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2 +Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2 +Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2 +Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2 +Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2 +Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2 +Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2 +Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2 +Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2 +Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2 +Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2 +Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2 +Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2 +Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3 +Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2 +Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2 +Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2 +Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2 +Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3 +Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3 +Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2 +Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2 +Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2 +Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2 +Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2 +Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2 +Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3 +Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2 +Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2 +Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2 +Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2 +Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2 +Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2 +Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3 +Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2 +Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2 +Id : 36954, {_}: inverse (divide (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 36094 with 36681 at 1,1,2 +Id : 37568, {_}: divide ?167565 (divide (divide ?167566 ?167567) (divide ?167566 ?167567)) =>= ?167565 [167567, 167566, 167565] by Demod 36954 with 37291 at 2 +Id : 33466, {_}: ?158075 =<= multiply (multiply ?158075 (divide ?158076 ?158077)) (divide ?158077 ?158076) [158077, 158076, 158075] by Demod 33087 with 2 at 2 +Id : 33531, {_}: ?158517 =<= multiply (multiply ?158517 (multiply ?158518 ?158519)) (divide (inverse ?158519) ?158518) [158519, 158518, 158517] by Super 33466 with 3 at 2,1,3 +Id : 36952, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (divide ?158518 (inverse ?158519)) [158519, 158518, 158517] by Demod 33531 with 36681 at 3 +Id : 36955, {_}: ?158517 =<= divide (multiply ?158517 (multiply ?158518 ?158519)) (multiply ?158518 ?158519) [158519, 158518, 158517] by Demod 36952 with 3 at 2,3 +Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2 +Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2 +Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2 +Id : 38144, {_}: ?175420 =<= divide (multiply ?175420 (multiply (divide ?175421 ?175422) ?175422)) ?175421 [175422, 175421, 175420] by Super 36955 with 36819 at 2,3 +Id : 38311, {_}: ?175420 =<= divide (multiply ?175420 ?175421) ?175421 [175421, 175420] by Demod 38144 with 36819 at 2,1,3 +Id : 38590, {_}: divide ?177333 (divide (divide (multiply ?177334 ?177335) ?177335) ?177334) =>= ?177333 [177335, 177334, 177333] by Super 37568 with 38311 at 2,2,2 +Id : 38627, {_}: divide ?177333 (divide ?177334 ?177334) =>= ?177333 [177334, 177333] by Demod 38590 with 38311 at 1,2,2 +Id : 41488, {_}: divide (divide ?193733 ?193733) ?193734 =>= inverse ?193734 [193734, 193733] by Super 37291 with 38627 at 1,3 +Id : 42000, {_}: multiply (divide ?195057 ?195057) ?195058 =>= inverse (inverse ?195058) [195058, 195057] by Super 3 with 41488 at 3 +Id : 38603, {_}: divide ?177417 (multiply ?177418 ?177417) =>= inverse ?177418 [177418, 177417] by Super 37291 with 38311 at 1,3 +Id : 40108, {_}: divide (multiply ?188666 ?188667) ?188667 =>= inverse (inverse ?188666) [188667, 188666] by Super 37291 with 38603 at 1,3 +Id : 40636, {_}: ?188666 =<= inverse (inverse ?188666) [188666] by Demod 40108 with 38311 at 2 +Id : 43036, {_}: multiply (divide ?197334 ?197334) ?197335 =>= ?197335 [197335, 197334] by Demod 42000 with 40636 at 3 +Id : 43063, {_}: multiply (multiply (inverse ?197470) ?197470) ?197471 =>= ?197471 [197471, 197470] by Super 43036 with 3 at 1,2 +Id : 47549, {_}: a2 =?= a2 [] by Demod 1 with 43063 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP476-1.p +11374: solved GRP476-1.p in 30.053878 using kbo +11374: status Unsatisfiable for GRP476-1.p +NO CLASH, using fixed ground order +11392: Facts: +11392: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11392: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11392: Goal: +11392: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11392: Order: +11392: nrkbo +11392: Leaf order: +11392: inverse 2 1 0 +11392: divide 7 2 0 +11392: c3 2 0 2 2,2 +11392: multiply 5 2 4 0,2 +11392: b3 2 0 2 2,1,2 +11392: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11393: Facts: +11393: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11393: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11393: Goal: +11393: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11393: Order: +11393: kbo +11393: Leaf order: +11393: inverse 2 1 0 +11393: divide 7 2 0 +11393: c3 2 0 2 2,2 +11393: multiply 5 2 4 0,2 +11393: b3 2 0 2 2,1,2 +11393: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11395: Facts: +11395: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11395: Id : 3, {_}: + multiply ?7 ?8 =>= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11395: Goal: +11395: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11395: Order: +11395: lpo +11395: Leaf order: +11395: inverse 2 1 0 +11395: divide 7 2 0 +11395: c3 2 0 2 2,2 +11395: multiply 5 2 4 0,2 +11395: b3 2 0 2 2,1,2 +11395: a3 2 0 2 1,1,2 +Statistics : +Max weight : 49 +Found proof, 65.047626s +% SZS status Unsatisfiable for GRP477-1.p +% SZS output start CNFRefutation for GRP477-1.p +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2 +Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2 +Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2 +Id : 2201, {_}: divide (divide (inverse (divide (divide (divide ?9850 ?9851) ?9852) ?9853)) (divide ?9851 ?9850)) ?9852 =>= ?9853 [9853, 9852, 9851, 9850] by Super 17 with 20 at 1,2 +Id : 2216, {_}: divide (divide (inverse (divide (divide (divide (inverse ?9957) ?9958) ?9959) ?9960)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9960, 9959, 9958, 9957] by Super 2201 with 3 at 2,1,2 +Id : 2522, {_}: divide (divide (inverse (multiply (divide (divide ?11173 ?11174) ?11175) ?11176)) (divide ?11174 ?11173)) ?11175 =>= inverse ?11176 [11176, 11175, 11174, 11173] by Super 2201 with 3 at 1,1,1,2 +Id : 3974, {_}: divide (divide (inverse (multiply (divide (divide (inverse ?18265) ?18266) ?18267) ?18268)) (multiply ?18266 ?18265)) ?18267 =>= inverse ?18268 [18268, 18267, 18266, 18265] by Super 2522 with 3 at 2,1,2 +Id : 4011, {_}: divide (divide (inverse (multiply (divide (multiply (inverse ?18535) ?18536) ?18537) ?18538)) (multiply (inverse ?18536) ?18535)) ?18537 =>= inverse ?18538 [18538, 18537, 18536, 18535] by Super 3974 with 3 at 1,1,1,1,1,2 +Id : 3335, {_}: divide (divide (inverse (divide (divide (divide (inverse ?15160) ?15161) ?15162) ?15163)) (multiply ?15161 ?15160)) ?15162 =>= ?15163 [15163, 15162, 15161, 15160] by Super 2201 with 3 at 2,1,2 +Id : 3370, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?15416) ?15417) ?15418) ?15419)) (multiply (inverse ?15417) ?15416)) ?15418 =>= ?15419 [15419, 15418, 15417, 15416] by Super 3335 with 3 at 1,1,1,1,1,2 +Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2 +Id : 602, {_}: divide (inverse (divide (divide ?2300 ?2301) (divide ?2302 ?2301))) (multiply (divide ?2303 ?2304) (divide (divide (divide ?2304 ?2303) ?2305) (divide ?2300 ?2305))) =>= ?2302 [2305, 2304, 2303, 2302, 2301, 2300] by Demod 7 with 3 at 2,2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 300, {_}: inverse (divide (divide (divide ?1003 ?1004) ?1005) (divide (divide ?1006 (divide ?1004 ?1003)) ?1005)) =>= ?1006 [1006, 1005, 1004, 1003] by Super 2 with 6 at 2 +Id : 673, {_}: divide ?2877 (multiply (divide ?2878 ?2879) (divide (divide (divide ?2879 ?2878) ?2880) (divide (divide ?2881 ?2882) ?2880))) =>= divide ?2877 (divide ?2882 ?2881) [2882, 2881, 2880, 2879, 2878, 2877] by Super 602 with 300 at 1,2 +Id : 18343, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?89645) ?89646) ?89647) (divide ?89648 ?89649))) (multiply (inverse ?89646) ?89645)) ?89647 =?= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648, 89647, 89646, 89645] by Super 3370 with 673 at 1,1,1,2 +Id : 19039, {_}: divide ?92370 ?92371 =<= multiply (divide ?92372 ?92373) (divide (divide (divide ?92373 ?92372) ?92374) (divide (divide ?92371 ?92370) ?92374)) [92374, 92373, 92372, 92371, 92370] by Demod 18343 with 3370 at 2 +Id : 19158, {_}: divide ?93334 ?93335 =<= multiply (multiply ?93336 ?93337) (divide (divide (divide (inverse ?93337) ?93336) ?93338) (divide (divide ?93335 ?93334) ?93338)) [93338, 93337, 93336, 93335, 93334] by Super 19039 with 3 at 1,3 +Id : 2243, {_}: divide (divide (inverse (multiply (divide (divide ?10125 ?10126) ?10127) ?10128)) (divide ?10126 ?10125)) ?10127 =>= inverse ?10128 [10128, 10127, 10126, 10125] by Super 2201 with 3 at 1,1,1,2 +Id : 18627, {_}: divide ?89648 ?89649 =<= multiply (divide ?89650 ?89651) (divide (divide (divide ?89651 ?89650) ?89652) (divide (divide ?89649 ?89648) ?89652)) [89652, 89651, 89650, 89649, 89648] by Demod 18343 with 3370 at 2 +Id : 18986, {_}: divide (divide (inverse (divide ?91944 ?91945)) (divide ?91946 ?91947)) ?91948 =<= inverse (divide (divide (divide ?91948 (divide ?91947 ?91946)) ?91949) (divide (divide ?91945 ?91944) ?91949)) [91949, 91948, 91947, 91946, 91945, 91944] by Super 2243 with 18627 at 1,1,1,2 +Id : 19370, {_}: divide (divide (divide (inverse (divide ?93677 ?93678)) (divide ?93679 ?93680)) ?93681) (divide (divide ?93680 ?93679) ?93681) =>= divide ?93678 ?93677 [93681, 93680, 93679, 93678, 93677] by Super 2 with 18986 at 1,2 +Id : 33018, {_}: divide ?156119 ?156120 =<= multiply (multiply (divide ?156119 ?156120) (divide ?156121 ?156122)) (divide ?156122 ?156121) [156122, 156121, 156120, 156119] by Super 19158 with 19370 at 2,3 +Id : 33087, {_}: divide (inverse (divide (divide (divide ?156646 ?156647) ?156648) (divide ?156649 ?156648))) (divide ?156647 ?156646) =?= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649, 156648, 156647, 156646] by Super 33018 with 2 at 1,1,3 +Id : 33278, {_}: ?156649 =<= multiply (multiply ?156649 (divide ?156650 ?156651)) (divide ?156651 ?156650) [156651, 156650, 156649] by Demod 33087 with 2 at 2 +Id : 412, {_}: inverse (divide (divide (divide ?1605 ?1606) ?1607) (divide (divide ?1608 (divide ?1606 ?1605)) ?1607)) =>= ?1608 [1608, 1607, 1606, 1605] by Super 2 with 6 at 2 +Id : 433, {_}: inverse (divide (divide (divide ?1731 ?1732) (inverse ?1733)) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Super 412 with 3 at 2,1,2 +Id : 477, {_}: inverse (divide (multiply (divide ?1731 ?1732) ?1733) (multiply (divide ?1734 (divide ?1732 ?1731)) ?1733)) =>= ?1734 [1734, 1733, 1732, 1731] by Demod 433 with 3 at 1,1,2 +Id : 503, {_}: inverse (divide (multiply (divide ?1881 ?1882) ?1883) (multiply (divide ?1884 (divide ?1882 ?1881)) ?1883)) =>= ?1884 [1884, 1883, 1882, 1881] by Demod 433 with 3 at 1,1,2 +Id : 511, {_}: inverse (divide (multiply (divide (inverse ?1933) ?1934) ?1935) (multiply (divide ?1936 (multiply ?1934 ?1933)) ?1935)) =>= ?1936 [1936, 1935, 1934, 1933] by Super 503 with 3 at 2,1,2,1,2 +Id : 32469, {_}: divide (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (inverse (divide ?153396 ?153397)) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Super 18986 with 19370 at 1,3 +Id : 32700, {_}: multiply (divide (inverse (divide ?153394 ?153395)) (divide ?153395 ?153394)) (divide ?153396 ?153397) =>= inverse (divide ?153397 ?153396) [153397, 153396, 153395, 153394] by Demod 32469 with 3 at 2 +Id : 35765, {_}: inverse (divide (inverse (divide ?167563 ?167564)) (multiply (divide ?167565 (multiply (divide ?167566 ?167567) (divide ?167567 ?167566))) (divide ?167564 ?167563))) =>= ?167565 [167567, 167566, 167565, 167564, 167563] by Super 511 with 32700 at 1,1,2 +Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2 +Id : 32402, {_}: divide (inverse (divide ?152772 ?152773)) (multiply (divide ?152774 ?152775) (divide ?152773 ?152772)) =>= divide ?152775 ?152774 [152775, 152774, 152773, 152772] by Super 9 with 19370 at 1,1,2 +Id : 36094, {_}: inverse (divide (multiply (divide ?167566 ?167567) (divide ?167567 ?167566)) ?167565) =>= ?167565 [167565, 167567, 167566] by Demod 35765 with 32402 at 1,2 +Id : 36327, {_}: multiply (divide ?169738 (divide ?169739 ?169740)) (divide ?169739 ?169740) =>= ?169738 [169740, 169739, 169738] by Super 477 with 36094 at 2 +Id : 36681, {_}: divide ?171580 (divide ?171581 ?171582) =<= multiply ?171580 (divide ?171582 ?171581) [171582, 171581, 171580] by Super 33278 with 36327 at 1,3 +Id : 37087, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?173237) ?173238) ?173239) (divide ?173240 ?173241))) (multiply (inverse ?173238) ?173237)) ?173239 =>= inverse (divide ?173241 ?173240) [173241, 173240, 173239, 173238, 173237] by Super 4011 with 36681 at 1,1,1,2 +Id : 37291, {_}: divide ?173240 ?173241 =<= inverse (divide ?173241 ?173240) [173241, 173240] by Demod 37087 with 3370 at 2 +Id : 37631, {_}: divide (divide (divide ?9960 (divide (divide (inverse ?9957) ?9958) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9958, 9957, 9960] by Demod 2216 with 37291 at 1,1,2 +Id : 37745, {_}: divide ?174363 ?174364 =<= inverse (divide ?174364 ?174363) [174364, 174363] by Demod 37087 with 3370 at 2 +Id : 37810, {_}: divide (inverse ?174753) ?174754 =>= inverse (multiply ?174754 ?174753) [174754, 174753] by Super 37745 with 3 at 1,3 +Id : 38028, {_}: divide (divide (divide ?9960 (divide (inverse (multiply ?9958 ?9957)) ?9959)) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9959, 9957, 9958, 9960] by Demod 37631 with 37810 at 1,2,1,1,2 +Id : 38029, {_}: divide (divide (divide ?9960 (inverse (multiply ?9959 (multiply ?9958 ?9957)))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38028 with 37810 at 2,1,1,2 +Id : 38096, {_}: divide (divide (multiply ?9960 (multiply ?9959 (multiply ?9958 ?9957))) (multiply ?9958 ?9957)) ?9959 =>= ?9960 [9957, 9958, 9959, 9960] by Demod 38029 with 3 at 1,1,2 +Id : 36684, {_}: multiply (divide ?171593 (divide ?171594 ?171595)) (divide ?171594 ?171595) =>= ?171593 [171595, 171594, 171593] by Super 477 with 36094 at 2 +Id : 36687, {_}: multiply (divide ?171605 (divide (inverse (divide (divide (divide ?171606 ?171607) ?171608) (divide ?171609 ?171608))) (divide ?171607 ?171606))) ?171609 =>= ?171605 [171609, 171608, 171607, 171606, 171605] by Super 36684 with 2 at 2,2 +Id : 36819, {_}: multiply (divide ?171605 ?171609) ?171609 =>= ?171605 [171609, 171605] by Demod 36687 with 2 at 2,1,2 +Id : 51854, {_}: divide (divide ?212601 (multiply ?212602 ?212603)) ?212604 =>= divide ?212601 (multiply ?212604 (multiply ?212602 ?212603)) [212604, 212603, 212602, 212601] by Super 38096 with 36819 at 1,1,2 +Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3 +Id : 1822, {_}: multiply (divide (inverse (divide (divide (divide ?7521 ?7522) (inverse ?7523)) ?7524)) (divide ?7522 ?7521)) ?7523 =>= ?7524 [7524, 7523, 7522, 7521] by Super 18 with 20 at 1,2 +Id : 2348, {_}: multiply (divide (inverse (divide (multiply (divide ?10333 ?10334) ?10335) ?10336)) (divide ?10334 ?10333)) ?10335 =>= ?10336 [10336, 10335, 10334, 10333] by Demod 1822 with 3 at 1,1,1,1,2 +Id : 2690, {_}: multiply (divide (inverse (multiply (multiply (divide ?11645 ?11646) ?11647) ?11648)) (divide ?11646 ?11645)) ?11647 =>= inverse ?11648 [11648, 11647, 11646, 11645] by Super 2348 with 3 at 1,1,1,2 +Id : 2723, {_}: multiply (divide (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (divide (inverse ?11879) ?11878)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Super 2690 with 3 at 1,1,1,1,1,2 +Id : 38038, {_}: multiply (inverse (multiply (divide (inverse ?11879) ?11878) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11878, 11879] by Demod 2723 with 37810 at 1,2 +Id : 38039, {_}: multiply (inverse (multiply (inverse (multiply ?11878 ?11879)) (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881))) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38038 with 37810 at 1,1,1,2 +Id : 38184, {_}: multiply (inverse ?175473) ?175474 =<= inverse (multiply (inverse ?175474) ?175473) [175474, 175473] by Super 3 with 37810 at 3 +Id : 38716, {_}: multiply (multiply (inverse (multiply (multiply (multiply ?11878 ?11879) ?11880) ?11881)) (multiply ?11878 ?11879)) ?11880 =>= inverse ?11881 [11881, 11880, 11879, 11878] by Demod 38039 with 38184 at 1,2 +Id : 51866, {_}: divide (divide ?212677 (inverse ?212678)) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Super 51854 with 38716 at 2,1,2 +Id : 52301, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (multiply (multiply (inverse (multiply (multiply (multiply ?212680 ?212681) ?212682) ?212678)) (multiply ?212680 ?212681)) ?212682)) [212682, 212681, 212680, 212679, 212678, 212677] by Demod 51866 with 3 at 1,2 +Id : 52302, {_}: divide (multiply ?212677 ?212678) ?212679 =<= divide ?212677 (multiply ?212679 (inverse ?212678)) [212679, 212678, 212677] by Demod 52301 with 38716 at 2,2,3 +Id : 38247, {_}: divide ?175863 (inverse ?175864) =<= inverse (inverse (multiply ?175863 ?175864)) [175864, 175863] by Super 37291 with 37810 at 1,3 +Id : 38843, {_}: multiply ?176435 ?176436 =<= inverse (inverse (multiply ?176435 ?176436)) [176436, 176435] by Demod 38247 with 3 at 2 +Id : 3670, {_}: multiply (divide (inverse (divide (multiply (divide (inverse ?16718) ?16719) ?16720) ?16721)) (multiply ?16719 ?16718)) ?16720 =>= ?16721 [16721, 16720, 16719, 16718] by Super 2348 with 3 at 2,1,2 +Id : 3706, {_}: multiply (divide (inverse (divide (multiply (multiply (inverse ?16981) ?16982) ?16983) ?16984)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16984, 16983, 16982, 16981] by Super 3670 with 3 at 1,1,1,1,1,2 +Id : 37609, {_}: multiply (divide (divide ?16984 (multiply (multiply (inverse ?16981) ?16982) ?16983)) (multiply (inverse ?16982) ?16981)) ?16983 =>= ?16984 [16983, 16982, 16981, 16984] by Demod 3706 with 37291 at 1,1,2 +Id : 38847, {_}: multiply (divide (divide ?176447 (multiply (multiply (inverse ?176448) ?176449) ?176450)) (multiply (inverse ?176449) ?176448)) ?176450 =>= inverse (inverse ?176447) [176450, 176449, 176448, 176447] by Super 38843 with 37609 at 1,1,3 +Id : 38880, {_}: ?176447 =<= inverse (inverse ?176447) [176447] by Demod 38847 with 37609 at 2 +Id : 40331, {_}: multiply ?187278 (inverse ?187279) =>= divide ?187278 ?187279 [187279, 187278] by Super 3 with 38880 at 2,3 +Id : 52303, {_}: divide (multiply ?212677 ?212678) ?212679 =>= divide ?212677 (divide ?212679 ?212678) [212679, 212678, 212677] by Demod 52302 with 40331 at 2,3 +Id : 53261, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (divide (inverse ?214474) ?214473) [214474, 214473, 214472] by Super 3 with 52303 at 3 +Id : 53437, {_}: multiply (multiply ?214472 ?214473) ?214474 =<= divide ?214472 (inverse (multiply ?214473 ?214474)) [214474, 214473, 214472] by Demod 53261 with 37810 at 2,3 +Id : 53438, {_}: multiply (multiply ?214472 ?214473) ?214474 =>= multiply ?214472 (multiply ?214473 ?214474) [214474, 214473, 214472] by Demod 53437 with 3 at 3 +Id : 53834, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 53438 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP477-1.p +11393: solved GRP477-1.p in 32.410025 using kbo +11393: status Unsatisfiable for GRP477-1.p +NO CLASH, using fixed ground order +11411: Facts: +11411: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11411: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11411: Goal: +11411: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11411: Order: +11411: nrkbo +11411: Leaf order: +11411: divide 7 2 0 +11411: b1 2 0 2 1,1,3 +11411: multiply 3 2 2 0,2 +11411: inverse 4 1 2 0,1,2 +11411: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11412: Facts: +11412: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11412: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11412: Goal: +11412: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11412: Order: +11412: kbo +11412: Leaf order: +11412: divide 7 2 0 +11412: b1 2 0 2 1,1,3 +11412: multiply 3 2 2 0,2 +11412: inverse 4 1 2 0,1,2 +11412: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11413: Facts: +11413: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11413: Id : 3, {_}: + multiply ?7 ?8 =?= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11413: Goal: +11413: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +11413: Order: +11413: lpo +11413: Leaf order: +11413: divide 7 2 0 +11413: b1 2 0 2 1,1,3 +11413: multiply 3 2 2 0,2 +11413: inverse 4 1 2 0,1,2 +11413: a1 2 0 2 1,1,2 +% SZS status Timeout for GRP478-1.p +NO CLASH, using fixed ground order +11446: Facts: +11446: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11446: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11446: Goal: +11446: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11446: Order: +11446: nrkbo +11446: Leaf order: +11446: divide 7 2 0 +11446: a2 2 0 2 2,2 +11446: multiply 3 2 2 0,2 +11446: inverse 3 1 1 0,1,1,2 +11446: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11447: Facts: +11447: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11447: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11447: Goal: +11447: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11447: Order: +11447: kbo +11447: Leaf order: +11447: divide 7 2 0 +11447: a2 2 0 2 2,2 +11447: multiply 3 2 2 0,2 +11447: inverse 3 1 1 0,1,1,2 +11447: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11448: Facts: +11448: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11448: Id : 3, {_}: + multiply ?7 ?8 =?= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11448: Goal: +11448: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +11448: Order: +11448: lpo +11448: Leaf order: +11448: divide 7 2 0 +11448: a2 2 0 2 2,2 +11448: multiply 3 2 2 0,2 +11448: inverse 3 1 1 0,1,1,2 +11448: b2 2 0 2 1,1,1,2 +% SZS status Timeout for GRP479-1.p +NO CLASH, using fixed ground order +11491: Facts: +NO CLASH, using fixed ground order +11492: Facts: +11492: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11492: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11492: Goal: +11492: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11492: Order: +11492: kbo +11492: Leaf order: +11492: inverse 2 1 0 +11492: divide 7 2 0 +11492: c3 2 0 2 2,2 +11492: multiply 5 2 4 0,2 +11492: b3 2 0 2 2,1,2 +11492: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11493: Facts: +11493: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11493: Id : 3, {_}: + multiply ?7 ?8 =>= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11493: Goal: +11493: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11493: Order: +11493: lpo +11493: Leaf order: +11493: inverse 2 1 0 +11493: divide 7 2 0 +11493: c3 2 0 2 2,2 +11493: multiply 5 2 4 0,2 +11493: b3 2 0 2 2,1,2 +11493: a3 2 0 2 1,1,2 +11491: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +11491: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +11491: Goal: +11491: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +11491: Order: +11491: nrkbo +11491: Leaf order: +11491: inverse 2 1 0 +11491: divide 7 2 0 +11491: c3 2 0 2 2,2 +11491: multiply 5 2 4 0,2 +11491: b3 2 0 2 2,1,2 +11491: a3 2 0 2 1,1,2 +Statistics : +Max weight : 78 +Found proof, 69.885629s +% SZS status Unsatisfiable for GRP480-1.p +% SZS output start CNFRefutation for GRP480-1.p +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2 +Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2 +Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2 +Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2 +Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2 +Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2 +Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2 +Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2 +Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2 +Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2 +Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2 +Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2 +Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2 +Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2 +Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2 +Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2 +Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2 +Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2 +Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2 +Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2 +Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2 +Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2 +Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2 +Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2 +Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3 +Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2 +Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3 +Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2 +Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3 +Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2 +Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3 +Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3 +Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2 +Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2 +Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2 +Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2 +Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2 +Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2 +Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2 +Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2 +Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2 +Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2 +Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2 +Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2 +Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2 +Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2 +Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3 +Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2 +Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3 +Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3 +Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3 +Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2 +Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3 +Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2 +Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2 +Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2 +Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2 +Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3 +Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2 +Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2 +Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2 +Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2 +Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3 +Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2 +Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3 +Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2 +Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2 +Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2 +Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2 +Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2 +Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2 +Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2 +Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2 +Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2 +Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2 +Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3 +Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2 +Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2 +Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2 +Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2 +Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2 +Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2 +Id : 102474, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2 +Id : 102475, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102474 with 101980 at 2,2 +Id : 102476, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102475 at 2,3 +Id : 102520, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102476 with 101980 at 2,3 +Id : 102785, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102520 with 102475 at 1,2 +Id : 102786, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102785 with 102475 at 3 +Id : 104734, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102786 at 1,2 +Id : 104735, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104734 with 102786 at 3 +Id : 104736, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 212] by Demod 104735 with 100849 at 2,1,2 +Id : 104737, {_}: multiply (divide ?212 (inverse ?211)) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104736 with 100849 at 2,3 +Id : 104738, {_}: multiply (multiply ?212 ?211) ?213 =<= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (inverse ?215) [215, 213, 211, 212] by Demod 104737 with 3 at 1,2 +Id : 104739, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) ?215 [215, 213, 211, 212] by Demod 104738 with 3 at 3 +Id : 104774, {_}: multiply (multiply ?542474 ?542475) ?542476 =<= multiply (divide ?542474 (divide ?542477 (multiply ?542475 ?542476))) ?542477 [542477, 542476, 542475, 542474] by Demod 104738 with 3 at 3 +Id : 104783, {_}: multiply (multiply ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Super 104774 with 101386 at 2,2,1,3 +Id : 102917, {_}: multiply ?539648 (divide ?539649 ?539650) =>= divide ?539648 (divide ?539650 ?539649) [539650, 539649, 539648] by Super 102475 with 102786 at 2,2 +Id : 104878, {_}: multiply (divide ?542524 (divide ?542525 ?542525)) ?542526 =?= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542525, 542524] by Demod 104783 with 102917 at 1,2 +Id : 104879, {_}: multiply ?542524 ?542526 =<= multiply (divide ?542524 (divide ?542527 ?542526)) ?542527 [542527, 542526, 542524] by Demod 104878 with 93111 at 1,2 +Id : 107171, {_}: multiply (multiply ?212 ?211) ?213 =?= multiply ?212 (multiply ?211 ?213) [213, 211, 212] by Demod 104739 with 104879 at 3 +Id : 107392, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 107171 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP480-1.p +11491: solved GRP480-1.p in 34.906181 using nrkbo +11491: status Unsatisfiable for GRP480-1.p +NO CLASH, using fixed ground order +11510: Facts: +11510: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11510: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11510: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11510: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11510: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11510: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11510: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11510: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11510: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +11510: Goal: +11510: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +11510: Order: +11510: nrkbo +11510: Leaf order: +11510: meet 17 2 4 0,2 +11510: join 19 2 4 0,2,2 +11510: c 2 0 2 2,2,2 +11510: b 4 0 4 1,2,2 +11510: a 4 0 4 1,2 +NO CLASH, using fixed ground order +11511: Facts: +11511: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11511: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11511: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11511: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11511: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11511: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11511: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11511: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11511: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +11511: Goal: +11511: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +11511: Order: +11511: kbo +11511: Leaf order: +11511: meet 17 2 4 0,2 +11511: join 19 2 4 0,2,2 +11511: c 2 0 2 2,2,2 +11511: b 4 0 4 1,2,2 +11511: a 4 0 4 1,2 +NO CLASH, using fixed ground order +11512: Facts: +11512: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11512: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11512: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11512: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11512: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11512: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11512: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11512: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11512: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +11512: Goal: +11512: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +11512: Order: +11512: lpo +11512: Leaf order: +11512: meet 17 2 4 0,2 +11512: join 19 2 4 0,2,2 +11512: c 2 0 2 2,2,2 +11512: b 4 0 4 1,2,2 +11512: a 4 0 4 1,2 +% SZS status Timeout for LAT168-1.p +NO CLASH, using fixed ground order +11539: Facts: +11539: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11539: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11539: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11539: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11539: Goal: +11539: Id : 1, {_}: + implies (implies (implies a b) (implies b a)) (implies b a) =>= truth + [] by prove_wajsberg_mv_4 +11539: Order: +11539: nrkbo +11539: Leaf order: +11539: not 2 1 0 +11539: truth 4 0 1 3 +11539: implies 18 2 5 0,2 +11539: b 3 0 3 2,1,1,2 +11539: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +11540: Facts: +11540: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11540: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11540: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11540: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11540: Goal: +11540: Id : 1, {_}: + implies (implies (implies a b) (implies b a)) (implies b a) =>= truth + [] by prove_wajsberg_mv_4 +11540: Order: +11540: kbo +11540: Leaf order: +11540: not 2 1 0 +11540: truth 4 0 1 3 +11540: implies 18 2 5 0,2 +11540: b 3 0 3 2,1,1,2 +11540: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +11541: Facts: +11541: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11541: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11541: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11541: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11541: Goal: +11541: Id : 1, {_}: + implies (implies (implies a b) (implies b a)) (implies b a) =>= truth + [] by prove_wajsberg_mv_4 +11541: Order: +11541: lpo +11541: Leaf order: +11541: not 2 1 0 +11541: truth 4 0 1 3 +11541: implies 18 2 5 0,2 +11541: b 3 0 3 2,1,1,2 +11541: a 3 0 3 1,1,1,2 +% SZS status Timeout for LCL109-2.p +NO CLASH, using fixed ground order +11558: Facts: +11558: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11558: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11558: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11558: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11558: Goal: +11558: Id : 1, {_}: + implies x (implies y z) =>= implies y (implies x z) + [] by prove_wajsberg_lemma +11558: Order: +11558: nrkbo +11558: Leaf order: +11558: not 2 1 0 +11558: truth 3 0 0 +11558: implies 17 2 4 0,2 +11558: z 2 0 2 2,2,2 +11558: y 2 0 2 1,2,2 +11558: x 2 0 2 1,2 +NO CLASH, using fixed ground order +11559: Facts: +11559: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11559: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11559: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11559: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11559: Goal: +11559: Id : 1, {_}: + implies x (implies y z) =>= implies y (implies x z) + [] by prove_wajsberg_lemma +11559: Order: +11559: kbo +11559: Leaf order: +11559: not 2 1 0 +11559: truth 3 0 0 +11559: implies 17 2 4 0,2 +11559: z 2 0 2 2,2,2 +11559: y 2 0 2 1,2,2 +11559: x 2 0 2 1,2 +NO CLASH, using fixed ground order +11560: Facts: +11560: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11560: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11560: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11560: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11560: Goal: +11560: Id : 1, {_}: + implies x (implies y z) =>= implies y (implies x z) + [] by prove_wajsberg_lemma +11560: Order: +11560: lpo +11560: Leaf order: +11560: not 2 1 0 +11560: truth 3 0 0 +11560: implies 17 2 4 0,2 +11560: z 2 0 2 2,2,2 +11560: y 2 0 2 1,2,2 +11560: x 2 0 2 1,2 +% SZS status Timeout for LCL138-1.p +NO CLASH, using fixed ground order +11593: Facts: +11593: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11593: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11593: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11593: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11593: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +11593: Id : 7, {_}: + or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +11593: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +11593: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +11593: Id : 10, {_}: + and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +11593: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +11593: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +11593: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +11593: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +11593: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +11593: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +11593: Id : 17, {_}: not truth =>= falsehood [] by false_definition +11593: Goal: +11593: Id : 1, {_}: + xor x (xor truth y) =<= xor (xor x truth) y + [] by prove_alternative_wajsberg_axiom +11593: Order: +11593: nrkbo +11593: Leaf order: +11593: falsehood 1 0 0 +11593: and_star 7 2 0 +11593: and 9 2 0 +11593: or 10 2 0 +11593: not 12 1 0 +11593: implies 14 2 0 +11593: xor 7 2 4 0,2 +11593: y 2 0 2 2,2,2 +11593: truth 6 0 2 1,2,2 +11593: x 2 0 2 1,2 +NO CLASH, using fixed ground order +11594: Facts: +11594: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11594: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11594: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11594: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11594: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +11594: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +11594: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +11594: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +11594: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +11594: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +11594: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +11594: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +11594: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +11594: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +11594: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +11594: Id : 17, {_}: not truth =>= falsehood [] by false_definition +11594: Goal: +11594: Id : 1, {_}: + xor x (xor truth y) =<= xor (xor x truth) y + [] by prove_alternative_wajsberg_axiom +11594: Order: +11594: kbo +11594: Leaf order: +11594: falsehood 1 0 0 +11594: and_star 7 2 0 +11594: and 9 2 0 +11594: or 10 2 0 +11594: not 12 1 0 +11594: implies 14 2 0 +11594: xor 7 2 4 0,2 +11594: y 2 0 2 2,2,2 +11594: truth 6 0 2 1,2,2 +11594: x 2 0 2 1,2 +NO CLASH, using fixed ground order +11595: Facts: +11595: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +11595: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +11595: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +11595: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +11595: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +11595: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +11595: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +11595: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +11595: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +11595: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +11595: Id : 12, {_}: + xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +11595: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +11595: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +11595: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +11595: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +11595: Id : 17, {_}: not truth =>= falsehood [] by false_definition +11595: Goal: +11595: Id : 1, {_}: + xor x (xor truth y) =<= xor (xor x truth) y + [] by prove_alternative_wajsberg_axiom +11595: Order: +11595: lpo +11595: Leaf order: +11595: falsehood 1 0 0 +11595: and_star 7 2 0 +11595: and 9 2 0 +11595: or 10 2 0 +11595: not 12 1 0 +11595: implies 14 2 0 +11595: xor 7 2 4 0,2 +11595: y 2 0 2 2,2,2 +11595: truth 6 0 2 1,2,2 +11595: x 2 0 2 1,2 +Statistics : +Max weight : 25 +Found proof, 7.279985s +% SZS status Unsatisfiable for LCL159-1.p +% SZS output start CNFRefutation for LCL159-1.p +Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12 +Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19 +Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112 +Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57 +Id : 17, {_}: not truth =>= falsehood [] by false_definition +Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15 +Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9 +Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32 +Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25 +Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41 +Id : 12, {_}: xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35 +Id : 207, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3 +Id : 212, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 207 at 1,3 +Id : 213, {_}: xor ?34 ?35 =>= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 212 with 207 at 2,3 +Id : 219, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 207 at 2 +Id : 220, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 219 with 207 at 3 +Id : 240, {_}: or truth ?463 =<= implies falsehood ?463 [463] by Super 6 with 17 at 1,3 +Id : 286, {_}: implies (implies ?477 falsehood) falsehood =>= implies (or truth ?477) ?477 [477] by Super 4 with 240 at 1,3 +Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2 +Id : 784, {_}: implies (implies ?990 truth) (implies ?991 (implies ?990 ?991)) =>= truth [991, 990] by Super 20 with 2 at 1,2,2 +Id : 785, {_}: implies (implies truth truth) (implies ?993 ?993) =>= truth [993] by Super 784 with 2 at 2,2,2 +Id : 818, {_}: implies truth (implies ?993 ?993) =>= truth [993] by Demod 785 with 2 at 1,2 +Id : 819, {_}: implies ?993 ?993 =>= truth [993] by Demod 818 with 2 at 2 +Id : 870, {_}: implies (implies (implies ?1070 ?1070) ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071, 1070] by Super 22 with 819 at 2,1,2,2 +Id : 898, {_}: implies (implies truth ?1071) (implies (implies ?1071 truth) truth) =>= truth [1071] by Demod 870 with 819 at 1,1,2 +Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3 +Id : 864, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 819 at 3 +Id : 899, {_}: implies (implies truth ?1071) truth =>= truth [1071] by Demod 898 with 864 at 2,2 +Id : 900, {_}: implies ?1071 truth =>= truth [1071] by Demod 899 with 2 at 1,2 +Id : 980, {_}: or ?1117 truth =>= truth [1117] by Super 6 with 900 at 3 +Id : 1078, {_}: or truth ?1157 =>= truth [1157] by Super 8 with 980 at 3 +Id : 1116, {_}: implies (implies ?477 falsehood) falsehood =>= implies truth ?477 [477] by Demod 286 with 1078 at 1,3 +Id : 1117, {_}: implies (implies ?477 falsehood) falsehood =>= ?477 [477] by Demod 1116 with 2 at 3 +Id : 218, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 207 at 2 +Id : 239, {_}: and_star truth ?461 =<= not (or falsehood (not ?461)) [461] by Super 218 with 17 at 1,1,3 +Id : 517, {_}: or (or falsehood (not ?805)) ?806 =<= implies (and_star truth ?805) ?806 [806, 805] by Super 6 with 239 at 1,3 +Id : 1565, {_}: or falsehood (or (not ?1468) ?1469) =<= implies (and_star truth ?1468) ?1469 [1469, 1468] by Demod 517 with 7 at 2 +Id : 1566, {_}: or falsehood (or (not ?1471) ?1472) =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Super 1565 with 220 at 1,3 +Id : 525, {_}: or falsehood (or (not ?805) ?806) =<= implies (and_star truth ?805) ?806 [806, 805] by Demod 517 with 7 at 2 +Id : 520, {_}: and_star truth ?814 =<= not (or falsehood (not ?814)) [814] by Super 218 with 17 at 1,1,3 +Id : 521, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 520 with 17 at 2,1,3 +Id : 564, {_}: or (or falsehood falsehood) ?828 =<= implies (and_star truth truth) ?828 [828] by Super 6 with 521 at 1,3 +Id : 589, {_}: or falsehood (or falsehood ?828) =<= implies (and_star truth truth) ?828 [828] by Demod 564 with 7 at 2 +Id : 1273, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 1117 with 589 at 1,2 +Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2 +Id : 241, {_}: implies (or ?465 falsehood) (implies truth ?465) =>= truth [465] by Super 69 with 17 at 2,1,2 +Id : 260, {_}: implies (or ?465 falsehood) ?465 =>= truth [465] by Demod 241 with 2 at 2,2 +Id : 1322, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 1117 with 260 at 1,2 +Id : 1344, {_}: falsehood =<= or falsehood falsehood [] by Demod 1322 with 2 at 2 +Id : 1375, {_}: or falsehood ?1348 =<= or falsehood (or falsehood ?1348) [1348] by Super 7 with 1344 at 1,2 +Id : 2080, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 1273 with 1375 at 1,2 +Id : 2081, {_}: truth =<= and_star truth truth [] by Demod 2080 with 260 at 2 +Id : 2088, {_}: or falsehood (or (not truth) ?1976) =<= implies truth ?1976 [1976] by Super 525 with 2081 at 1,3 +Id : 2092, {_}: or falsehood (or falsehood ?1976) =<= implies truth ?1976 [1976] by Demod 2088 with 17 at 1,2,2 +Id : 2093, {_}: or falsehood (or falsehood ?1976) =>= ?1976 [1976] by Demod 2092 with 2 at 3 +Id : 2094, {_}: or falsehood ?1976 =>= ?1976 [1976] by Demod 2093 with 1375 at 2 +Id : 2619, {_}: or (not ?1471) ?1472 =<= implies (and_star ?1471 truth) ?1472 [1472, 1471] by Demod 1566 with 2094 at 2 +Id : 2636, {_}: implies (or (not ?2581) falsehood) falsehood =>= and_star ?2581 truth [2581] by Super 1117 with 2619 at 1,2 +Id : 2658, {_}: implies (or falsehood (not ?2581)) falsehood =>= and_star ?2581 truth [2581] by Demod 2636 with 8 at 1,2 +Id : 2659, {_}: implies (not ?2581) falsehood =>= and_star ?2581 truth [2581] by Demod 2658 with 2094 at 1,2 +Id : 2660, {_}: or ?2581 falsehood =>= and_star ?2581 truth [2581] by Demod 2659 with 6 at 2 +Id : 1407, {_}: or falsehood ?1358 =<= or falsehood (or falsehood ?1358) [1358] by Super 7 with 1344 at 1,2 +Id : 1408, {_}: or falsehood ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Super 1407 with 8 at 2,3 +Id : 2132, {_}: ?1360 =<= or falsehood (or ?1360 falsehood) [1360] by Demod 1408 with 2094 at 2 +Id : 2133, {_}: ?1360 =<= or ?1360 falsehood [1360] by Demod 2132 with 2094 at 3 +Id : 2661, {_}: ?2581 =<= and_star ?2581 truth [2581] by Demod 2660 with 2133 at 2 +Id : 2708, {_}: or (not ?1471) ?1472 =<= implies ?1471 ?1472 [1472, 1471] by Demod 2619 with 2661 at 1,3 +Id : 2725, {_}: or (not (implies ?477 falsehood)) falsehood =>= ?477 [477] by Demod 1117 with 2708 at 2 +Id : 2726, {_}: or (not (or (not ?477) falsehood)) falsehood =>= ?477 [477] by Demod 2725 with 2708 at 1,1,2 +Id : 2767, {_}: or falsehood (not (or (not ?477) falsehood)) =>= ?477 [477] by Demod 2726 with 8 at 2 +Id : 2768, {_}: not (or (not ?477) falsehood) =>= ?477 [477] by Demod 2767 with 2094 at 2 +Id : 2769, {_}: not (or falsehood (not ?477)) =>= ?477 [477] by Demod 2768 with 8 at 1,2 +Id : 2770, {_}: not (not ?477) =>= ?477 [477] by Demod 2769 with 2094 at 1,2 +Id : 2131, {_}: and_star truth ?461 =<= not (not ?461) [461] by Demod 239 with 2094 at 1,3 +Id : 2771, {_}: and_star truth ?477 =>= ?477 [477] by Demod 2770 with 2131 at 2 +Id : 563, {_}: and_star (or falsehood falsehood) ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Super 218 with 521 at 1,1,3 +Id : 3108, {_}: and_star falsehood ?826 =<= not (or (and_star truth truth) (not ?826)) [826] by Demod 563 with 2094 at 1,2 +Id : 3109, {_}: and_star falsehood ?826 =<= not (or truth (not ?826)) [826] by Demod 3108 with 2771 at 1,1,3 +Id : 3110, {_}: and_star falsehood ?826 =?= not truth [826] by Demod 3109 with 1078 at 1,3 +Id : 3111, {_}: and_star falsehood ?826 =>= falsehood [826] by Demod 3110 with 17 at 3 +Id : 2777, {_}: ?461 =<= not (not ?461) [461] by Demod 2131 with 2771 at 2 +Id : 3185, {_}: or (and_star y x) (and_star (not y) (not x)) === or (and_star y x) (and_star (not y) (not x)) [] by Demod 3184 with 220 at 1,2 +Id : 3184, {_}: or (and_star x y) (and_star (not y) (not x)) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3183 with 8 at 2 +Id : 3183, {_}: or (and_star (not y) (not x)) (and_star x y) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3182 with 2777 at 2,2,2 +Id : 3182, {_}: or (and_star (not y) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3181 with 2094 at 1,1,2 +Id : 3181, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star y x) (and_star (not y) (not x)) [] by Demod 3180 with 8 at 3 +Id : 3180, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (not y))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3179 with 2094 at 1,2,2,2 +Id : 3179, {_}: or (and_star (or falsehood (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3178 with 3111 at 1,1,1,2 +Id : 3178, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =>= or (and_star (not y) (not x)) (and_star y x) [] by Demod 3177 with 2777 at 2,2,3 +Id : 3177, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or falsehood (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3176 with 3111 at 1,1,2,2,2 +Id : 3176, {_}: or (and_star (or (and_star falsehood y) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3175 with 220 at 1,1,1,2 +Id : 3175, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (not x))) [] by Demod 3174 with 2094 at 1,2,2,3 +Id : 3174, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (not x)) (and_star y (not (or falsehood (not x)))) [] by Demod 3173 with 2094 at 2,1,3 +Id : 3173, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star falsehood y) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3172 with 220 at 1,1,2,2,2 +Id : 3172, {_}: or (and_star (or (and_star y falsehood) (not y)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3171 with 8 at 1,1,2 +Id : 3171, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or falsehood (not x)))) [] by Demod 3170 with 3111 at 1,1,2,2,3 +Id : 3170, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or falsehood (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3169 with 3111 at 1,2,1,3 +Id : 3169, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (and_star y falsehood) (not y)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3168 with 8 at 1,2,2,2 +Id : 3168, {_}: or (and_star (or (not y) (and_star y falsehood)) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3167 with 17 at 2,2,1,1,2 +Id : 3167, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (not x)))) [] by Demod 3166 with 2771 at 2,1,2,2,3 +Id : 3166, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star falsehood x) (and_star truth (not x))))) [] by Demod 3165 with 220 at 1,1,2,2,3 +Id : 3165, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (not x))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3164 with 2771 at 2,2,1,3 +Id : 3164, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star falsehood x) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3163 with 220 at 1,2,1,3 +Id : 3163, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y falsehood)))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3162 with 17 at 2,2,1,2,2,2 +Id : 3162, {_}: or (and_star (or (not y) (and_star y (not truth))) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3161 with 220 at 2,1,1,2 +Id : 3161, {_}: or (and_star (or (not y) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3160 with 2771 at 1,1,1,2 +Id : 3160, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star truth (not x))))) [] by Demod 3159 with 220 at 2,1,2,2,3 +Id : 3159, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x falsehood) (and_star (not x) truth)))) [] by Demod 3158 with 17 at 2,1,1,2,2,3 +Id : 3158, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star truth (not x)))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3157 with 220 at 2,2,1,3 +Id : 3157, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x falsehood) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3156 with 17 at 2,1,2,1,3 +Id : 3156, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star y (not truth))))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3155 with 220 at 2,1,2,2,2 +Id : 3155, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (not y) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3154 with 2771 at 1,1,2,2,2 +Id : 3154, {_}: or (and_star (or (and_star truth (not y)) (and_star (not truth) y)) (not x)) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3153 with 220 at 1,2 +Id : 3153, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (or (and_star x (not truth)) (and_star (not x) truth)))) [] by Demod 3152 with 213 at 1,2,2,3 +Id : 3152, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (or (and_star x (not truth)) (and_star (not x) truth))) (and_star y (not (xor x truth))) [] by Demod 3151 with 213 at 2,1,3 +Id : 3151, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (or (and_star truth (not y)) (and_star (not truth) y)))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3150 with 213 at 1,2,2,2 +Id : 3150, {_}: or (and_star (not x) (or (and_star truth (not y)) (and_star (not truth) y))) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3149 with 213 at 2,1,2 +Id : 3149, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star y (not (xor x truth))) [] by Demod 3148 with 220 at 2,3 +Id : 3148, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (not y) (xor x truth)) (and_star (not (xor x truth)) y) [] by Demod 3147 with 220 at 1,3 +Id : 3147, {_}: or (and_star (not x) (xor truth y)) (and_star x (not (xor truth y))) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3146 with 8 at 2 +Id : 3146, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= or (and_star (xor x truth) (not y)) (and_star (not (xor x truth)) y) [] by Demod 3145 with 213 at 3 +Id : 3145, {_}: or (and_star x (not (xor truth y))) (and_star (not x) (xor truth y)) =<= xor (xor x truth) y [] by Demod 1 with 213 at 2 +Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom +% SZS output end CNFRefutation for LCL159-1.p +11595: solved LCL159-1.p in 3.608225 using lpo +11595: status Unsatisfiable for LCL159-1.p +NO CLASH, using fixed ground order +11600: Facts: +11600: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11600: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11600: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11600: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11600: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11600: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11600: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11600: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11600: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11600: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11600: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11600: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11600: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11600: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11600: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11600: Goal: +11600: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +11600: Order: +11600: nrkbo +11600: Leaf order: +11600: commutator 1 2 0 +11600: additive_inverse 6 1 0 +11600: multiply 22 2 0 +11600: additive_identity 8 0 0 +11600: associator 4 3 3 0,2 +11600: add 18 2 2 0,3,2 +11600: v 2 0 2 2,3,2 +11600: u 2 0 2 1,3,2 +11600: y 3 0 3 2,2 +11600: x 3 0 3 1,2 +NO CLASH, using fixed ground order +11601: Facts: +11601: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11601: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11601: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11601: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11601: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11601: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11601: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11601: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11601: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11601: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11601: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11601: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11601: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11601: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11601: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11601: Goal: +11601: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +11601: Order: +11601: kbo +11601: Leaf order: +11601: commutator 1 2 0 +11601: additive_inverse 6 1 0 +11601: multiply 22 2 0 +11601: additive_identity 8 0 0 +11601: associator 4 3 3 0,2 +11601: add 18 2 2 0,3,2 +11601: v 2 0 2 2,3,2 +11601: u 2 0 2 1,3,2 +11601: y 3 0 3 2,2 +11601: x 3 0 3 1,2 +NO CLASH, using fixed ground order +11602: Facts: +11602: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11602: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11602: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11602: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11602: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11602: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11602: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11602: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11602: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11602: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11602: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11602: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11602: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11602: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11602: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11602: Goal: +11602: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +11602: Order: +11602: lpo +11602: Leaf order: +11602: commutator 1 2 0 +11602: additive_inverse 6 1 0 +11602: multiply 22 2 0 +11602: additive_identity 8 0 0 +11602: associator 4 3 3 0,2 +11602: add 18 2 2 0,3,2 +11602: v 2 0 2 2,3,2 +11602: u 2 0 2 1,3,2 +11602: y 3 0 3 2,2 +11602: x 3 0 3 1,2 +% SZS status Timeout for RNG019-6.p +NO CLASH, using fixed ground order +11618: Facts: +11618: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11618: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11618: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11618: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11618: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11618: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11618: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11618: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11618: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11618: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11618: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11618: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11618: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11618: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11618: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11618: Goal: +11618: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +11618: Order: +11618: nrkbo +11618: Leaf order: +11618: commutator 1 2 0 +11618: additive_inverse 6 1 0 +11618: multiply 22 2 0 +11618: additive_identity 8 0 0 +11618: associator 4 3 3 0,2 +11618: y 3 0 3 3,2 +11618: x 3 0 3 2,2 +11618: add 18 2 2 0,1,2 +11618: v 2 0 2 2,1,2 +11618: u 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11619: Facts: +11619: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11619: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11619: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11619: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11619: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11619: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11619: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11619: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11619: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11619: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11619: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11619: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11619: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11619: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11619: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11619: Goal: +11619: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +11619: Order: +11619: kbo +11619: Leaf order: +11619: commutator 1 2 0 +11619: additive_inverse 6 1 0 +11619: multiply 22 2 0 +11619: additive_identity 8 0 0 +11619: associator 4 3 3 0,2 +11619: y 3 0 3 3,2 +11619: x 3 0 3 2,2 +11619: add 18 2 2 0,1,2 +11619: v 2 0 2 2,1,2 +11619: u 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11620: Facts: +11620: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11620: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11620: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11620: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11620: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11620: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11620: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11620: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11620: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11620: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11620: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11620: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11620: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11620: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11620: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11620: Goal: +11620: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +11620: Order: +11620: lpo +11620: Leaf order: +11620: commutator 1 2 0 +11620: additive_inverse 6 1 0 +11620: multiply 22 2 0 +11620: additive_identity 8 0 0 +11620: associator 4 3 3 0,2 +11620: y 3 0 3 3,2 +11620: x 3 0 3 2,2 +11620: add 18 2 2 0,1,2 +11620: v 2 0 2 2,1,2 +11620: u 2 0 2 1,1,2 +% SZS status Timeout for RNG021-6.p +NO CLASH, using fixed ground order +11722: Facts: +11722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11722: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11722: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11722: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11722: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11722: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11722: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11722: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11722: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11722: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11722: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11722: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11722: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11722: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11722: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11722: Goal: +11722: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +11722: Order: +11722: nrkbo +11722: Leaf order: +11722: commutator 1 2 0 +11722: additive_inverse 6 1 0 +11722: multiply 22 2 0 +11722: add 16 2 0 +11722: additive_identity 9 0 1 3 +11722: associator 2 3 1 0,2 +11722: y 1 0 1 2,2 +11722: x 2 0 2 1,2 +NO CLASH, using fixed ground order +11723: Facts: +11723: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11723: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11723: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11723: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11723: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11723: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11723: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11723: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11723: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11723: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11723: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11723: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11723: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11723: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11723: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11723: Goal: +11723: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +11723: Order: +11723: kbo +11723: Leaf order: +11723: commutator 1 2 0 +11723: additive_inverse 6 1 0 +11723: multiply 22 2 0 +11723: add 16 2 0 +11723: additive_identity 9 0 1 3 +11723: associator 2 3 1 0,2 +11723: y 1 0 1 2,2 +11723: x 2 0 2 1,2 +NO CLASH, using fixed ground order +11724: Facts: +11724: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11724: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11724: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11724: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11724: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11724: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11724: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11724: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11724: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11724: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11724: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11724: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11724: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11724: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11724: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11724: Goal: +11724: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +11724: Order: +11724: lpo +11724: Leaf order: +11724: commutator 1 2 0 +11724: additive_inverse 6 1 0 +11724: multiply 22 2 0 +11724: add 16 2 0 +11724: additive_identity 9 0 1 3 +11724: associator 2 3 1 0,2 +11724: y 1 0 1 2,2 +11724: x 2 0 2 1,2 +% SZS status Timeout for RNG025-6.p +NO CLASH, using fixed ground order +11740: Facts: +11740: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +11740: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +11740: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +11740: Id : 5, {_}: add c c =>= c [] by idempotence +11740: Goal: +11740: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +11740: Order: +11740: nrkbo +11740: Leaf order: +11740: c 3 0 0 +11740: add 13 2 3 0,2 +11740: negate 9 1 5 0,1,2 +11740: b 3 0 3 1,2,1,1,2 +11740: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11741: Facts: +11741: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +11741: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +11741: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +11741: Id : 5, {_}: add c c =>= c [] by idempotence +11741: Goal: +11741: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +11741: Order: +11741: kbo +11741: Leaf order: +11741: c 3 0 0 +11741: add 13 2 3 0,2 +11741: negate 9 1 5 0,1,2 +11741: b 3 0 3 1,2,1,1,2 +11741: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +11742: Facts: +11742: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +11742: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +11742: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +11742: Id : 5, {_}: add c c =>= c [] by idempotence +11742: Goal: +11742: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +11742: Order: +11742: lpo +11742: Leaf order: +11742: c 3 0 0 +11742: add 13 2 3 0,2 +11742: negate 9 1 5 0,1,2 +11742: b 3 0 3 1,2,1,1,2 +11742: a 2 0 2 1,1,1,2 +% SZS status Timeout for ROB005-1.p +NO CLASH, using fixed ground order +11769: Facts: +11769: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +11769: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9 +11769: Id : 4, {_}: + multiply (inverse ?11) ?11 ?12 =>= ?12 + [12, 11] by left_inverse ?11 ?12 +11769: Id : 5, {_}: + multiply ?14 ?15 (inverse ?15) =>= ?14 + [15, 14] by right_inverse ?14 ?15 +11769: Goal: +11769: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant +11769: Order: +11769: nrkbo +11769: Leaf order: +11769: inverse 2 1 0 +11769: multiply 9 3 1 0,2 +11769: x 3 0 3 2,2 +11769: y 1 0 1 1,2 +NO CLASH, using fixed ground order +11770: Facts: +11770: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +11770: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9 +11770: Id : 4, {_}: + multiply (inverse ?11) ?11 ?12 =>= ?12 + [12, 11] by left_inverse ?11 ?12 +11770: Id : 5, {_}: + multiply ?14 ?15 (inverse ?15) =>= ?14 + [15, 14] by right_inverse ?14 ?15 +11770: Goal: +11770: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant +11770: Order: +11770: kbo +11770: Leaf order: +11770: inverse 2 1 0 +11770: multiply 9 3 1 0,2 +11770: x 3 0 3 2,2 +11770: y 1 0 1 1,2 +NO CLASH, using fixed ground order +11771: Facts: +11771: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +11771: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9 +11771: Id : 4, {_}: + multiply (inverse ?11) ?11 ?12 =>= ?12 + [12, 11] by left_inverse ?11 ?12 +11771: Id : 5, {_}: + multiply ?14 ?15 (inverse ?15) =>= ?14 + [15, 14] by right_inverse ?14 ?15 +11771: Goal: +11771: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant +11771: Order: +11771: lpo +11771: Leaf order: +11771: inverse 2 1 0 +11771: multiply 9 3 1 0,2 +11771: x 3 0 3 2,2 +11771: y 1 0 1 1,2 +% SZS status Timeout for BOO019-1.p +CLASH, statistics insufficient +11791: Facts: +11791: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +11791: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +11791: Id : 4, {_}: + multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10 + [11, 10] by b1 ?10 ?11 +11791: Id : 5, {_}: + multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13 + [14, 13] by majority1 ?13 ?14 +11791: Id : 6, {_}: + multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16 + [17, 16] by majority2 ?16 ?17 +11791: Id : 7, {_}: + multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20 + [20, 19] by majority3 ?19 ?20 +11791: Goal: +11791: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11791: Order: +11791: nrkbo +11791: Leaf order: +11791: add 11 2 0 +11791: multiply 11 2 0 +11791: inverse 3 1 2 0,2 +11791: a 2 0 2 1,1,2 +CLASH, statistics insufficient +11792: Facts: +11792: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +11792: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +11792: Id : 4, {_}: + multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10 + [11, 10] by b1 ?10 ?11 +11792: Id : 5, {_}: + multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13 + [14, 13] by majority1 ?13 ?14 +11792: Id : 6, {_}: + multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16 + [17, 16] by majority2 ?16 ?17 +11792: Id : 7, {_}: + multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20 + [20, 19] by majority3 ?19 ?20 +11792: Goal: +11792: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11792: Order: +11792: kbo +11792: Leaf order: +11792: add 11 2 0 +11792: multiply 11 2 0 +11792: inverse 3 1 2 0,2 +11792: a 2 0 2 1,1,2 +CLASH, statistics insufficient +11793: Facts: +11793: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +11793: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +11793: Id : 4, {_}: + multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10 + [11, 10] by b1 ?10 ?11 +11793: Id : 5, {_}: + multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13 + [14, 13] by majority1 ?13 ?14 +11793: Id : 6, {_}: + multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16 + [17, 16] by majority2 ?16 ?17 +11793: Id : 7, {_}: + multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20 + [20, 19] by majority3 ?19 ?20 +11793: Goal: +11793: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11793: Order: +11793: lpo +11793: Leaf order: +11793: add 11 2 0 +11793: multiply 11 2 0 +11793: inverse 3 1 2 0,2 +11793: a 2 0 2 1,1,2 +% SZS status Timeout for BOO030-1.p +CLASH, statistics insufficient +11822: Facts: +11822: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +11822: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +11822: Id : 4, {_}: + multiply (add ?10 (inverse ?10)) ?11 =>= ?11 + [11, 10] by property3 ?10 ?11 +11822: Id : 5, {_}: + multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13 + [15, 14, 13] by l2 ?13 ?14 ?15 +11822: Id : 6, {_}: + multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18 + [19, 18, 17] by l4 ?17 ?18 ?19 +11822: Id : 7, {_}: + add (multiply ?21 (inverse ?21)) ?22 =>= ?22 + [22, 21] by property3_dual ?21 ?22 +11822: Id : 8, {_}: + add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24 + [25, 24] by majority1 ?24 ?25 +11822: Id : 9, {_}: + add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27 + [28, 27] by majority2 ?27 ?28 +11822: Id : 10, {_}: + add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31 + [31, 30] by majority3 ?30 ?31 +11822: Id : 11, {_}: + multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33 + [34, 33] by majority1_dual ?33 ?34 +11822: Id : 12, {_}: + multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36 + [37, 36] by majority2_dual ?36 ?37 +11822: Id : 13, {_}: + multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40 + [40, 39] by majority3_dual ?39 ?40 +11822: Goal: +11822: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11822: Order: +11822: lpo +11822: Leaf order: +11822: add 21 2 0 +11822: multiply 21 2 0 +11822: inverse 4 1 2 0,2 +11822: a 2 0 2 1,1,2 +CLASH, statistics insufficient +11821: Facts: +11821: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +11821: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +11821: Id : 4, {_}: + multiply (add ?10 (inverse ?10)) ?11 =>= ?11 + [11, 10] by property3 ?10 ?11 +11821: Id : 5, {_}: + multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13 + [15, 14, 13] by l2 ?13 ?14 ?15 +11821: Id : 6, {_}: + multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18 + [19, 18, 17] by l4 ?17 ?18 ?19 +11821: Id : 7, {_}: + add (multiply ?21 (inverse ?21)) ?22 =>= ?22 + [22, 21] by property3_dual ?21 ?22 +11821: Id : 8, {_}: + add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24 + [25, 24] by majority1 ?24 ?25 +11821: Id : 9, {_}: + add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27 + [28, 27] by majority2 ?27 ?28 +11821: Id : 10, {_}: + add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31 + [31, 30] by majority3 ?30 ?31 +11821: Id : 11, {_}: + multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33 + [34, 33] by majority1_dual ?33 ?34 +11821: Id : 12, {_}: + multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36 + [37, 36] by majority2_dual ?36 ?37 +11821: Id : 13, {_}: + multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40 + [40, 39] by majority3_dual ?39 ?40 +11821: Goal: +11821: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11821: Order: +11821: kbo +11821: Leaf order: +11821: add 21 2 0 +11821: multiply 21 2 0 +11821: inverse 4 1 2 0,2 +11821: a 2 0 2 1,1,2 +CLASH, statistics insufficient +11820: Facts: +11820: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +11820: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +11820: Id : 4, {_}: + multiply (add ?10 (inverse ?10)) ?11 =>= ?11 + [11, 10] by property3 ?10 ?11 +11820: Id : 5, {_}: + multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13 + [15, 14, 13] by l2 ?13 ?14 ?15 +11820: Id : 6, {_}: + multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18 + [19, 18, 17] by l4 ?17 ?18 ?19 +11820: Id : 7, {_}: + add (multiply ?21 (inverse ?21)) ?22 =>= ?22 + [22, 21] by property3_dual ?21 ?22 +11820: Id : 8, {_}: + add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24 + [25, 24] by majority1 ?24 ?25 +11820: Id : 9, {_}: + add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27 + [28, 27] by majority2 ?27 ?28 +11820: Id : 10, {_}: + add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31 + [31, 30] by majority3 ?30 ?31 +11820: Id : 11, {_}: + multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33 + [34, 33] by majority1_dual ?33 ?34 +11820: Id : 12, {_}: + multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36 + [37, 36] by majority2_dual ?36 ?37 +11820: Id : 13, {_}: + multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40 + [40, 39] by majority3_dual ?39 ?40 +11820: Goal: +11820: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11820: Order: +11820: nrkbo +11820: Leaf order: +11820: add 21 2 0 +11820: multiply 21 2 0 +11820: inverse 4 1 2 0,2 +11820: a 2 0 2 1,1,2 +% SZS status Timeout for BOO032-1.p +NO CLASH, using fixed ground order +11838: Facts: +11838: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =<= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +11838: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +11838: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +11838: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +11838: Id : 6, {_}: + multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17 + [18, 17] by majority1 ?17 ?18 +11838: Id : 7, {_}: + multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20 + [21, 20] by majority2 ?20 ?21 +11838: Id : 8, {_}: + multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24 + [24, 23] by majority3 ?23 ?24 +11838: Goal: +11838: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11838: Order: +11838: nrkbo +11838: Leaf order: +11838: add 15 2 0 multiply +11838: multiply 16 2 0 add +11838: inverse 3 1 2 0,2 +11838: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11839: Facts: +11839: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =<= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +11839: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +11839: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +11839: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +11839: Id : 6, {_}: + multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17 + [18, 17] by majority1 ?17 ?18 +11839: Id : 7, {_}: + multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20 + [21, 20] by majority2 ?20 ?21 +11839: Id : 8, {_}: + multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24 + [24, 23] by majority3 ?23 ?24 +11839: Goal: +11839: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11839: Order: +11839: kbo +11839: Leaf order: +11839: add 15 2 0 multiply +11839: multiply 16 2 0 add +11839: inverse 3 1 2 0,2 +11839: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +11840: Facts: +11840: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =<= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +11840: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +11840: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +11840: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +11840: Id : 6, {_}: + multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17 + [18, 17] by majority1 ?17 ?18 +11840: Id : 7, {_}: + multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20 + [21, 20] by majority2 ?20 ?21 +11840: Id : 8, {_}: + multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24 + [24, 23] by majority3 ?23 ?24 +11840: Goal: +11840: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +11840: Order: +11840: lpo +11840: Leaf order: +11840: add 15 2 0 multiply +11840: multiply 16 2 0 add +11840: inverse 3 1 2 0,2 +11840: a 2 0 2 1,1,2 +% SZS status Timeout for BOO033-1.p +NO CLASH, using fixed ground order +11868: Facts: +11868: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +11868: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +11868: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) + (apply (apply b (apply b w)) (apply (apply b b) b)) + [] by strong_fixed_point +11868: Goal: +11868: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +11868: Order: +11868: nrkbo +11868: Leaf order: +11868: w 4 0 0 +11868: b 7 0 0 +11868: apply 20 2 3 0,2 +11868: fixed_pt 3 0 3 2,2 +11868: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +11869: Facts: +11869: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +11869: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +11869: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) + (apply (apply b (apply b w)) (apply (apply b b) b)) + [] by strong_fixed_point +11869: Goal: +11869: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +11869: Order: +11869: kbo +11869: Leaf order: +11869: w 4 0 0 +11869: b 7 0 0 +11869: apply 20 2 3 0,2 +11869: fixed_pt 3 0 3 2,2 +11869: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +11870: Facts: +11870: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +11870: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +11870: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) + (apply (apply b (apply b w)) (apply (apply b b) b)) + [] by strong_fixed_point +11870: Goal: +11870: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +11870: Order: +11870: lpo +11870: Leaf order: +11870: w 4 0 0 +11870: b 7 0 0 +11870: apply 20 2 3 0,2 +11870: fixed_pt 3 0 3 2,2 +11870: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL003-20.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +11889: Facts: +11889: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +11889: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +11889: Goal: +11889: Id : 1, {_}: + apply + (apply + (apply (apply s (apply k (apply s (apply (apply s k) k)))) + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) + x) y + =>= + apply y (apply (apply x x) y) + [] by prove_u_combinator +11889: Order: +11889: kbo +11889: Leaf order: +11889: y 3 0 3 2,2 +11889: x 3 0 3 2,1,2 +11889: apply 25 2 17 0,2 +11889: k 8 0 7 1,2,1,1,1,2 +11889: s 7 0 6 1,1,1,1,2 +11888: Facts: +11888: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +11888: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +11888: Goal: +11888: Id : 1, {_}: + apply + (apply + (apply (apply s (apply k (apply s (apply (apply s k) k)))) + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) + x) y + =>= + apply y (apply (apply x x) y) + [] by prove_u_combinator +11888: Order: +11888: nrkbo +11888: Leaf order: +11888: y 3 0 3 2,2 +11888: x 3 0 3 2,1,2 +11888: apply 25 2 17 0,2 +11888: k 8 0 7 1,2,1,1,1,2 +11888: s 7 0 6 1,1,1,1,2 +NO CLASH, using fixed ground order +11890: Facts: +11890: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +11890: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +11890: Goal: +11890: Id : 1, {_}: + apply + (apply + (apply (apply s (apply k (apply s (apply (apply s k) k)))) + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) + x) y + =>= + apply y (apply (apply x x) y) + [] by prove_u_combinator +11890: Order: +11890: lpo +11890: Leaf order: +11890: y 3 0 3 2,2 +11890: x 3 0 3 2,1,2 +11890: apply 25 2 17 0,2 +11890: k 8 0 7 1,2,1,1,1,2 +11890: s 7 0 6 1,1,1,1,2 +Statistics : +Max weight : 29 +Found proof, 0.014068s +% SZS status Unsatisfiable for COL004-3.p +% SZS output start CNFRefutation for COL004-3.p +Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4 +Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2 +Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2 +Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2 +Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2 +Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2 +Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2 +Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2 +Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2 +Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2 +Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2 +Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator +% SZS output end CNFRefutation for COL004-3.p +11890: solved COL004-3.p in 0.020001 using lpo +11890: status Unsatisfiable for COL004-3.p +CLASH, statistics insufficient +11895: Facts: +11895: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +11895: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +11895: Goal: +11895: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1 +11895: Order: +11895: nrkbo +11895: Leaf order: +11895: w 1 0 0 +11895: s 1 0 0 +11895: apply 11 2 1 0,3 +11895: combinator 1 0 1 1,3 +CLASH, statistics insufficient +11896: Facts: +11896: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +11896: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +11896: Goal: +11896: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1 +11896: Order: +11896: kbo +11896: Leaf order: +11896: w 1 0 0 +11896: s 1 0 0 +11896: apply 11 2 1 0,3 +11896: combinator 1 0 1 1,3 +CLASH, statistics insufficient +11897: Facts: +11897: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +11897: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +11897: Goal: +11897: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1 +11897: Order: +11897: lpo +11897: Leaf order: +11897: w 1 0 0 +11897: s 1 0 0 +11897: apply 11 2 1 0,3 +11897: combinator 1 0 1 1,3 +% SZS status Timeout for COL005-1.p +CLASH, statistics insufficient +11929: Facts: +11929: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11929: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +11929: Id : 4, {_}: + apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 + [11, 10, 9] by v_definition ?9 ?10 ?11 +11929: Goal: +11929: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +11929: Order: +11929: nrkbo +11929: Leaf order: +11929: v 1 0 0 +11929: m 1 0 0 +11929: b 1 0 0 +11929: apply 15 2 3 0,2 +11929: f 3 1 3 0,2,2 +CLASH, statistics insufficient +11930: Facts: +11930: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11930: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +11930: Id : 4, {_}: + apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 + [11, 10, 9] by v_definition ?9 ?10 ?11 +11930: Goal: +11930: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +11930: Order: +11930: kbo +11930: Leaf order: +11930: v 1 0 0 +11930: m 1 0 0 +11930: b 1 0 0 +11930: apply 15 2 3 0,2 +11930: f 3 1 3 0,2,2 +CLASH, statistics insufficient +11931: Facts: +11931: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11931: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +11931: Id : 4, {_}: + apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10 + [11, 10, 9] by v_definition ?9 ?10 ?11 +11931: Goal: +11931: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +11931: Order: +11931: lpo +11931: Leaf order: +11931: v 1 0 0 +11931: m 1 0 0 +11931: b 1 0 0 +11931: apply 15 2 3 0,2 +11931: f 3 1 3 0,2,2 +Goal subsumed +Statistics : +Max weight : 78 +Found proof, 6.233757s +% SZS status Unsatisfiable for COL038-1.p +% SZS output start CNFRefutation for COL038-1.p +Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11 +Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49 +Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2 +Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2 +Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3 +Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3 +Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3 +Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3 +Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2 +Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3 +Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2 +Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3 +Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2 +Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2 +Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2 +Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2 +Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3 +Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2 +Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3 +Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2 +Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3 +Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2 +Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3 +Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2 +Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3 +Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3 +Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2 +Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2 +Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3 +Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3 +Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL038-1.p +11930: solved COL038-1.p in 3.116194 using kbo +11930: status Unsatisfiable for COL038-1.p +CLASH, statistics insufficient +11936: Facts: +11936: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +11936: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +11936: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11 +11936: Goal: +11936: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +11936: Order: +11936: nrkbo +11936: Leaf order: +11936: m 1 0 0 +11936: b 1 0 0 +11936: s 1 0 0 +11936: apply 16 2 3 0,2 +11936: f 3 1 3 0,2,2 +CLASH, statistics insufficient +11937: Facts: +11937: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +11937: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +11937: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11 +11937: Goal: +11937: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +11937: Order: +11937: kbo +11937: Leaf order: +11937: m 1 0 0 +11937: b 1 0 0 +11937: s 1 0 0 +11937: apply 16 2 3 0,2 +11937: f 3 1 3 0,2,2 +CLASH, statistics insufficient +11938: Facts: +11938: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +11938: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +11938: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11 +11938: Goal: +11938: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +11938: Order: +11938: lpo +11938: Leaf order: +11938: m 1 0 0 +11938: b 1 0 0 +11938: s 1 0 0 +11938: apply 16 2 3 0,2 +11938: f 3 1 3 0,2,2 +% SZS status Timeout for COL046-1.p +CLASH, statistics insufficient +11954: Facts: +11954: Id : 2, {_}: + apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4) + [4, 3] by l_definition ?3 ?4 +11954: Id : 3, {_}: + apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8) + [8, 7, 6] by q_definition ?6 ?7 ?8 +11954: Goal: +11954: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_model ?1 +11954: Order: +11954: nrkbo +11954: Leaf order: +11954: q 1 0 0 +11954: l 1 0 0 +11954: apply 12 2 3 0,2 +11954: f 3 1 3 0,2,2 +CLASH, statistics insufficient +11955: Facts: +11955: Id : 2, {_}: + apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4) + [4, 3] by l_definition ?3 ?4 +11955: Id : 3, {_}: + apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8) + [8, 7, 6] by q_definition ?6 ?7 ?8 +11955: Goal: +11955: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_model ?1 +11955: Order: +11955: kbo +11955: Leaf order: +11955: q 1 0 0 +11955: l 1 0 0 +11955: apply 12 2 3 0,2 +11955: f 3 1 3 0,2,2 +CLASH, statistics insufficient +11956: Facts: +11956: Id : 2, {_}: + apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4) + [4, 3] by l_definition ?3 ?4 +11956: Id : 3, {_}: + apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8) + [8, 7, 6] by q_definition ?6 ?7 ?8 +11956: Goal: +11956: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_model ?1 +11956: Order: +11956: lpo +11956: Leaf order: +11956: q 1 0 0 +11956: l 1 0 0 +11956: apply 12 2 3 0,2 +11956: f 3 1 3 0,2,2 +% SZS status Timeout for COL047-1.p +CLASH, statistics insufficient +11983: Facts: +11983: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11983: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11983: Goal: +11983: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (g ?1) (apply (f ?1) (h ?1)) + [1] by prove_q_combinator ?1 +11983: Order: +11983: nrkbo +11983: Leaf order: +11983: t 1 0 0 +11983: b 1 0 0 +11983: h 2 1 2 0,2,2 +11983: g 2 1 2 0,2,1,2 +11983: apply 13 2 5 0,2 +11983: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +11984: Facts: +11984: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11984: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11984: Goal: +11984: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (g ?1) (apply (f ?1) (h ?1)) + [1] by prove_q_combinator ?1 +11984: Order: +11984: kbo +11984: Leaf order: +11984: t 1 0 0 +11984: b 1 0 0 +11984: h 2 1 2 0,2,2 +11984: g 2 1 2 0,2,1,2 +11984: apply 13 2 5 0,2 +11984: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +11985: Facts: +11985: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11985: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11985: Goal: +11985: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (g ?1) (apply (f ?1) (h ?1)) + [1] by prove_q_combinator ?1 +11985: Order: +11985: lpo +11985: Leaf order: +11985: t 1 0 0 +11985: b 1 0 0 +11985: h 2 1 2 0,2,2 +11985: g 2 1 2 0,2,1,2 +11985: apply 13 2 5 0,2 +11985: f 2 1 2 0,2,1,1,2 +Goal subsumed +Statistics : +Max weight : 76 +Found proof, 1.436300s +% SZS status Unsatisfiable for COL060-1.p +% SZS output start CNFRefutation for COL060-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2 +Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1 +% SZS output end CNFRefutation for COL060-1.p +11983: solved COL060-1.p in 0.376023 using nrkbo +11983: status Unsatisfiable for COL060-1.p +CLASH, statistics insufficient +11990: Facts: +11990: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11990: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11990: Goal: +11990: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (f ?1) (apply (h ?1) (g ?1)) + [1] by prove_q1_combinator ?1 +11990: Order: +11990: nrkbo +11990: Leaf order: +11990: t 1 0 0 +11990: b 1 0 0 +11990: h 2 1 2 0,2,2 +11990: g 2 1 2 0,2,1,2 +11990: apply 13 2 5 0,2 +11990: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +11991: Facts: +11991: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11991: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11991: Goal: +11991: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (f ?1) (apply (h ?1) (g ?1)) + [1] by prove_q1_combinator ?1 +11991: Order: +11991: kbo +11991: Leaf order: +11991: t 1 0 0 +11991: b 1 0 0 +11991: h 2 1 2 0,2,2 +11991: g 2 1 2 0,2,1,2 +11991: apply 13 2 5 0,2 +11991: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +11992: Facts: +11992: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11992: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11992: Goal: +11992: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (f ?1) (apply (h ?1) (g ?1)) + [1] by prove_q1_combinator ?1 +11992: Order: +11992: lpo +11992: Leaf order: +11992: t 1 0 0 +11992: b 1 0 0 +11992: h 2 1 2 0,2,2 +11992: g 2 1 2 0,2,1,2 +11992: apply 13 2 5 0,2 +11992: f 2 1 2 0,2,1,1,2 +Goal subsumed +Statistics : +Max weight : 76 +Found proof, 2.573692s +% SZS status Unsatisfiable for COL061-1.p +% SZS output start CNFRefutation for COL061-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2 +Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1 +% SZS output end CNFRefutation for COL061-1.p +11990: solved COL061-1.p in 0.344021 using nrkbo +11990: status Unsatisfiable for COL061-1.p +CLASH, statistics insufficient +11997: Facts: +11997: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11997: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11997: Goal: +11997: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (h ?1)) (g ?1) + [1] by prove_c_combinator ?1 +11997: Order: +11997: nrkbo +11997: Leaf order: +11997: t 1 0 0 +11997: b 1 0 0 +11997: h 2 1 2 0,2,2 +11997: g 2 1 2 0,2,1,2 +11997: apply 13 2 5 0,2 +11997: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +11998: Facts: +11998: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11998: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11998: Goal: +11998: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (h ?1)) (g ?1) + [1] by prove_c_combinator ?1 +11998: Order: +11998: kbo +11998: Leaf order: +11998: t 1 0 0 +11998: b 1 0 0 +11998: h 2 1 2 0,2,2 +11998: g 2 1 2 0,2,1,2 +11998: apply 13 2 5 0,2 +11998: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +11999: Facts: +11999: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +11999: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +11999: Goal: +11999: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (h ?1)) (g ?1) + [1] by prove_c_combinator ?1 +11999: Order: +11999: lpo +11999: Leaf order: +11999: t 1 0 0 +11999: b 1 0 0 +11999: h 2 1 2 0,2,2 +11999: g 2 1 2 0,2,1,2 +11999: apply 13 2 5 0,2 +11999: f 2 1 2 0,2,1,1,2 +Goal subsumed +Statistics : +Max weight : 100 +Found proof, 3.178698s +% SZS status Unsatisfiable for COL062-1.p +% SZS output start CNFRefutation for COL062-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2 +Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2 +Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2 +Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1 +% SZS output end CNFRefutation for COL062-1.p +11997: solved COL062-1.p in 1.812113 using nrkbo +11997: status Unsatisfiable for COL062-1.p +CLASH, statistics insufficient +12004: Facts: +12004: Id : 2, {_}: + apply (apply (apply n ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?5) ?4) ?5 + [5, 4, 3] by n_definition ?3 ?4 ?5 +CLASH, statistics insufficient +12006: Facts: +12006: Id : 2, {_}: + apply (apply (apply n ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?5) ?4) ?5 + [5, 4, 3] by n_definition ?3 ?4 ?5 +12006: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +12006: Goal: +12006: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +12006: Order: +12006: lpo +12006: Leaf order: +12006: q 1 0 0 +12006: n 1 0 0 +12006: apply 14 2 3 0,2 +12006: f 3 1 3 0,2,2 +12004: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +12004: Goal: +12004: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +12004: Order: +12004: nrkbo +12004: Leaf order: +12004: q 1 0 0 +12004: n 1 0 0 +12004: apply 14 2 3 0,2 +12004: f 3 1 3 0,2,2 +CLASH, statistics insufficient +12005: Facts: +12005: Id : 2, {_}: + apply (apply (apply n ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?5) ?4) ?5 + [5, 4, 3] by n_definition ?3 ?4 ?5 +12005: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +12005: Goal: +12005: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +12005: Order: +12005: kbo +12005: Leaf order: +12005: q 1 0 0 +12005: n 1 0 0 +12005: apply 14 2 3 0,2 +12005: f 3 1 3 0,2,2 +% SZS status Timeout for COL071-1.p +CLASH, statistics insufficient +12093: Facts: +12093: Id : 2, {_}: + apply (apply (apply n1 ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?4) ?4) ?5 + [5, 4, 3] by n1_definition ?3 ?4 ?5 +12093: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +12093: Goal: +12093: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +12093: Order: +12093: nrkbo +12093: Leaf order: +12093: b 1 0 0 +12093: n1 1 0 0 +12093: apply 14 2 3 0,2 +12093: f 3 1 3 0,2,2 +CLASH, statistics insufficient +12094: Facts: +12094: Id : 2, {_}: + apply (apply (apply n1 ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?4) ?4) ?5 + [5, 4, 3] by n1_definition ?3 ?4 ?5 +12094: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +12094: Goal: +12094: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +12094: Order: +12094: kbo +12094: Leaf order: +12094: b 1 0 0 +12094: n1 1 0 0 +12094: apply 14 2 3 0,2 +12094: f 3 1 3 0,2,2 +CLASH, statistics insufficient +12095: Facts: +12095: Id : 2, {_}: + apply (apply (apply n1 ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?4) ?4) ?5 + [5, 4, 3] by n1_definition ?3 ?4 ?5 +12095: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +12095: Goal: +12095: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +12095: Order: +12095: lpo +12095: Leaf order: +12095: b 1 0 0 +12095: n1 1 0 0 +12095: apply 14 2 3 0,2 +12095: f 3 1 3 0,2,2 +% SZS status Timeout for COL073-1.p +NO CLASH, using fixed ground order +12117: Facts: +12117: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12117: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12117: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12117: Id : 5, {_}: + commutator ?10 ?11 + =<= + multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11)) + [11, 10] by name ?10 ?11 +12117: Id : 6, {_}: + commutator (commutator ?13 ?14) ?15 + =?= + commutator ?13 (commutator ?14 ?15) + [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15 +12117: Goal: +12117: Id : 1, {_}: + multiply a (commutator b c) =<= multiply (commutator b c) a + [] by prove_center +12117: Order: +12117: nrkbo +12117: Leaf order: +12117: inverse 3 1 0 +12117: identity 2 0 0 +12117: multiply 11 2 2 0,2 +12117: commutator 7 2 2 0,2,2 +12117: c 2 0 2 2,2,2 +12117: b 2 0 2 1,2,2 +12117: a 2 0 2 1,2 +NO CLASH, using fixed ground order +12118: Facts: +12118: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12118: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12118: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12118: Id : 5, {_}: + commutator ?10 ?11 + =<= + multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11)) + [11, 10] by name ?10 ?11 +12118: Id : 6, {_}: + commutator (commutator ?13 ?14) ?15 + =>= + commutator ?13 (commutator ?14 ?15) + [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15 +12118: Goal: +12118: Id : 1, {_}: + multiply a (commutator b c) =<= multiply (commutator b c) a + [] by prove_center +12118: Order: +12118: kbo +12118: Leaf order: +12118: inverse 3 1 0 +12118: identity 2 0 0 +12118: multiply 11 2 2 0,2 +12118: commutator 7 2 2 0,2,2 +12118: c 2 0 2 2,2,2 +12118: b 2 0 2 1,2,2 +12118: a 2 0 2 1,2 +NO CLASH, using fixed ground order +12119: Facts: +12119: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12119: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12119: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12119: Id : 5, {_}: + commutator ?10 ?11 + =>= + multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11)) + [11, 10] by name ?10 ?11 +12119: Id : 6, {_}: + commutator (commutator ?13 ?14) ?15 + =>= + commutator ?13 (commutator ?14 ?15) + [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15 +12119: Goal: +12119: Id : 1, {_}: + multiply a (commutator b c) =<= multiply (commutator b c) a + [] by prove_center +12119: Order: +12119: lpo +12119: Leaf order: +12119: inverse 3 1 0 +12119: identity 2 0 0 +12119: multiply 11 2 2 0,2 +12119: commutator 7 2 2 0,2,2 +12119: c 2 0 2 2,2,2 +12119: b 2 0 2 1,2,2 +12119: a 2 0 2 1,2 +% SZS status Timeout for GRP024-5.p +CLASH, statistics insufficient +12145: Facts: +12145: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12145: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12145: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12145: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +12145: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +12145: Id : 7, {_}: + inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) + [14, 13] by inverse_product_lemma ?13 ?14 +12145: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16 +12145: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18 +12145: Id : 10, {_}: + intersection ?20 ?21 =?= intersection ?21 ?20 + [21, 20] by intersection_commutative ?20 ?21 +CLASH, statistics insufficient +12146: Facts: +12146: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12146: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12146: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12146: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +12146: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +12146: Id : 7, {_}: + inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13) + [14, 13] by inverse_product_lemma ?13 ?14 +12146: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16 +12146: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18 +12146: Id : 10, {_}: + intersection ?20 ?21 =?= intersection ?21 ?20 + [21, 20] by intersection_commutative ?20 ?21 +12146: Id : 11, {_}: + union ?23 ?24 =?= union ?24 ?23 + [24, 23] by union_commutative ?23 ?24 +12146: Id : 12, {_}: + intersection ?26 (intersection ?27 ?28) + =<= + intersection (intersection ?26 ?27) ?28 + [28, 27, 26] by intersection_associative ?26 ?27 ?28 +12146: Id : 13, {_}: + union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 + [32, 31, 30] by union_associative ?30 ?31 ?32 +12146: Id : 14, {_}: + union (intersection ?34 ?35) ?35 =>= ?35 + [35, 34] by union_intersection_absorbtion ?34 ?35 +12146: Id : 15, {_}: + intersection (union ?37 ?38) ?38 =>= ?38 + [38, 37] by intersection_union_absorbtion ?37 ?38 +12146: Id : 16, {_}: + multiply ?40 (union ?41 ?42) + =>= + union (multiply ?40 ?41) (multiply ?40 ?42) + [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +12146: Id : 17, {_}: + multiply ?44 (intersection ?45 ?46) + =>= + intersection (multiply ?44 ?45) (multiply ?44 ?46) + [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +12146: Id : 18, {_}: + multiply (union ?48 ?49) ?50 + =>= + union (multiply ?48 ?50) (multiply ?49 ?50) + [50, 49, 48] by multiply_union2 ?48 ?49 ?50 +12146: Id : 19, {_}: + multiply (intersection ?52 ?53) ?54 + =>= + intersection (multiply ?52 ?54) (multiply ?53 ?54) + [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54 +12146: Id : 20, {_}: + positive_part ?56 =>= union ?56 identity + [56] by positive_part ?56 +12146: Id : 21, {_}: + negative_part ?58 =>= intersection ?58 identity + [58] by negative_part ?58 +12146: Goal: +12146: Id : 1, {_}: + multiply (positive_part a) (negative_part a) =>= a + [] by prove_product +12146: Order: +12146: lpo +12146: Leaf order: +12146: union 14 2 0 +12146: intersection 14 2 0 +12146: inverse 7 1 0 +12146: identity 6 0 0 +12146: multiply 21 2 1 0,2 +12146: negative_part 2 1 1 0,2,2 +12146: positive_part 2 1 1 0,1,2 +12146: a 3 0 3 1,1,2 +12145: Id : 11, {_}: + union ?23 ?24 =?= union ?24 ?23 + [24, 23] by union_commutative ?23 ?24 +12145: Id : 12, {_}: + intersection ?26 (intersection ?27 ?28) + =<= + intersection (intersection ?26 ?27) ?28 + [28, 27, 26] by intersection_associative ?26 ?27 ?28 +12145: Id : 13, {_}: + union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 + [32, 31, 30] by union_associative ?30 ?31 ?32 +12145: Id : 14, {_}: + union (intersection ?34 ?35) ?35 =>= ?35 + [35, 34] by union_intersection_absorbtion ?34 ?35 +12145: Id : 15, {_}: + intersection (union ?37 ?38) ?38 =>= ?38 + [38, 37] by intersection_union_absorbtion ?37 ?38 +12145: Id : 16, {_}: + multiply ?40 (union ?41 ?42) + =<= + union (multiply ?40 ?41) (multiply ?40 ?42) + [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +12145: Id : 17, {_}: + multiply ?44 (intersection ?45 ?46) + =<= + intersection (multiply ?44 ?45) (multiply ?44 ?46) + [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +12145: Id : 18, {_}: + multiply (union ?48 ?49) ?50 + =<= + union (multiply ?48 ?50) (multiply ?49 ?50) + [50, 49, 48] by multiply_union2 ?48 ?49 ?50 +12145: Id : 19, {_}: + multiply (intersection ?52 ?53) ?54 + =<= + intersection (multiply ?52 ?54) (multiply ?53 ?54) + [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54 +12145: Id : 20, {_}: + positive_part ?56 =<= union ?56 identity + [56] by positive_part ?56 +12145: Id : 21, {_}: + negative_part ?58 =<= intersection ?58 identity + [58] by negative_part ?58 +12145: Goal: +12145: Id : 1, {_}: + multiply (positive_part a) (negative_part a) =>= a + [] by prove_product +12145: Order: +12145: kbo +12145: Leaf order: +12145: union 14 2 0 +12145: intersection 14 2 0 +12145: inverse 7 1 0 +12145: identity 6 0 0 +12145: multiply 21 2 1 0,2 +12145: negative_part 2 1 1 0,2,2 +12145: positive_part 2 1 1 0,1,2 +12145: a 3 0 3 1,1,2 +CLASH, statistics insufficient +12144: Facts: +12144: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12144: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12144: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12144: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +12144: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +12144: Id : 7, {_}: + inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) + [14, 13] by inverse_product_lemma ?13 ?14 +12144: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16 +12144: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18 +12144: Id : 10, {_}: + intersection ?20 ?21 =?= intersection ?21 ?20 + [21, 20] by intersection_commutative ?20 ?21 +12144: Id : 11, {_}: + union ?23 ?24 =?= union ?24 ?23 + [24, 23] by union_commutative ?23 ?24 +12144: Id : 12, {_}: + intersection ?26 (intersection ?27 ?28) + =?= + intersection (intersection ?26 ?27) ?28 + [28, 27, 26] by intersection_associative ?26 ?27 ?28 +12144: Id : 13, {_}: + union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 + [32, 31, 30] by union_associative ?30 ?31 ?32 +12144: Id : 14, {_}: + union (intersection ?34 ?35) ?35 =>= ?35 + [35, 34] by union_intersection_absorbtion ?34 ?35 +12144: Id : 15, {_}: + intersection (union ?37 ?38) ?38 =>= ?38 + [38, 37] by intersection_union_absorbtion ?37 ?38 +12144: Id : 16, {_}: + multiply ?40 (union ?41 ?42) + =<= + union (multiply ?40 ?41) (multiply ?40 ?42) + [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +12144: Id : 17, {_}: + multiply ?44 (intersection ?45 ?46) + =<= + intersection (multiply ?44 ?45) (multiply ?44 ?46) + [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +12144: Id : 18, {_}: + multiply (union ?48 ?49) ?50 + =<= + union (multiply ?48 ?50) (multiply ?49 ?50) + [50, 49, 48] by multiply_union2 ?48 ?49 ?50 +12144: Id : 19, {_}: + multiply (intersection ?52 ?53) ?54 + =<= + intersection (multiply ?52 ?54) (multiply ?53 ?54) + [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54 +12144: Id : 20, {_}: + positive_part ?56 =<= union ?56 identity + [56] by positive_part ?56 +12144: Id : 21, {_}: + negative_part ?58 =<= intersection ?58 identity + [58] by negative_part ?58 +12144: Goal: +12144: Id : 1, {_}: + multiply (positive_part a) (negative_part a) =>= a + [] by prove_product +12144: Order: +12144: nrkbo +12144: Leaf order: +12144: union 14 2 0 +12144: intersection 14 2 0 +12144: inverse 7 1 0 +12144: identity 6 0 0 +12144: multiply 21 2 1 0,2 +12144: negative_part 2 1 1 0,2,2 +12144: positive_part 2 1 1 0,1,2 +12144: a 3 0 3 1,1,2 +Statistics : +Max weight : 15 +Found proof, 17.397670s +% SZS status Unsatisfiable for GRP114-1.p +% SZS output start CNFRefutation for GRP114-1.p +Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =<= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28 +Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35 +Id : 13, {_}: union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32 +Id : 235, {_}: multiply (union ?499 ?500) ?501 =<= union (multiply ?499 ?501) (multiply ?500 ?501) [501, 500, 499] by multiply_union2 ?499 ?500 ?501 +Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38 +Id : 195, {_}: multiply ?427 (intersection ?428 ?429) =<= intersection (multiply ?427 ?428) (multiply ?427 ?429) [429, 428, 427] by multiply_intersection1 ?427 ?428 ?429 +Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21 +Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58 +Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +Id : 7, {_}: inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) [14, 13] by inverse_product_lemma ?13 ?14 +Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24 +Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56 +Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +Id : 48, {_}: inverse (multiply ?104 ?105) =<= multiply (inverse ?105) (inverse ?104) [105, 104] by inverse_product_lemma ?104 ?105 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =>= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69 +Id : 28, {_}: multiply identity ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Super 26 with 3 at 1,2 +Id : 32, {_}: ?74 =<= multiply (inverse ?75) (multiply ?75 ?74) [75, 74] by Demod 28 with 2 at 2 +Id : 50, {_}: inverse (multiply (inverse ?109) ?110) =>= multiply (inverse ?110) ?109 [110, 109] by Super 48 with 6 at 2,3 +Id : 49, {_}: inverse (multiply identity ?107) =<= multiply (inverse ?107) identity [107] by Super 48 with 5 at 2,3 +Id : 835, {_}: inverse ?1371 =<= multiply (inverse ?1371) identity [1371] by Demod 49 with 2 at 1,2 +Id : 841, {_}: inverse (inverse ?1382) =<= multiply ?1382 identity [1382] by Super 835 with 6 at 1,3 +Id : 864, {_}: ?1382 =<= multiply ?1382 identity [1382] by Demod 841 with 6 at 2 +Id : 881, {_}: multiply ?1419 (union ?1420 identity) =?= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Super 16 with 864 at 2,3 +Id : 900, {_}: multiply ?1419 (positive_part ?1420) =<= union (multiply ?1419 ?1420) ?1419 [1420, 1419] by Demod 881 with 20 at 2,2 +Id : 2897, {_}: multiply ?3964 (positive_part ?3965) =<= union ?3964 (multiply ?3964 ?3965) [3965, 3964] by Demod 900 with 11 at 3 +Id : 2901, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union (inverse ?3975) identity [3975] by Super 2897 with 3 at 2,3 +Id : 2938, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= union identity (inverse ?3975) [3975] by Demod 2901 with 11 at 3 +Id : 296, {_}: union identity ?627 =>= positive_part ?627 [627] by Super 11 with 20 at 3 +Id : 2939, {_}: multiply (inverse ?3975) (positive_part ?3975) =>= positive_part (inverse ?3975) [3975] by Demod 2938 with 296 at 3 +Id : 2958, {_}: inverse (positive_part (inverse ?4028)) =<= multiply (inverse (positive_part ?4028)) ?4028 [4028] by Super 50 with 2939 at 1,2 +Id : 3609, {_}: ?4904 =<= multiply (inverse (inverse (positive_part ?4904))) (inverse (positive_part (inverse ?4904))) [4904] by Super 32 with 2958 at 2,3 +Id : 3661, {_}: ?4904 =<= inverse (multiply (positive_part (inverse ?4904)) (inverse (positive_part ?4904))) [4904] by Demod 3609 with 7 at 3 +Id : 52, {_}: inverse (multiply ?114 (inverse ?115)) =>= multiply ?115 (inverse ?114) [115, 114] by Super 48 with 6 at 1,3 +Id : 3662, {_}: ?4904 =<= multiply (positive_part ?4904) (inverse (positive_part (inverse ?4904))) [4904] by Demod 3661 with 52 at 3 +Id : 875, {_}: multiply ?1405 (intersection ?1406 identity) =?= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Super 17 with 864 at 2,3 +Id : 906, {_}: multiply ?1405 (negative_part ?1406) =<= intersection (multiply ?1405 ?1406) ?1405 [1406, 1405] by Demod 875 with 21 at 2,2 +Id : 3727, {_}: multiply ?5043 (negative_part ?5044) =<= intersection ?5043 (multiply ?5043 ?5044) [5044, 5043] by Demod 906 with 10 at 3 +Id : 40, {_}: multiply ?89 (inverse ?89) =>= identity [89] by Super 3 with 6 at 1,2 +Id : 3734, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= intersection ?5063 identity [5063] by Super 3727 with 40 at 2,3 +Id : 3782, {_}: multiply ?5063 (negative_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 3734 with 21 at 3 +Id : 201, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= intersection identity (multiply (inverse ?449) ?450) [450, 449] by Super 195 with 3 at 1,3 +Id : 311, {_}: intersection identity ?654 =>= negative_part ?654 [654] by Super 10 with 21 at 3 +Id : 8114, {_}: multiply (inverse ?449) (intersection ?449 ?450) =>= negative_part (multiply (inverse ?449) ?450) [450, 449] by Demod 201 with 311 at 3 +Id : 135, {_}: intersection ?38 (union ?37 ?38) =>= ?38 [37, 38] by Demod 15 with 10 at 2 +Id : 701, {_}: intersection ?1238 (positive_part ?1238) =>= ?1238 [1238] by Super 135 with 296 at 2,2 +Id : 241, {_}: multiply (union (inverse ?521) ?522) ?521 =>= union identity (multiply ?522 ?521) [522, 521] by Super 235 with 3 at 1,3 +Id : 8575, {_}: multiply (union (inverse ?10997) ?10998) ?10997 =>= positive_part (multiply ?10998 ?10997) [10998, 10997] by Demod 241 with 296 at 3 +Id : 699, {_}: union identity (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Super 13 with 296 at 1,3 +Id : 716, {_}: positive_part (union ?1233 ?1234) =>= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 699 with 296 at 2 +Id : 299, {_}: union ?634 (union ?635 identity) =>= positive_part (union ?634 ?635) [635, 634] by Super 13 with 20 at 3 +Id : 307, {_}: union ?634 (positive_part ?635) =<= positive_part (union ?634 ?635) [635, 634] by Demod 299 with 20 at 2,2 +Id : 1223, {_}: union ?1233 (positive_part ?1234) =<= union (positive_part ?1233) ?1234 [1234, 1233] by Demod 716 with 307 at 2 +Id : 2971, {_}: multiply (inverse ?4064) (positive_part ?4064) =>= positive_part (inverse ?4064) [4064] by Demod 2938 with 296 at 3 +Id : 121, {_}: union ?35 (intersection ?34 ?35) =>= ?35 [34, 35] by Demod 14 with 11 at 2 +Id : 700, {_}: positive_part (intersection ?1236 identity) =>= identity [1236] by Super 121 with 296 at 2 +Id : 715, {_}: positive_part (negative_part ?1236) =>= identity [1236] by Demod 700 with 21 at 1,2 +Id : 2976, {_}: multiply (inverse (negative_part ?4073)) identity =>= positive_part (inverse (negative_part ?4073)) [4073] by Super 2971 with 715 at 2,2 +Id : 3014, {_}: inverse (negative_part ?4073) =<= positive_part (inverse (negative_part ?4073)) [4073] by Demod 2976 with 864 at 2 +Id : 3035, {_}: union (inverse (negative_part ?4112)) (positive_part ?4113) =>= union (inverse (negative_part ?4112)) ?4113 [4113, 4112] by Super 1223 with 3014 at 1,3 +Id : 8597, {_}: multiply (union (inverse (negative_part ?11063)) ?11064) (negative_part ?11063) =>= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11064, 11063] by Super 8575 with 3035 at 1,2 +Id : 8560, {_}: multiply (union (inverse ?521) ?522) ?521 =>= positive_part (multiply ?522 ?521) [522, 521] by Demod 241 with 296 at 3 +Id : 8643, {_}: positive_part (multiply ?11064 (negative_part ?11063)) =<= positive_part (multiply (positive_part ?11064) (negative_part ?11063)) [11063, 11064] by Demod 8597 with 8560 at 2 +Id : 907, {_}: multiply ?1405 (negative_part ?1406) =<= intersection ?1405 (multiply ?1405 ?1406) [1406, 1405] by Demod 906 with 10 at 3 +Id : 8600, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part (multiply identity ?11072) [11072] by Super 8575 with 20 at 1,2 +Id : 8645, {_}: multiply (positive_part (inverse ?11072)) ?11072 =>= positive_part ?11072 [11072] by Demod 8600 with 2 at 1,3 +Id : 8660, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part (inverse ?11112)) (positive_part ?11112) [11112] by Super 907 with 8645 at 2,3 +Id : 8719, {_}: multiply (positive_part (inverse ?11112)) (negative_part ?11112) =>= intersection (positive_part ?11112) (positive_part (inverse ?11112)) [11112] by Demod 8660 with 10 at 3 +Id : 9585, {_}: positive_part (multiply (inverse ?11973) (negative_part ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Super 8643 with 8719 at 1,3 +Id : 3731, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection (inverse ?5054) identity [5054] by Super 3727 with 3 at 2,3 +Id : 3776, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= intersection identity (inverse ?5054) [5054] by Demod 3731 with 10 at 3 +Id : 3777, {_}: multiply (inverse ?5054) (negative_part ?5054) =>= negative_part (inverse ?5054) [5054] by Demod 3776 with 311 at 3 +Id : 9660, {_}: positive_part (negative_part (inverse ?11973)) =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9585 with 3777 at 1,2 +Id : 9661, {_}: identity =<= positive_part (intersection (positive_part ?11973) (positive_part (inverse ?11973))) [11973] by Demod 9660 with 715 at 2 +Id : 37105, {_}: intersection (intersection (positive_part ?38557) (positive_part (inverse ?38557))) identity =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Super 701 with 9661 at 2,2 +Id : 37338, {_}: intersection identity (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37105 with 10 at 2 +Id : 37339, {_}: negative_part (intersection (positive_part ?38557) (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37338 with 311 at 2 +Id : 314, {_}: intersection ?661 (intersection ?662 identity) =>= negative_part (intersection ?661 ?662) [662, 661] by Super 12 with 21 at 3 +Id : 321, {_}: intersection ?661 (negative_part ?662) =<= negative_part (intersection ?661 ?662) [662, 661] by Demod 314 with 21 at 2,2 +Id : 37340, {_}: intersection (positive_part ?38557) (negative_part (positive_part (inverse ?38557))) =>= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37339 with 321 at 2 +Id : 743, {_}: intersection identity (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Super 12 with 311 at 1,3 +Id : 757, {_}: negative_part (intersection ?1274 ?1275) =>= intersection (negative_part ?1274) ?1275 [1275, 1274] by Demod 743 with 311 at 2 +Id : 1432, {_}: intersection ?2159 (negative_part ?2160) =<= intersection (negative_part ?2159) ?2160 [2160, 2159] by Demod 757 with 321 at 2 +Id : 738, {_}: negative_part (union ?1265 identity) =>= identity [1265] by Super 135 with 311 at 2 +Id : 761, {_}: negative_part (positive_part ?1265) =>= identity [1265] by Demod 738 with 20 at 1,2 +Id : 1437, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= intersection identity ?2174 [2174, 2173] by Super 1432 with 761 at 1,3 +Id : 1472, {_}: intersection (positive_part ?2173) (negative_part ?2174) =>= negative_part ?2174 [2174, 2173] by Demod 1437 with 311 at 3 +Id : 37341, {_}: negative_part (positive_part (inverse ?38557)) =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37340 with 1472 at 2 +Id : 37342, {_}: identity =<= intersection (positive_part ?38557) (positive_part (inverse ?38557)) [38557] by Demod 37341 with 761 at 2 +Id : 37637, {_}: multiply (inverse (positive_part ?38828)) identity =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Super 8114 with 37342 at 2,2 +Id : 37769, {_}: inverse (positive_part ?38828) =<= negative_part (multiply (inverse (positive_part ?38828)) (positive_part (inverse ?38828))) [38828] by Demod 37637 with 864 at 2 +Id : 8675, {_}: multiply (positive_part (inverse ?11150)) ?11150 =>= positive_part ?11150 [11150] by Demod 8600 with 2 at 1,3 +Id : 8679, {_}: multiply (positive_part ?11157) (inverse ?11157) =>= positive_part (inverse ?11157) [11157] by Super 8675 with 6 at 1,1,2 +Id : 8754, {_}: inverse ?11202 =<= multiply (inverse (positive_part ?11202)) (positive_part (inverse ?11202)) [11202] by Super 32 with 8679 at 2,3 +Id : 37770, {_}: inverse (positive_part ?38828) =<= negative_part (inverse ?38828) [38828] by Demod 37769 with 8754 at 1,3 +Id : 37939, {_}: multiply ?5063 (inverse (positive_part ?5063)) =>= negative_part ?5063 [5063] by Demod 3782 with 37770 at 2,2 +Id : 8672, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part (inverse (inverse ?11144)))) [11144] by Super 52 with 8645 at 1,2 +Id : 8705, {_}: inverse (positive_part (inverse ?11144)) =<= multiply ?11144 (inverse (positive_part ?11144)) [11144] by Demod 8672 with 6 at 1,1,2,3 +Id : 37967, {_}: inverse (positive_part (inverse ?5063)) =>= negative_part ?5063 [5063] by Demod 37939 with 8705 at 2 +Id : 37970, {_}: ?4904 =<= multiply (positive_part ?4904) (negative_part ?4904) [4904] by Demod 3662 with 37967 at 2,3 +Id : 38259, {_}: a =?= a [] by Demod 1 with 37970 at 2 +Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product +% SZS output end CNFRefutation for GRP114-1.p +12145: solved GRP114-1.p in 5.996374 using kbo +12145: status Unsatisfiable for GRP114-1.p +NO CLASH, using fixed ground order +12157: Facts: +12157: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12157: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12157: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12157: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12157: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12157: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12157: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12157: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12157: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12157: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12157: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12157: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12157: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12157: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12157: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12157: Id : 17, {_}: inverse identity =>= identity [] by p19_1 +12157: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51 +12157: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p19_3 ?53 ?54 +12157: Goal: +12157: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +12157: Order: +12157: nrkbo +12157: Leaf order: +12157: inverse 7 1 0 +12157: multiply 21 2 1 0,3 +12157: greatest_lower_bound 14 2 1 0,2,3 +12157: least_upper_bound 14 2 1 0,1,3 +12157: identity 6 0 2 2,1,3 +12157: a 3 0 3 2 +NO CLASH, using fixed ground order +12158: Facts: +12158: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12158: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12158: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12158: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12158: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12158: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12158: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12158: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12158: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12158: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12158: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12158: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12158: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12158: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12158: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12158: Id : 17, {_}: inverse identity =>= identity [] by p19_1 +12158: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51 +12158: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p19_3 ?53 ?54 +12158: Goal: +12158: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +12158: Order: +12158: kbo +12158: Leaf order: +12158: inverse 7 1 0 +12158: multiply 21 2 1 0,3 +12158: greatest_lower_bound 14 2 1 0,2,3 +12158: least_upper_bound 14 2 1 0,1,3 +12158: identity 6 0 2 2,1,3 +12158: a 3 0 3 2 +NO CLASH, using fixed ground order +12159: Facts: +12159: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12159: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12159: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12159: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12159: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12159: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12159: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12159: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12159: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12159: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12159: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12159: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12159: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12159: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12159: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12159: Id : 17, {_}: inverse identity =>= identity [] by p19_1 +12159: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51 +12159: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p19_3 ?53 ?54 +12159: Goal: +12159: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +12159: Order: +12159: lpo +12159: Leaf order: +12159: inverse 7 1 0 +12159: multiply 21 2 1 0,3 +12159: greatest_lower_bound 14 2 1 0,2,3 +12159: least_upper_bound 14 2 1 0,1,3 +12159: identity 6 0 2 2,1,3 +12159: a 3 0 3 2 +% SZS status Timeout for GRP167-4.p +NO CLASH, using fixed ground order +12195: Facts: +12195: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12195: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12195: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12195: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12195: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12195: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12195: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12195: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12195: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12195: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12195: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12195: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12195: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12195: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12195: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12195: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1 +12195: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2 +12195: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3 +12195: Goal: +12195: Id : 1, {_}: + greatest_lower_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + greatest_lower_bound a (multiply b c) + [] by prove_p08b +12195: Order: +12195: nrkbo +12195: Leaf order: +12195: least_upper_bound 13 2 0 +12195: inverse 1 1 0 +12195: identity 8 0 0 +12195: greatest_lower_bound 21 2 5 0,2 +12195: multiply 21 2 3 0,2,1,2 +12195: c 4 0 3 2,2,1,2 +12195: b 4 0 3 1,2,1,2 +12195: a 5 0 4 1,1,2 +NO CLASH, using fixed ground order +12196: Facts: +12196: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12196: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12196: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12196: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12196: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12196: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12196: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12196: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12196: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12196: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12196: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12196: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12196: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12196: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12196: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12196: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1 +12196: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2 +12196: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3 +12196: Goal: +12196: Id : 1, {_}: + greatest_lower_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + greatest_lower_bound a (multiply b c) + [] by prove_p08b +12196: Order: +12196: kbo +12196: Leaf order: +12196: least_upper_bound 13 2 0 +12196: inverse 1 1 0 +12196: identity 8 0 0 +12196: greatest_lower_bound 21 2 5 0,2 +12196: multiply 21 2 3 0,2,1,2 +12196: c 4 0 3 2,2,1,2 +12196: b 4 0 3 1,2,1,2 +12196: a 5 0 4 1,1,2 +NO CLASH, using fixed ground order +12197: Facts: +12197: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12197: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12197: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12197: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12197: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12197: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12197: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12197: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12197: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12197: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12197: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12197: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12197: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12197: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12197: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12197: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1 +12197: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2 +12197: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3 +12197: Goal: +12197: Id : 1, {_}: + greatest_lower_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + greatest_lower_bound a (multiply b c) + [] by prove_p08b +12197: Order: +12197: lpo +12197: Leaf order: +12197: least_upper_bound 13 2 0 +12197: inverse 1 1 0 +12197: identity 8 0 0 +12197: greatest_lower_bound 21 2 5 0,2 +12197: multiply 21 2 3 0,2,1,2 +12197: c 4 0 3 2,2,1,2 +12197: b 4 0 3 1,2,1,2 +12197: a 5 0 4 1,1,2 +% SZS status Timeout for GRP177-2.p +NO CLASH, using fixed ground order +12224: Facts: +12224: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12224: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12224: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12224: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12224: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12224: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12224: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12224: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12224: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12224: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12224: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12224: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12224: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12224: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12224: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12224: Id : 17, {_}: inverse identity =>= identity [] by p18_1 +12224: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51 +12224: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p18_3 ?53 ?54 +12224: Goal: +12224: Id : 1, {_}: + least_upper_bound (inverse a) identity + =<= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +12224: Order: +12224: nrkbo +12224: Leaf order: +12224: multiply 20 2 0 +12224: greatest_lower_bound 14 2 1 0,1,3 +12224: least_upper_bound 14 2 1 0,2 +12224: identity 6 0 2 2,2 +12224: inverse 9 1 2 0,1,2 +12224: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12225: Facts: +12225: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12225: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12225: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12225: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12225: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12225: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12225: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12225: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12225: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +NO CLASH, using fixed ground order +12226: Facts: +12226: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12226: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12226: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12226: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12226: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12226: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12226: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12226: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12226: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12226: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12226: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12226: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12226: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12226: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12226: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12226: Id : 17, {_}: inverse identity =>= identity [] by p18_1 +12226: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51 +12226: Id : 19, {_}: + inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53) + [54, 53] by p18_3 ?53 ?54 +12226: Goal: +12226: Id : 1, {_}: + least_upper_bound (inverse a) identity + =<= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +12226: Order: +12226: lpo +12226: Leaf order: +12226: multiply 20 2 0 +12226: greatest_lower_bound 14 2 1 0,1,3 +12226: least_upper_bound 14 2 1 0,2 +12226: identity 6 0 2 2,2 +12226: inverse 9 1 2 0,1,2 +12226: a 2 0 2 1,1,2 +12225: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12225: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12225: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12225: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12225: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12225: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12225: Id : 17, {_}: inverse identity =>= identity [] by p18_1 +12225: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51 +12225: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p18_3 ?53 ?54 +12225: Goal: +12225: Id : 1, {_}: + least_upper_bound (inverse a) identity + =<= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +12225: Order: +12225: kbo +12225: Leaf order: +12225: multiply 20 2 0 +12225: greatest_lower_bound 14 2 1 0,1,3 +12225: least_upper_bound 14 2 1 0,2 +12225: identity 6 0 2 2,2 +12225: inverse 9 1 2 0,1,2 +12225: a 2 0 2 1,1,2 +% SZS status Timeout for GRP179-3.p +NO CLASH, using fixed ground order +12243: Facts: +12243: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12243: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12243: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12243: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12243: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12243: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12243: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12243: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12243: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12243: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12243: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12243: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12243: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12243: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12243: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12243: Id : 17, {_}: inverse identity =>= identity [] by p11_1 +12243: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51 +12243: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p11_3 ?53 ?54 +12243: Goal: +12243: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +12243: Order: +12243: nrkbo +12243: Leaf order: +12243: identity 4 0 0 +12243: least_upper_bound 14 2 1 0,3 +12243: multiply 22 2 2 0,2 +12243: inverse 8 1 1 0,1,2,2 +12243: greatest_lower_bound 14 2 1 0,1,1,2,2 +12243: b 3 0 3 2,1,1,2,2 +12243: a 3 0 3 1,2 +NO CLASH, using fixed ground order +12244: Facts: +12244: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12244: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12244: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12244: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12244: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12244: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12244: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12244: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12244: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12244: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12244: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12244: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12244: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12244: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12244: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12244: Id : 17, {_}: inverse identity =>= identity [] by p11_1 +12244: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51 +12244: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p11_3 ?53 ?54 +12244: Goal: +12244: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +12244: Order: +12244: kbo +12244: Leaf order: +12244: identity 4 0 0 +12244: least_upper_bound 14 2 1 0,3 +12244: multiply 22 2 2 0,2 +12244: inverse 8 1 1 0,1,2,2 +12244: greatest_lower_bound 14 2 1 0,1,1,2,2 +12244: b 3 0 3 2,1,1,2,2 +12244: a 3 0 3 1,2 +NO CLASH, using fixed ground order +12245: Facts: +12245: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12245: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12245: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12245: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12245: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12245: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12245: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12245: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12245: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12245: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12245: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12245: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12245: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12245: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12245: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12245: Id : 17, {_}: inverse identity =>= identity [] by p11_1 +12245: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51 +12245: Id : 19, {_}: + inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53) + [54, 53] by p11_3 ?53 ?54 +12245: Goal: +12245: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +12245: Order: +12245: lpo +12245: Leaf order: +12245: identity 4 0 0 +12245: least_upper_bound 14 2 1 0,3 +12245: multiply 22 2 2 0,2 +12245: inverse 8 1 1 0,1,2,2 +12245: greatest_lower_bound 14 2 1 0,1,1,2,2 +12245: b 3 0 3 2,1,1,2,2 +12245: a 3 0 3 1,2 +% SZS status Timeout for GRP180-2.p +CLASH, statistics insufficient +12274: Facts: +12274: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12274: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12274: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12274: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12274: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12274: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12274: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12274: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12274: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12274: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12274: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12274: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12274: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12274: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12274: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12274: Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +12274: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +12274: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12x_3 ?53 ?54 +12274: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_4 +12274: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +12274: Id : 22, {_}: + inverse (greatest_lower_bound ?58 ?59) + =<= + least_upper_bound (inverse ?58) (inverse ?59) + [59, 58] by p12x_6 ?58 ?59 +12274: Id : 23, {_}: + inverse (least_upper_bound ?61 ?62) + =<= + greatest_lower_bound (inverse ?61) (inverse ?62) + [62, 61] by p12x_7 ?61 ?62 +12274: Goal: +12274: Id : 1, {_}: a =>= b [] by prove_p12x +12274: Order: +12274: nrkbo +12274: Leaf order: +12274: c 4 0 0 +12274: least_upper_bound 17 2 0 +12274: greatest_lower_bound 17 2 0 +12274: inverse 13 1 0 +12274: multiply 20 2 0 +12274: identity 4 0 0 +12274: b 3 0 1 3 +12274: a 3 0 1 2 +CLASH, statistics insufficient +12275: Facts: +12275: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12275: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12275: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12275: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12275: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12275: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12275: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12275: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12275: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12275: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12275: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12275: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12275: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12275: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12275: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12275: Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +12275: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +12275: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12x_3 ?53 ?54 +12275: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_4 +12275: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +12275: Id : 22, {_}: + inverse (greatest_lower_bound ?58 ?59) + =<= + least_upper_bound (inverse ?58) (inverse ?59) + [59, 58] by p12x_6 ?58 ?59 +12275: Id : 23, {_}: + inverse (least_upper_bound ?61 ?62) + =<= + greatest_lower_bound (inverse ?61) (inverse ?62) + [62, 61] by p12x_7 ?61 ?62 +12275: Goal: +12275: Id : 1, {_}: a =>= b [] by prove_p12x +12275: Order: +12275: kbo +12275: Leaf order: +12275: c 4 0 0 +12275: least_upper_bound 17 2 0 +12275: greatest_lower_bound 17 2 0 +12275: inverse 13 1 0 +12275: multiply 20 2 0 +12275: identity 4 0 0 +12275: b 3 0 1 3 +12275: a 3 0 1 2 +CLASH, statistics insufficient +12276: Facts: +12276: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12276: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12276: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12276: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12276: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12276: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12276: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12276: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12276: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12276: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12276: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12276: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12276: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12276: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12276: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12276: Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +12276: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +12276: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12x_3 ?53 ?54 +12276: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_4 +12276: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +12276: Id : 22, {_}: + inverse (greatest_lower_bound ?58 ?59) + =>= + least_upper_bound (inverse ?58) (inverse ?59) + [59, 58] by p12x_6 ?58 ?59 +12276: Id : 23, {_}: + inverse (least_upper_bound ?61 ?62) + =>= + greatest_lower_bound (inverse ?61) (inverse ?62) + [62, 61] by p12x_7 ?61 ?62 +12276: Goal: +12276: Id : 1, {_}: a =>= b [] by prove_p12x +12276: Order: +12276: lpo +12276: Leaf order: +12276: c 4 0 0 +12276: least_upper_bound 17 2 0 +12276: greatest_lower_bound 17 2 0 +12276: inverse 13 1 0 +12276: multiply 20 2 0 +12276: identity 4 0 0 +12276: b 3 0 1 3 +12276: a 3 0 1 2 +Statistics : +Max weight : 16 +Found proof, 22.107626s +% SZS status Unsatisfiable for GRP181-4.p +% SZS output start CNFRefutation for GRP181-4.p +Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11 +Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4 +Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588 +Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930 +Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517 +Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8 +Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73 +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846 +Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3 +Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3 +Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3 +Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2 +Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3 +Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2 +Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3 +Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2 +Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3 +Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3 +Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3 +Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2 +Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3 +Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3 +Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3 +Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3 +Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3 +Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3 +Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2 +Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2 +Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3 +Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2 +Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3 +Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2 +Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3 +Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2 +Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2 +Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3 +Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3 +Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2 +Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3 +Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2 +Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3 +Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2 +Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2 +Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2 +Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3 +Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3 +Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2 +Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2 +Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3 +Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2 +Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3 +Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2 +Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3 +Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2 +Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2 +Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2 +Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3 +Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2 +Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2 +Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2 +Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2 +Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3 +Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2 +Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3 +Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3 +Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2 +Id : 1, {_}: a =>= b [] by prove_p12x +% SZS output end CNFRefutation for GRP181-4.p +12274: solved GRP181-4.p in 8.100505 using nrkbo +12274: status Unsatisfiable for GRP181-4.p +NO CLASH, using fixed ground order +12282: Facts: +12282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12282: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12282: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12282: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12282: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12282: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12282: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12282: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12282: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12282: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12282: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12282: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12282: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12282: Goal: +12282: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +12282: Order: +12282: kbo +12282: Leaf order: +12282: multiply 18 2 0 +12282: inverse 2 1 1 0,2,2 +12282: greatest_lower_bound 15 2 2 0,2 +12282: least_upper_bound 14 2 1 0,1,2 +12282: identity 5 0 3 2,1,2 +12282: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12283: Facts: +12283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12283: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12283: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12283: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12283: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12283: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12283: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12283: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12283: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12283: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12283: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12283: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12283: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12283: Goal: +12283: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +12283: Order: +12283: lpo +12283: Leaf order: +12283: multiply 18 2 0 +12283: inverse 2 1 1 0,2,2 +12283: greatest_lower_bound 15 2 2 0,2 +12283: least_upper_bound 14 2 1 0,1,2 +12283: identity 5 0 3 2,1,2 +12283: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12281: Facts: +12281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12281: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12281: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12281: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12281: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12281: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12281: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12281: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12281: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12281: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12281: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12281: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12281: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12281: Goal: +12281: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +12281: Order: +12281: nrkbo +12281: Leaf order: +12281: multiply 18 2 0 +12281: inverse 2 1 1 0,2,2 +12281: greatest_lower_bound 15 2 2 0,2 +12281: least_upper_bound 14 2 1 0,1,2 +12281: identity 5 0 3 2,1,2 +12281: a 2 0 2 1,1,2 +% SZS status Timeout for GRP183-1.p +NO CLASH, using fixed ground order +12310: Facts: +12310: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12310: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12310: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12310: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12310: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12310: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12310: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12310: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12310: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12310: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12310: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12310: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12310: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12310: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12310: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12310: Goal: +12310: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +12310: Order: +12310: nrkbo +12310: Leaf order: +12310: multiply 18 2 0 +12310: greatest_lower_bound 14 2 1 0,2 +12310: inverse 2 1 1 0,1,2,2 +12310: least_upper_bound 15 2 2 0,1,2 +12310: identity 5 0 3 2,1,2 +12310: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12311: Facts: +12311: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12311: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12311: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12311: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12311: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12311: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12311: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12311: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12311: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12311: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12311: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12311: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12311: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12311: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12311: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12311: Goal: +12311: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +12311: Order: +12311: kbo +12311: Leaf order: +12311: multiply 18 2 0 +12311: greatest_lower_bound 14 2 1 0,2 +12311: inverse 2 1 1 0,1,2,2 +12311: least_upper_bound 15 2 2 0,1,2 +12311: identity 5 0 3 2,1,2 +12311: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12312: Facts: +12312: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12312: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12312: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12312: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12312: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12312: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12312: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12312: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12312: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12312: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12312: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12312: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12312: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12312: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12312: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12312: Goal: +12312: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +12312: Order: +12312: lpo +12312: Leaf order: +12312: multiply 18 2 0 +12312: greatest_lower_bound 14 2 1 0,2 +12312: inverse 2 1 1 0,1,2,2 +12312: least_upper_bound 15 2 2 0,1,2 +12312: identity 5 0 3 2,1,2 +12312: a 2 0 2 1,1,2 +% SZS status Timeout for GRP183-3.p +NO CLASH, using fixed ground order +12349: Facts: +12349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12349: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12349: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12349: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12349: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12349: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12349: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12349: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12349: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12349: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12349: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12349: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12349: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12349: Id : 17, {_}: inverse identity =>= identity [] by p20x_1 +12349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51 +12349: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20x_3 ?53 ?54 +12349: Goal: +12349: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +12349: Order: +12349: nrkbo +12349: Leaf order: +12349: multiply 20 2 0 +12349: greatest_lower_bound 14 2 1 0,2 +12349: inverse 8 1 1 0,1,2,2 +12349: least_upper_bound 15 2 2 0,1,2 +12349: identity 7 0 3 2,1,2 +12349: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12350: Facts: +12350: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12350: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12350: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12350: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12350: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12350: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12350: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12350: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12350: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12350: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12350: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12350: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12350: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12350: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12350: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12350: Id : 17, {_}: inverse identity =>= identity [] by p20x_1 +12350: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51 +12350: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20x_3 ?53 ?54 +12350: Goal: +12350: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +12350: Order: +12350: kbo +12350: Leaf order: +12350: multiply 20 2 0 +12350: greatest_lower_bound 14 2 1 0,2 +12350: inverse 8 1 1 0,1,2,2 +12350: least_upper_bound 15 2 2 0,1,2 +12350: identity 7 0 3 2,1,2 +12350: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12351: Facts: +12351: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12351: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12351: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12351: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12351: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12351: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12351: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12351: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12351: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12351: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12351: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12351: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12351: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12351: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12351: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12351: Id : 17, {_}: inverse identity =>= identity [] by p20x_1 +12351: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51 +12351: Id : 19, {_}: + inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20x_3 ?53 ?54 +12351: Goal: +12351: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +12351: Order: +12351: lpo +12351: Leaf order: +12351: multiply 20 2 0 +12351: greatest_lower_bound 14 2 1 0,2 +12351: inverse 8 1 1 0,1,2,2 +12351: least_upper_bound 15 2 2 0,1,2 +12351: identity 7 0 3 2,1,2 +12351: a 2 0 2 1,1,2 +% SZS status Timeout for GRP183-4.p +NO CLASH, using fixed ground order +12378: Facts: +12378: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12378: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12378: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12378: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12378: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12378: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12378: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12378: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12378: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12378: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12378: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12378: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12378: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12378: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12378: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12378: Goal: +12378: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +12378: Order: +12378: nrkbo +12378: Leaf order: +12378: multiply 20 2 2 0,2 +12378: inverse 3 1 2 0,2,2 +12378: greatest_lower_bound 15 2 2 0,1,2,2 +12378: least_upper_bound 15 2 2 0,1,2 +12378: identity 6 0 4 2,1,2 +12378: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +12379: Facts: +12379: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12379: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12379: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12379: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12379: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12379: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12379: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12379: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12379: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12379: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12379: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12379: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12379: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12379: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12379: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12379: Goal: +12379: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +12379: Order: +12379: kbo +12379: Leaf order: +12379: multiply 20 2 2 0,2 +12379: inverse 3 1 2 0,2,2 +12379: greatest_lower_bound 15 2 2 0,1,2,2 +12379: least_upper_bound 15 2 2 0,1,2 +12379: identity 6 0 4 2,1,2 +12379: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +12380: Facts: +12380: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12380: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12380: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12380: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12380: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12380: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12380: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12380: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12380: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12380: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12380: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12380: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12380: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12380: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12380: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12380: Goal: +12380: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +12380: Order: +12380: lpo +12380: Leaf order: +12380: multiply 20 2 2 0,2 +12380: inverse 3 1 2 0,2,2 +12380: greatest_lower_bound 15 2 2 0,1,2,2 +12380: least_upper_bound 15 2 2 0,1,2 +12380: identity 6 0 4 2,1,2 +12380: a 4 0 4 1,1,2 +% SZS status Timeout for GRP184-1.p +NO CLASH, using fixed ground order +12396: Facts: +12396: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12396: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12396: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12396: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12396: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12396: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12396: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12396: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12396: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12396: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12396: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12396: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12396: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12396: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12396: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12396: Goal: +12396: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21x +12396: Order: +12396: nrkbo +12396: Leaf order: +12396: multiply 20 2 2 0,2 +12396: inverse 3 1 2 0,2,2 +12396: greatest_lower_bound 15 2 2 0,1,2,2 +12396: least_upper_bound 15 2 2 0,1,2 +12396: identity 6 0 4 2,1,2 +12396: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +12397: Facts: +12397: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12397: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12397: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12397: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12397: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12397: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12397: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12397: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12397: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12397: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12397: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12397: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12397: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12397: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12397: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12397: Goal: +12397: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21x +12397: Order: +12397: kbo +12397: Leaf order: +12397: multiply 20 2 2 0,2 +12397: inverse 3 1 2 0,2,2 +12397: greatest_lower_bound 15 2 2 0,1,2,2 +12397: least_upper_bound 15 2 2 0,1,2 +12397: identity 6 0 4 2,1,2 +12397: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +12398: Facts: +12398: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12398: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12398: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12398: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12398: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12398: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12398: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12398: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12398: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12398: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12398: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12398: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12398: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12398: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12398: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12398: Goal: +12398: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21x +12398: Order: +12398: lpo +12398: Leaf order: +12398: multiply 20 2 2 0,2 +12398: inverse 3 1 2 0,2,2 +12398: greatest_lower_bound 15 2 2 0,1,2,2 +12398: least_upper_bound 15 2 2 0,1,2 +12398: identity 6 0 4 2,1,2 +12398: a 4 0 4 1,1,2 +% SZS status Timeout for GRP184-3.p +NO CLASH, using fixed ground order +12794: Facts: +12794: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12794: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12794: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12794: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12794: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12794: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12794: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12794: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12794: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12794: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12794: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12794: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12794: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12794: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12794: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12794: Goal: +12794: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +12794: Order: +12794: nrkbo +12794: Leaf order: +12794: inverse 1 1 0 +12794: greatest_lower_bound 14 2 1 0,2 +12794: least_upper_bound 17 2 4 0,1,2 +12794: identity 6 0 4 2,1,2 +12794: multiply 21 2 3 0,1,1,2 +12794: b 3 0 3 2,1,1,2 +12794: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +12795: Facts: +12795: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12795: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12795: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12795: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12795: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12795: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12795: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12795: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12795: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12795: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +NO CLASH, using fixed ground order +12796: Facts: +12796: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12796: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12796: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12796: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12796: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12796: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12796: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12796: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12796: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12796: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12796: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12795: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12795: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12795: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12795: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12795: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12795: Goal: +12795: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +12795: Order: +12795: kbo +12795: Leaf order: +12795: inverse 1 1 0 +12795: greatest_lower_bound 14 2 1 0,2 +12795: least_upper_bound 17 2 4 0,1,2 +12795: identity 6 0 4 2,1,2 +12795: multiply 21 2 3 0,1,1,2 +12795: b 3 0 3 2,1,1,2 +12795: a 3 0 3 1,1,1,2 +12796: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12796: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12796: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12796: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12796: Goal: +12796: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +12796: Order: +12796: lpo +12796: Leaf order: +12796: inverse 1 1 0 +12796: greatest_lower_bound 14 2 1 0,2 +12796: least_upper_bound 17 2 4 0,1,2 +12796: identity 6 0 4 2,1,2 +12796: multiply 21 2 3 0,1,1,2 +12796: b 3 0 3 2,1,1,2 +12796: a 3 0 3 1,1,1,2 +Statistics : +Max weight : 21 +Found proof, 1.752071s +% SZS status Unsatisfiable for GRP185-3.p +% SZS output start CNFRefutation for GRP185-3.p +Id : 120, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2 +Id : 436, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2 +Id : 438, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 436 with 3 at 2,3 +Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2 +Id : 444, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 436 with 27 at 2,3 +Id : 599, {_}: ?599 =<= multiply ?599 identity [599] by Demod 438 with 444 at 3 +Id : 63, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3 +Id : 894, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 120 with 6 at 2,2 +Id : 901, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 894 with 8 at 2,2 +Id : 2450, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2449 with 901 at 2 +Id : 2449, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2448 with 2 at 1,2,2,2,2 +Id : 2448, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2447 with 2 at 1,2,2,2 +Id : 2447, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2446 with 63 at 2,2,2 +Id : 2446, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2445 with 599 at 1,2,2 +Id : 2445, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2444 with 8 at 2,2 +Id : 2444, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2443 with 15 at 2,2,2 +Id : 2443, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2442 with 15 at 1,2,2 +Id : 2442, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2441 with 6 at 2,2 +Id : 2441, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2440 with 6 at 3 +Id : 2440, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2439 with 13 at 2,2 +Id : 2439, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2 +Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b +% SZS output end CNFRefutation for GRP185-3.p +12796: solved GRP185-3.p in 0.64804 using lpo +12796: status Unsatisfiable for GRP185-3.p +NO CLASH, using fixed ground order +12801: Facts: +12801: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12801: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12801: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12801: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12801: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12801: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12801: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12801: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12801: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12801: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12801: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12801: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12801: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12801: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12801: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12801: Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +12801: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +12801: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22b_3 ?53 ?54 +12801: Goal: +12801: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +12801: Order: +12801: nrkbo +12801: Leaf order: +12801: inverse 7 1 0 +12801: greatest_lower_bound 14 2 1 0,2 +12801: least_upper_bound 17 2 4 0,1,2 +12801: identity 8 0 4 2,1,2 +12801: multiply 23 2 3 0,1,1,2 +12801: b 3 0 3 2,1,1,2 +12801: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +12802: Facts: +12802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12802: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12802: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12802: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12802: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12802: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12802: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12802: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12802: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12802: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12802: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12802: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12802: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12802: Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +12802: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +12802: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22b_3 ?53 ?54 +12802: Goal: +12802: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +12802: Order: +12802: kbo +12802: Leaf order: +12802: inverse 7 1 0 +12802: greatest_lower_bound 14 2 1 0,2 +12802: least_upper_bound 17 2 4 0,1,2 +12802: identity 8 0 4 2,1,2 +12802: multiply 23 2 3 0,1,1,2 +12802: b 3 0 3 2,1,1,2 +12802: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +12803: Facts: +12803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12803: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12803: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12803: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12803: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12803: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12803: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12803: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12803: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12803: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12803: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12803: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12803: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12803: Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +12803: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +12803: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22b_3 ?53 ?54 +12803: Goal: +12803: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +12803: Order: +12803: lpo +12803: Leaf order: +12803: inverse 7 1 0 +12803: greatest_lower_bound 14 2 1 0,2 +12803: least_upper_bound 17 2 4 0,1,2 +12803: identity 8 0 4 2,1,2 +12803: multiply 23 2 3 0,1,1,2 +12803: b 3 0 3 2,1,1,2 +12803: a 3 0 3 1,1,1,2 +Statistics : +Max weight : 21 +Found proof, 2.993705s +% SZS status Unsatisfiable for GRP185-4.p +% SZS output start CNFRefutation for GRP185-4.p +Id : 123, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258 +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +Id : 382, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 383, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 382 with 17 at 2,3 +Id : 422, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 383 with 2 at 1,2 +Id : 424, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 422 with 18 at 1,3 +Id : 432, {_}: ?572 =<= multiply ?572 identity [572] by Demod 424 with 18 at 2 +Id : 66, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3 +Id : 766, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 123 with 6 at 2,2 +Id : 773, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 766 with 8 at 2,2 +Id : 4003, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 4002 with 773 at 2 +Id : 4002, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4001 with 2 at 1,2,2,2,2 +Id : 4001, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound b (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 4000 with 2 at 1,2,2,2 +Id : 4000, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity b) (least_upper_bound (multiply identity identity) (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3999 with 66 at 2,2,2 +Id : 3999, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound a (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3998 with 432 at 1,2,2 +Id : 3998, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a identity) (least_upper_bound (multiply identity identity) (least_upper_bound (multiply a b) (multiply identity b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 3997 with 8 at 2,2 +Id : 3997, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (least_upper_bound (multiply a b) (multiply identity b))) =>= least_upper_bound identity (multiply a b) [] by Demod 3996 with 15 at 2,2,2 +Id : 3996, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a identity) (multiply identity identity)) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3995 with 15 at 1,2,2 +Id : 3995, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) identity) (multiply (least_upper_bound a identity) b)) =>= least_upper_bound identity (multiply a b) [] by Demod 3994 with 6 at 2,2 +Id : 3994, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 3993 with 6 at 3 +Id : 3993, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 3992 with 13 at 2,2 +Id : 3992, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2 +Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b +% SZS output end CNFRefutation for GRP185-4.p +12803: solved GRP185-4.p in 0.988061 using lpo +12803: status Unsatisfiable for GRP185-4.p +NO CLASH, using fixed ground order +12808: Facts: +12808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12808: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12808: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12808: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12808: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12808: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12808: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12808: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12808: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12808: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12808: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12808: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12808: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12808: Id : 17, {_}: inverse identity =>= identity [] by p23_1 +12808: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51 +12808: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p23_3 ?53 ?54 +12808: Goal: +12808: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +12808: Order: +12808: nrkbo +12808: Leaf order: +12808: greatest_lower_bound 14 2 1 0,1,2,3 +12808: inverse 9 1 2 0,2,3 +12808: least_upper_bound 14 2 1 0,2 +12808: identity 5 0 1 2,2 +12808: multiply 22 2 2 0,1,2 +12808: b 2 0 2 2,1,2 +12808: a 3 0 3 1,1,2 +NO CLASH, using fixed ground order +12809: Facts: +12809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12809: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12809: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12809: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12809: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12809: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12809: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12809: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12809: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12809: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12809: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12809: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12809: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12809: Id : 17, {_}: inverse identity =>= identity [] by p23_1 +12809: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51 +12809: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p23_3 ?53 ?54 +12809: Goal: +12809: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +12809: Order: +12809: kbo +12809: Leaf order: +12809: greatest_lower_bound 14 2 1 0,1,2,3 +12809: inverse 9 1 2 0,2,3 +12809: least_upper_bound 14 2 1 0,2 +12809: identity 5 0 1 2,2 +12809: multiply 22 2 2 0,1,2 +12809: b 2 0 2 2,1,2 +12809: a 3 0 3 1,1,2 +NO CLASH, using fixed ground order +12810: Facts: +12810: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12810: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +12810: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +12810: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +12810: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +12810: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +12810: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +12810: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +12810: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +12810: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +12810: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +12810: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +12810: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +12810: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +12810: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +12810: Id : 17, {_}: inverse identity =>= identity [] by p23_1 +12810: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51 +12810: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p23_3 ?53 ?54 +12810: Goal: +12810: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +12810: Order: +12810: lpo +12810: Leaf order: +12810: greatest_lower_bound 14 2 1 0,1,2,3 +12810: inverse 9 1 2 0,2,3 +12810: least_upper_bound 14 2 1 0,2 +12810: identity 5 0 1 2,2 +12810: multiply 22 2 2 0,1,2 +12810: b 2 0 2 2,1,2 +12810: a 3 0 3 1,1,2 +% SZS status Timeout for GRP186-2.p +NO CLASH, using fixed ground order +12831: Facts: +12831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12831: Id : 3, {_}: + multiply (left_inverse ?4) ?4 =>= identity + [4] by left_inverse ?4 +12831: Id : 4, {_}: + multiply (multiply ?6 (multiply ?7 ?8)) ?6 + =?= + multiply (multiply ?6 ?7) (multiply ?8 ?6) + [8, 7, 6] by moufang1 ?6 ?7 ?8 +12831: Goal: +12831: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +12831: Order: +12831: nrkbo +12831: Leaf order: +12831: left_inverse 1 1 0 +12831: identity 2 0 0 +12831: c 2 0 2 2,1,2 +12831: multiply 14 2 6 0,2 +12831: b 4 0 4 2,1,1,2 +12831: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +12833: Facts: +12833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12833: Id : 3, {_}: + multiply (left_inverse ?4) ?4 =>= identity + [4] by left_inverse ?4 +12833: Id : 4, {_}: + multiply (multiply ?6 (multiply ?7 ?8)) ?6 + =>= + multiply (multiply ?6 ?7) (multiply ?8 ?6) + [8, 7, 6] by moufang1 ?6 ?7 ?8 +12833: Goal: +12833: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +12833: Order: +12833: lpo +12833: Leaf order: +12833: left_inverse 1 1 0 +12833: identity 2 0 0 +12833: c 2 0 2 2,1,2 +12833: multiply 14 2 6 0,2 +12833: b 4 0 4 2,1,1,2 +12833: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +12832: Facts: +12832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12832: Id : 3, {_}: + multiply (left_inverse ?4) ?4 =>= identity + [4] by left_inverse ?4 +12832: Id : 4, {_}: + multiply (multiply ?6 (multiply ?7 ?8)) ?6 + =>= + multiply (multiply ?6 ?7) (multiply ?8 ?6) + [8, 7, 6] by moufang1 ?6 ?7 ?8 +12832: Goal: +12832: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +12832: Order: +12832: kbo +12832: Leaf order: +12832: left_inverse 1 1 0 +12832: identity 2 0 0 +12832: c 2 0 2 2,1,2 +12832: multiply 14 2 6 0,2 +12832: b 4 0 4 2,1,1,2 +12832: a 2 0 2 1,1,1,2 +% SZS status Timeout for GRP204-1.p +CLASH, statistics insufficient +12860: Facts: +12860: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12860: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +12860: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +12860: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +12860: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +12860: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +12860: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +12860: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +12860: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =?= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +12860: Goal: +12860: Id : 1, {_}: + multiply x (multiply (multiply y z) x) + =<= + multiply (multiply x y) (multiply z x) + [] by prove_moufang4 +12860: Order: +12860: nrkbo +12860: Leaf order: +12860: left_inverse 1 1 0 +12860: right_inverse 1 1 0 +12860: right_division 2 2 0 +12860: left_division 2 2 0 +12860: identity 4 0 0 +12860: multiply 20 2 6 0,2 +12860: z 2 0 2 2,1,2,2 +12860: y 2 0 2 1,1,2,2 +12860: x 4 0 4 1,2 +CLASH, statistics insufficient +12861: Facts: +12861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12861: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +12861: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +12861: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +12861: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +12861: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +12861: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +12861: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +12861: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +12861: Goal: +12861: Id : 1, {_}: + multiply x (multiply (multiply y z) x) + =<= + multiply (multiply x y) (multiply z x) + [] by prove_moufang4 +12861: Order: +12861: kbo +12861: Leaf order: +12861: left_inverse 1 1 0 +12861: right_inverse 1 1 0 +12861: right_division 2 2 0 +12861: left_division 2 2 0 +12861: identity 4 0 0 +12861: multiply 20 2 6 0,2 +12861: z 2 0 2 2,1,2,2 +12861: y 2 0 2 1,1,2,2 +12861: x 4 0 4 1,2 +CLASH, statistics insufficient +12862: Facts: +12862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +12862: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +12862: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +12862: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +12862: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +12862: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +12862: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +12862: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +12862: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +12862: Goal: +12862: Id : 1, {_}: + multiply x (multiply (multiply y z) x) + =<= + multiply (multiply x y) (multiply z x) + [] by prove_moufang4 +12862: Order: +12862: lpo +12862: Leaf order: +12862: left_inverse 1 1 0 +12862: right_inverse 1 1 0 +12862: right_division 2 2 0 +12862: left_division 2 2 0 +12862: identity 4 0 0 +12862: multiply 20 2 6 0,2 +12862: z 2 0 2 2,1,2,2 +12862: y 2 0 2 1,1,2,2 +12862: x 4 0 4 1,2 +Statistics : +Max weight : 20 +Found proof, 29.150598s +% SZS status Unsatisfiable for GRP205-1.p +% SZS output start CNFRefutation for GRP205-1.p +Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128 +Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7 +Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20 +Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10 +Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18 +Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13 +Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24 +Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16 +Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2 +Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2 +Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2 +Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2 +Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2 +Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3 +Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2 +Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3 +Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3 +Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2 +Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2 +Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2 +Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2 +Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2 +Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2 +Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2 +Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2 +Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2 +Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3 +Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2 +Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2 +Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2 +Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2 +Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2 +Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2 +Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2 +Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3 +Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2 +Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3 +Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2 +Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2 +Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2 +Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2 +Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3 +Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3 +Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2 +Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2 +Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3 +Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2 +Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2 +Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3 +Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3 +Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3 +Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3 +Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3 +Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2 +Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3 +Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2 +Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2 +Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2 +Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2 +Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2 +Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3 +Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3 +Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2 +Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2 +Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3 +Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2 +Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3 +Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2 +Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2 +Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3 +Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2 +Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3 +Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2 +Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3 +Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2 +Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3 +Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3 +Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2 +Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2 +Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3 +Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2 +Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3 +Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2 +Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3 +Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3 +Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3 +Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2 +Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3 +Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3 +Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2 +Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3 +Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2 +Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2 +Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3 +Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3 +Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2 +Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2 +Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3 +Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2 +Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2 +Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2 +Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2 +Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2 +Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3 +Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2 +Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3 +Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2 +Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3 +Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2 +Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3 +Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3 +Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2 +Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2 +Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3 +Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2 +Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2 +Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2 +Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3 +Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2 +Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3 +Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2 +Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3 +Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2 +Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2 +Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3 +Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2 +Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3 +Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2 +Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3 +Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2 +Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2 +Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3 +Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3 +Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2 +Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2 +Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2 +Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3 +Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2 +Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2 +Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3 +Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2 +Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3 +Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3 +Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2 +Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2 +Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2 +Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3 +Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2 +Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3 +Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3 +Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3 +Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3 +Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4 +% SZS output end CNFRefutation for GRP205-1.p +12861: solved GRP205-1.p in 14.652915 using kbo +12861: status Unsatisfiable for GRP205-1.p +NO CLASH, using fixed ground order +12867: Facts: +12867: Id : 2, {_}: + multiply ?2 + (inverse + (multiply ?3 + (multiply + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?2 ?3))) ?2))) + =>= + ?2 + [4, 3, 2] by single_non_axiom ?2 ?3 ?4 +12867: Goal: +12867: Id : 1, {_}: + multiply x + (inverse + (multiply y + (multiply + (multiply (multiply z (inverse z)) (inverse (multiply u y))) + x))) + =>= + u + [] by try_prove_this_axiom +12867: Order: +12867: nrkbo +12867: Leaf order: +12867: u 2 0 2 1,1,2,1,2,1,2,2 +12867: multiply 12 2 6 0,2 +12867: inverse 6 1 3 0,2,2 +12867: z 2 0 2 1,1,1,2,1,2,2 +12867: y 2 0 2 1,1,2,2 +12867: x 2 0 2 1,2 +NO CLASH, using fixed ground order +12868: Facts: +12868: Id : 2, {_}: + multiply ?2 + (inverse + (multiply ?3 + (multiply + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?2 ?3))) ?2))) + =>= + ?2 + [4, 3, 2] by single_non_axiom ?2 ?3 ?4 +12868: Goal: +12868: Id : 1, {_}: + multiply x + (inverse + (multiply y + (multiply + (multiply (multiply z (inverse z)) (inverse (multiply u y))) + x))) + =>= + u + [] by try_prove_this_axiom +12868: Order: +12868: kbo +12868: Leaf order: +12868: u 2 0 2 1,1,2,1,2,1,2,2 +12868: multiply 12 2 6 0,2 +12868: inverse 6 1 3 0,2,2 +12868: z 2 0 2 1,1,1,2,1,2,2 +12868: y 2 0 2 1,1,2,2 +12868: x 2 0 2 1,2 +NO CLASH, using fixed ground order +12869: Facts: +12869: Id : 2, {_}: + multiply ?2 + (inverse + (multiply ?3 + (multiply + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?2 ?3))) ?2))) + =>= + ?2 + [4, 3, 2] by single_non_axiom ?2 ?3 ?4 +12869: Goal: +12869: Id : 1, {_}: + multiply x + (inverse + (multiply y + (multiply + (multiply (multiply z (inverse z)) (inverse (multiply u y))) + x))) + =>= + u + [] by try_prove_this_axiom +12869: Order: +12869: lpo +12869: Leaf order: +12869: u 2 0 2 1,1,2,1,2,1,2,2 +12869: multiply 12 2 6 0,2 +12869: inverse 6 1 3 0,2,2 +12869: z 2 0 2 1,1,1,2,1,2,2 +12869: y 2 0 2 1,1,2,2 +12869: x 2 0 2 1,2 +% SZS status Timeout for GRP207-1.p +Fatal error: exception Assert_failure("matitaprover.ml", 265, 46) +NO CLASH, using fixed ground order +12900: Facts: +12900: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +12900: Goal: +12900: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +12900: Order: +12900: nrkbo +12900: Leaf order: +12900: inverse 7 1 0 +12900: c3 2 0 2 2,2 +12900: multiply 10 2 4 0,2 +12900: b3 2 0 2 2,1,2 +12900: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12901: Facts: +12901: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +12901: Goal: +12901: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +12901: Order: +12901: kbo +12901: Leaf order: +12901: inverse 7 1 0 +12901: c3 2 0 2 2,2 +12901: multiply 10 2 4 0,2 +12901: b3 2 0 2 2,1,2 +12901: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12902: Facts: +12902: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +12902: Goal: +12902: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +12902: Order: +12902: lpo +12902: Leaf order: +12902: inverse 7 1 0 +12902: c3 2 0 2 2,2 +12902: multiply 10 2 4 0,2 +12902: b3 2 0 2 2,1,2 +12902: a3 2 0 2 1,1,2 +% SZS status Timeout for GRP420-1.p +NO CLASH, using fixed ground order +12949: Facts: +12949: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +12949: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +12949: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +12949: Goal: +12949: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +12949: Order: +12949: nrkbo +12949: Leaf order: +12949: inverse 1 1 0 +12949: divide 13 2 0 +12949: c3 2 0 2 2,2 +12949: multiply 5 2 4 0,2 +12949: b3 2 0 2 2,1,2 +12949: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12950: Facts: +12950: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +12950: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +12950: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +12950: Goal: +12950: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +12950: Order: +12950: kbo +12950: Leaf order: +12950: inverse 1 1 0 +12950: divide 13 2 0 +12950: c3 2 0 2 2,2 +12950: multiply 5 2 4 0,2 +12950: b3 2 0 2 2,1,2 +12950: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +12951: Facts: +12951: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +12951: Id : 3, {_}: + multiply ?6 ?7 =?= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +12951: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +12951: Goal: +12951: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +12951: Order: +12951: lpo +12951: Leaf order: +12951: inverse 1 1 0 +12951: divide 13 2 0 +12951: c3 2 0 2 2,2 +12951: multiply 5 2 4 0,2 +12951: b3 2 0 2 2,1,2 +12951: a3 2 0 2 1,1,2 +Statistics : +Max weight : 38 +Found proof, 2.410071s +% SZS status Unsatisfiable for GRP453-1.p +% SZS output start CNFRefutation for GRP453-1.p +Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91 +Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15 +Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11 +Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8 +Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3 +Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2 +Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2 +Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3 +Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3 +Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3 +Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3 +Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3 +Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3 +Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3 +Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2 +Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3 +Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2 +Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2 +Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2 +Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2 +Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3 +Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3 +Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2 +Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2 +Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3 +Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3 +Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2 +Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3 +Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3 +Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3 +Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2 +Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3 +Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2 +Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2 +Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2 +Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2 +Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3 +Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3 +Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2 +Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2 +Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2 +Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2 +Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2 +Id : 2653, {_}: inverse (inverse ?5844) =<= divide (multiply ?5844 (inverse (inverse ?5845))) ?5845 [5845, 5844] by Demod 1854 with 29 at 1,3 +Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2 +Id : 2679, {_}: inverse (inverse (inverse (inverse (divide ?5935 ?5935)))) =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Super 2653 with 224 at 1,3 +Id : 2732, {_}: divide ?5935 ?5935 =?= divide (inverse (inverse (inverse (inverse ?5936)))) ?5936 [5936, 5935] by Demod 2679 with 1559 at 2 +Id : 2733, {_}: divide ?5935 ?5935 =?= divide ?5936 ?5936 [5936, 5935] by Demod 2732 with 1559 at 1,3 +Id : 2794, {_}: divide (inverse (divide ?6115 (divide (inverse ?6116) (divide (inverse ?6115) ?6117)))) ?6117 =?= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6117, 6116, 6115] by Super 145 with 2733 at 2,1,3 +Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2 +Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2 +Id : 2869, {_}: inverse ?6116 =<= inverse (divide ?6116 (divide ?6118 ?6118)) [6118, 6116] by Demod 2794 with 31 at 2 +Id : 2925, {_}: divide ?6471 (divide ?6472 ?6472) =>= inverse (inverse (inverse (inverse ?6471))) [6472, 6471] by Super 1559 with 2869 at 1,1,1,3 +Id : 2977, {_}: divide ?6471 (divide ?6472 ?6472) =>= ?6471 [6472, 6471] by Demod 2925 with 1559 at 3 +Id : 3050, {_}: divide (inverse (divide ?6728 ?6729)) (divide ?6730 ?6730) =>= inverse (inverse (multiply ?6729 (inverse ?6728))) [6730, 6729, 6728] by Super 250 with 2977 at 2,1,1,3 +Id : 3110, {_}: inverse (divide ?6728 ?6729) =<= inverse (inverse (multiply ?6729 (inverse ?6728))) [6729, 6728] by Demod 3050 with 2977 at 2 +Id : 3383, {_}: inverse (divide ?7439 ?7440) =<= divide (inverse (inverse ?7440)) ?7439 [7440, 7439] by Demod 3110 with 936 at 3 +Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2 +Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3 +Id : 3111, {_}: inverse (divide ?6728 ?6729) =<= divide (inverse (inverse ?6729)) ?6728 [6729, 6728] by Demod 3110 with 936 at 3 +Id : 3340, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3111 at 1,1,3 +Id : 3404, {_}: inverse (divide ?7516 (inverse (divide ?7517 ?7518))) =>= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Super 3383 with 3340 at 1,3 +Id : 3497, {_}: inverse (multiply ?7516 (divide ?7517 ?7518)) =<= divide (multiply ?7518 (inverse ?7517)) ?7516 [7518, 7517, 7516] by Demod 3404 with 29 at 1,2 +Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3 +Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3 +Id : 3338, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3111 at 3 +Id : 3343, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3338 with 29 at 1,3 +Id : 3051, {_}: multiply ?6732 (divide ?6733 ?6733) =>= inverse (inverse ?6732) [6733, 6732] by Super 1825 with 2977 at 1,2 +Id : 3711, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3343 with 3051 at 1,3 +Id : 3714, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3711 at 2,2 +Id : 4200, {_}: inverse (multiply ?8647 (divide ?8648 ?8649)) =>= divide (divide ?8649 ?8648) ?8647 [8649, 8648, 8647] by Demod 3497 with 3714 at 1,3 +Id : 3401, {_}: inverse (divide ?7505 (inverse (inverse ?7506))) =>= divide ?7506 ?7505 [7506, 7505] by Super 3383 with 1559 at 1,3 +Id : 3496, {_}: inverse (multiply ?7505 (inverse ?7506)) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3401 with 29 at 1,2 +Id : 3715, {_}: inverse (divide ?7505 ?7506) =>= divide ?7506 ?7505 [7506, 7505] by Demod 3496 with 3714 at 1,2 +Id : 3725, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3715 at 1,2 +Id : 3337, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3111 at 2 +Id : 3721, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3337 with 3715 at 2 +Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2 +Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2 +Id : 3717, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3714 at 2 +Id : 3737, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3721 with 3717 at 2 +Id : 3738, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3725 with 3737 at 3 +Id : 4230, {_}: inverse (divide (divide ?8777 ?8778) ?8779) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8779, 8778, 8777] by Super 4200 with 3738 at 1,2 +Id : 4280, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (divide ?8779 (inverse ?8778)) ?8777 [8778, 8777, 8779] by Demod 4230 with 3715 at 2 +Id : 4281, {_}: divide ?8779 (divide ?8777 ?8778) =<= divide (multiply ?8779 ?8778) ?8777 [8778, 8777, 8779] by Demod 4280 with 29 at 1,3 +Id : 4962, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (divide (inverse ?10175) ?10174) [10175, 10174, 10173] by Super 29 with 4281 at 3 +Id : 4205, {_}: inverse (multiply ?8667 ?8668) =<= divide (divide (divide ?8669 ?8669) ?8668) ?8667 [8669, 8668, 8667] by Super 4200 with 2977 at 2,1,2 +Id : 4245, {_}: inverse (multiply ?8667 ?8668) =<= divide (inverse ?8668) ?8667 [8668, 8667] by Demod 4205 with 4 at 1,3 +Id : 5005, {_}: multiply (multiply ?10173 ?10174) ?10175 =<= divide ?10173 (inverse (multiply ?10174 ?10175)) [10175, 10174, 10173] by Demod 4962 with 4245 at 2,3 +Id : 5006, {_}: multiply (multiply ?10173 ?10174) ?10175 =>= multiply ?10173 (multiply ?10174 ?10175) [10175, 10174, 10173] by Demod 5005 with 29 at 3 +Id : 5130, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 5006 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP453-1.p +12950: solved GRP453-1.p in 1.216075 using kbo +12950: status Unsatisfiable for GRP453-1.p +Fatal error: exception Assert_failure("matitaprover.ml", 265, 46) +NO CLASH, using fixed ground order +12960: Facts: +12960: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +12960: Id : 3, {_}: + meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) + [7, 6, 5] by distribution ?5 ?6 ?7 +12960: Goal: +12960: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_associativity_of_join +12960: Order: +12960: nrkbo +12960: Leaf order: +12960: meet 4 2 0 +12960: c 2 0 2 2,2 +12960: join 7 2 4 0,2 +12960: b 2 0 2 2,1,2 +12960: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +12962: Facts: +12962: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +12962: Id : 3, {_}: + meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5) + [7, 6, 5] by distribution ?5 ?6 ?7 +12962: Goal: +12962: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_associativity_of_join +12962: Order: +12962: lpo +12962: Leaf order: +12962: meet 4 2 0 +12962: c 2 0 2 2,2 +12962: join 7 2 4 0,2 +12962: b 2 0 2 2,1,2 +12962: a 2 0 2 1,1,2 +12961: Facts: +12961: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +12961: Id : 3, {_}: + meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) + [7, 6, 5] by distribution ?5 ?6 ?7 +12961: Goal: +12961: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_associativity_of_join +12961: Order: +12961: kbo +12961: Leaf order: +12961: meet 4 2 0 +12961: c 2 0 2 2,2 +12961: join 7 2 4 0,2 +12961: b 2 0 2 2,1,2 +12961: a 2 0 2 1,1,2 +Statistics : +Max weight : 22 +Found proof, 37.088774s +% SZS status Unsatisfiable for LAT007-1.p +% SZS output start CNFRefutation for LAT007-1.p +Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7 +Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20 +Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3 +Id : 122, {_}: meet (meet ?274 ?275) (meet ?275 (join ?276 ?274)) =>= meet ?274 ?275 [276, 275, 274] by Super 2 with 3 at 2,2 +Id : 132, {_}: meet (meet ?317 ?318) ?318 =>= meet ?317 ?318 [318, 317] by Super 122 with 2 at 2,2 +Id : 166, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =<= join (meet ?382 ?380) (meet ?381 ?380) [382, 381, 380] by Super 3 with 132 at 1,3 +Id : 405, {_}: meet ?915 (join ?916 (meet ?917 ?915)) =>= meet ?915 (join ?916 ?917) [917, 916, 915] by Demod 166 with 3 at 3 +Id : 419, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =?= meet ?974 (join (meet ?976 ?974) ?975) [976, 975, 974] by Super 405 with 3 at 2,2 +Id : 165, {_}: meet ?376 (join (meet ?377 ?376) ?378) =<= join (meet ?378 ?376) (meet ?377 ?376) [378, 377, 376] by Super 3 with 132 at 2,3 +Id : 187, {_}: meet ?376 (join (meet ?377 ?376) ?378) =>= meet ?376 (join ?377 ?378) [378, 377, 376] by Demod 165 with 3 at 3 +Id : 473, {_}: meet ?1062 (meet ?1062 (join ?1063 ?1064)) =>= meet ?1062 (join ?1064 ?1063) [1064, 1063, 1062] by Demod 419 with 187 at 3 +Id : 484, {_}: meet ?1111 ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Super 473 with 2 at 2,2 +Id : 590, {_}: meet (join ?1333 ?1334) (join ?1333 ?1334) =>= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Super 8 with 484 at 1,3 +Id : 593, {_}: meet ?1344 ?1344 =>= ?1344 [1344] by Super 2 with 484 at 2 +Id : 2478, {_}: join ?1333 ?1334 =<= join (meet ?1334 ?1334) ?1333 [1334, 1333] by Demod 590 with 593 at 2 +Id : 2479, {_}: join ?1333 ?1334 =?= join ?1334 ?1333 [1334, 1333] by Demod 2478 with 593 at 1,3 +Id : 639, {_}: meet ?1436 (join ?1437 ?1436) =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Super 3 with 593 at 1,3 +Id : 631, {_}: ?1111 =<= meet ?1111 (join ?1112 ?1111) [1112, 1111] by Demod 484 with 593 at 2 +Id : 669, {_}: ?1436 =<= join ?1436 (meet ?1437 ?1436) [1437, 1436] by Demod 639 with 631 at 2 +Id : 53, {_}: meet (join ?112 ?113) (join ?112 ?114) =<= join (meet ?114 (join ?112 ?113)) ?112 [114, 113, 112] by Super 7 with 2 at 2,3 +Id : 62, {_}: meet (join ?150 ?151) (join ?150 ?150) =>= join ?150 ?150 [151, 150] by Super 53 with 2 at 1,3 +Id : 57, {_}: meet (join (meet ?128 ?129) (meet ?130 ?129)) (join (meet ?128 ?129) ?131) =>= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 130, 129, 128] by Super 53 with 3 at 2,1,3 +Id : 73, {_}: meet (meet ?129 (join ?130 ?128)) (join (meet ?128 ?129) ?131) =<= join (meet ?131 (meet ?129 (join ?130 ?128))) (meet ?128 ?129) [131, 128, 130, 129] by Demod 57 with 3 at 1,2 +Id : 642, {_}: meet (meet ?1444 (join ?1445 ?1444)) (join (meet ?1444 ?1444) ?1446) =>= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1446, 1445, 1444] by Super 73 with 593 at 2,3 +Id : 657, {_}: meet ?1444 (join (meet ?1444 ?1444) ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 642 with 631 at 1,2 +Id : 658, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 (meet ?1444 (join ?1445 ?1444))) ?1444 [1445, 1446, 1444] by Demod 657 with 593 at 1,2,2 +Id : 659, {_}: meet ?1444 (join ?1444 ?1446) =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 658 with 631 at 2,1,3 +Id : 699, {_}: ?1517 =<= join (meet ?1518 ?1517) ?1517 [1518, 1517] by Demod 659 with 2 at 2 +Id : 711, {_}: ?1557 =<= join ?1557 ?1557 [1557] by Super 699 with 593 at 1,3 +Id : 744, {_}: meet (join ?150 ?151) ?150 =>= join ?150 ?150 [151, 150] by Demod 62 with 711 at 2,2 +Id : 745, {_}: meet (join ?150 ?151) ?150 =>= ?150 [151, 150] by Demod 744 with 711 at 3 +Id : 713, {_}: join ?1562 ?1563 =<= join ?1563 (join ?1562 ?1563) [1563, 1562] by Super 699 with 631 at 1,3 +Id : 1157, {_}: meet (join ?2329 ?2330) ?2330 =>= ?2330 [2330, 2329] by Super 745 with 713 at 1,2 +Id : 1688, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= join (meet ?3264 ?3262) ?3262 [3264, 3263, 3262] by Super 3 with 1157 at 2,3 +Id : 660, {_}: ?1444 =<= join (meet ?1446 ?1444) ?1444 [1446, 1444] by Demod 659 with 2 at 2 +Id : 1738, {_}: meet ?3262 (join (join ?3263 ?3262) ?3264) =>= ?3262 [3264, 3263, 3262] by Demod 1688 with 660 at 3 +Id : 4104, {_}: join (join ?7363 ?7364) ?7365 =<= join (join (join ?7363 ?7364) ?7365) ?7364 [7365, 7364, 7363] by Super 669 with 1738 at 2,3 +Id : 9885, {_}: join (join ?18104 ?18105) ?18106 =<= join ?18105 (join (join ?18104 ?18105) ?18106) [18106, 18105, 18104] by Demod 4104 with 2479 at 3 +Id : 9889, {_}: join (join ?18120 ?18121) ?18122 =<= join ?18121 (join (join ?18121 ?18120) ?18122) [18122, 18121, 18120] by Super 9885 with 2479 at 1,2,3 +Id : 4118, {_}: meet ?7422 (join (join ?7423 ?7422) ?7424) =>= ?7422 [7424, 7423, 7422] by Demod 1688 with 660 at 3 +Id : 4122, {_}: meet ?7438 (join (join ?7438 ?7439) ?7440) =>= ?7438 [7440, 7439, 7438] by Super 4118 with 2479 at 1,2,2 +Id : 9604, {_}: join (join ?17475 ?17476) ?17477 =<= join (join (join ?17475 ?17476) ?17477) ?17475 [17477, 17476, 17475] by Super 669 with 4122 at 2,3 +Id : 9740, {_}: join (join ?17475 ?17476) ?17477 =<= join ?17475 (join (join ?17475 ?17476) ?17477) [17477, 17476, 17475] by Demod 9604 with 2479 at 3 +Id : 16688, {_}: join (join ?18120 ?18121) ?18122 =?= join (join ?18121 ?18120) ?18122 [18122, 18121, 18120] by Demod 9889 with 9740 at 3 +Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3 +Id : 753, {_}: meet ?1599 (join ?1600 ?1600) =>= meet ?1600 ?1599 [1600, 1599] by Super 3 with 711 at 3 +Id : 773, {_}: meet ?1599 ?1600 =?= meet ?1600 ?1599 [1600, 1599] by Demod 753 with 711 at 2,2 +Id : 2380, {_}: meet (join ?4513 ?4514) (join ?4515 ?4513) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4515, 4514, 4513] by Super 9 with 773 at 2,3 +Id : 2506, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =<= join ?4784 (meet ?4786 (join ?4785 ?4784)) [4786, 4785, 4784] by Super 9 with 2479 at 2,2,3 +Id : 1153, {_}: meet (join ?2312 (join ?2313 ?2312)) (join ?2314 ?2312) =>= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2313, 2312] by Super 9 with 713 at 2,2,3 +Id : 1191, {_}: meet (join ?2313 ?2312) (join ?2314 ?2312) =<= join ?2312 (meet ?2314 (join ?2313 ?2312)) [2314, 2312, 2313] by Demod 1153 with 713 at 1,2 +Id : 5434, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =?= meet (join ?4785 ?4784) (join ?4786 ?4784) [4786, 4785, 4784] by Demod 2506 with 1191 at 3 +Id : 455, {_}: meet ?974 (meet ?974 (join ?975 ?976)) =>= meet ?974 (join ?976 ?975) [976, 975, 974] by Demod 419 with 187 at 3 +Id : 757, {_}: meet ?1611 (meet ?1611 ?1612) =?= meet ?1611 (join ?1612 ?1612) [1612, 1611] by Super 455 with 711 at 2,2,2 +Id : 767, {_}: meet ?1611 (meet ?1611 ?1612) =>= meet ?1611 ?1612 [1612, 1611] by Demod 757 with 711 at 2,3 +Id : 1239, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =<= join (meet ?2428 (meet ?2426 ?2427)) (meet ?2426 ?2427) [2428, 2427, 2426] by Super 3 with 767 at 2,3 +Id : 1275, {_}: meet (meet ?2426 ?2427) (join ?2426 ?2428) =>= meet ?2426 ?2427 [2428, 2427, 2426] by Demod 1239 with 660 at 3 +Id : 30976, {_}: meet (join ?55510 ?55511) (join (meet ?55510 ?55512) ?55511) =>= join ?55511 (meet ?55510 ?55512) [55512, 55511, 55510] by Super 1191 with 1275 at 2,3 +Id : 30986, {_}: meet (join ?55551 ?55552) (join (meet ?55553 ?55551) ?55552) =>= join ?55552 (meet ?55551 ?55553) [55553, 55552, 55551] by Super 30976 with 773 at 1,2,2 +Id : 3010, {_}: meet (join ?5441 ?5442) (join ?5443 ?5442) =<= join ?5442 (meet ?5443 (join ?5441 ?5442)) [5443, 5442, 5441] by Demod 1153 with 713 at 1,2 +Id : 3031, {_}: meet (join (meet ?5530 ?5531) ?5532) (join ?5531 ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5532, 5531, 5530] by Super 3010 with 187 at 2,3 +Id : 3109, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= join ?5532 (meet ?5531 (join ?5530 ?5532)) [5530, 5532, 5531] by Demod 3031 with 773 at 2 +Id : 3110, {_}: meet (join ?5531 ?5532) (join (meet ?5530 ?5531) ?5532) =>= meet (join ?5530 ?5532) (join ?5531 ?5532) [5530, 5532, 5531] by Demod 3109 with 1191 at 3 +Id : 31246, {_}: meet (join ?55553 ?55552) (join ?55551 ?55552) =>= join ?55552 (meet ?55551 ?55553) [55551, 55552, 55553] by Demod 30986 with 3110 at 2 +Id : 31561, {_}: meet (join ?4784 ?4785) (join ?4786 ?4784) =>= join ?4784 (meet ?4786 ?4785) [4786, 4785, 4784] by Demod 5434 with 31246 at 3 +Id : 31569, {_}: join ?4513 (meet ?4515 ?4514) =<= join ?4513 (meet (join ?4513 ?4514) ?4515) [4514, 4515, 4513] by Demod 2380 with 31561 at 2 +Id : 31659, {_}: join ?56550 (meet (join ?56551 ?56552) ?56552) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56552, 56551, 56550] by Super 31569 with 31246 at 2,3 +Id : 31781, {_}: join ?56550 (meet ?56552 (join ?56551 ?56552)) =?= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31659 with 773 at 2,2 +Id : 32533, {_}: join ?58368 ?58369 =<= join ?58368 (join ?58369 (meet ?58370 ?58368)) [58370, 58369, 58368] by Demod 31781 with 631 at 2,2 +Id : 32536, {_}: join (join ?58380 ?58381) ?58382 =<= join (join ?58380 ?58381) (join ?58382 ?58380) [58382, 58381, 58380] by Super 32533 with 2 at 2,2,3 +Id : 35660, {_}: join (join ?62824 ?62825) (join ?62825 ?62826) =>= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Super 2479 with 32536 at 3 +Id : 188, {_}: meet ?380 (join ?381 (meet ?382 ?380)) =>= meet ?380 (join ?381 ?382) [382, 381, 380] by Demod 166 with 3 at 3 +Id : 1695, {_}: meet ?3292 (join ?3293 ?3292) =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Super 188 with 1157 at 2,2,2 +Id : 1732, {_}: ?3292 =<= meet ?3292 (join ?3293 (join ?3294 ?3292)) [3294, 3293, 3292] by Demod 1695 with 631 at 2 +Id : 3955, {_}: join ?7063 (join ?7064 ?7065) =<= join (join ?7063 (join ?7064 ?7065)) ?7065 [7065, 7064, 7063] by Super 669 with 1732 at 2,3 +Id : 9413, {_}: join ?17183 (join ?17184 ?17185) =<= join ?17185 (join ?17183 (join ?17184 ?17185)) [17185, 17184, 17183] by Demod 3955 with 2479 at 3 +Id : 9417, {_}: join ?17199 (join ?17200 ?17201) =<= join ?17201 (join ?17199 (join ?17201 ?17200)) [17201, 17200, 17199] by Super 9413 with 2479 at 2,2,3 +Id : 3974, {_}: ?7142 =<= meet ?7142 (join ?7143 (join ?7144 ?7142)) [7144, 7143, 7142] by Demod 1695 with 631 at 2 +Id : 3978, {_}: ?7158 =<= meet ?7158 (join ?7159 (join ?7158 ?7160)) [7160, 7159, 7158] by Super 3974 with 2479 at 2,2,3 +Id : 8662, {_}: join ?15620 (join ?15621 ?15622) =<= join (join ?15620 (join ?15621 ?15622)) ?15621 [15622, 15621, 15620] by Super 669 with 3978 at 2,3 +Id : 8767, {_}: join ?15620 (join ?15621 ?15622) =<= join ?15621 (join ?15620 (join ?15621 ?15622)) [15622, 15621, 15620] by Demod 8662 with 2479 at 3 +Id : 15553, {_}: join ?17199 (join ?17200 ?17201) =?= join ?17199 (join ?17201 ?17200) [17201, 17200, 17199] by Demod 9417 with 8767 at 3 +Id : 31782, {_}: join ?56550 ?56552 =<= join ?56550 (join ?56552 (meet ?56551 ?56550)) [56551, 56552, 56550] by Demod 31781 with 631 at 2,2 +Id : 35263, {_}: join ?62192 (join (meet ?62193 ?62192) ?62194) =>= join ?62192 ?62194 [62194, 62193, 62192] by Super 15553 with 31782 at 3 +Id : 35296, {_}: join (join ?62350 ?62351) (join ?62351 ?62352) =>= join (join ?62350 ?62351) ?62352 [62352, 62351, 62350] by Super 35263 with 631 at 1,2,2 +Id : 38052, {_}: join (join ?62824 ?62825) ?62826 =?= join (join ?62825 ?62826) ?62824 [62826, 62825, 62824] by Demod 35660 with 35296 at 2 +Id : 38125, {_}: join ?67897 (join ?67898 ?67899) =<= join (join ?67899 ?67897) ?67898 [67899, 67898, 67897] by Super 2479 with 38052 at 3 +Id : 38567, {_}: join ?18121 (join ?18122 ?18120) =<= join (join ?18121 ?18120) ?18122 [18120, 18122, 18121] by Demod 16688 with 38125 at 2 +Id : 38568, {_}: join ?18121 (join ?18122 ?18120) =?= join ?18120 (join ?18122 ?18121) [18120, 18122, 18121] by Demod 38567 with 38125 at 3 +Id : 39014, {_}: join c (join b a) =?= join c (join b a) [] by Demod 39013 with 2479 at 2,2 +Id : 39013, {_}: join c (join a b) =?= join c (join b a) [] by Demod 39012 with 38568 at 3 +Id : 39012, {_}: join c (join a b) =<= join a (join b c) [] by Demod 1 with 2479 at 2 +Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join +% SZS output end CNFRefutation for LAT007-1.p +12961: solved LAT007-1.p in 17.645102 using kbo +12961: status Unsatisfiable for LAT007-1.p +NO CLASH, using fixed ground order +12978: Facts: +12978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +12978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +12978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +12978: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +12978: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +12978: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +12978: Id : 8, {_}: + join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +12978: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +12978: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +12978: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +12978: Goal: +12978: Id : 1, {_}: + join (complement (join (meet a (complement b)) (complement a))) + (join (meet a (complement b)) + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (complement (meet (join a (complement b)) (join a b)))))) + =>= + n1 + [] by prove_e1 +12978: Order: +12978: nrkbo +12978: Leaf order: +12978: n0 1 0 0 +12978: n1 2 0 1 3 +12978: join 20 2 8 0,2 +12978: meet 15 2 6 0,1,1,1,2 +12978: complement 18 1 9 0,1,2 +12978: b 6 0 6 1,2,1,1,1,2 +12978: a 9 0 9 1,1,1,1,2 +NO CLASH, using fixed ground order +12979: Facts: +12979: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +12979: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +12979: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +12979: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +12979: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +12979: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +12979: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +12979: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +12979: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +12979: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +12979: Goal: +12979: Id : 1, {_}: + join (complement (join (meet a (complement b)) (complement a))) + (join (meet a (complement b)) + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (complement (meet (join a (complement b)) (join a b)))))) + =>= + n1 + [] by prove_e1 +12979: Order: +12979: kbo +12979: Leaf order: +12979: n0 1 0 0 +12979: n1 2 0 1 3 +12979: join 20 2 8 0,2 +12979: meet 15 2 6 0,1,1,1,2 +12979: complement 18 1 9 0,1,2 +12979: b 6 0 6 1,2,1,1,1,2 +12979: a 9 0 9 1,1,1,1,2 +NO CLASH, using fixed ground order +12980: Facts: +12980: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +12980: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +12980: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +12980: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +12980: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +12980: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +12980: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +12980: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +12980: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +12980: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +12980: Goal: +12980: Id : 1, {_}: + join (complement (join (meet a (complement b)) (complement a))) + (join (meet a (complement b)) + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (complement (meet (join a (complement b)) (join a b)))))) + =>= + n1 + [] by prove_e1 +12980: Order: +12980: lpo +12980: Leaf order: +12980: n0 1 0 0 +12980: n1 2 0 1 3 +12980: join 20 2 8 0,2 +12980: meet 15 2 6 0,1,1,1,2 +12980: complement 18 1 9 0,1,2 +12980: b 6 0 6 1,2,1,1,1,2 +12980: a 9 0 9 1,1,1,1,2 +% SZS status Timeout for LAT016-1.p +NO CLASH, using fixed ground order +12998: Facts: +12998: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +12998: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +NO CLASH, using fixed ground order +12999: Facts: +12999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +12999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +12999: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +12999: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +12999: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +12999: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +12999: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +NO CLASH, using fixed ground order +13000: Facts: +13000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13000: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +13000: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +13000: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +13000: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +13000: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +13000: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +13000: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28 +13000: Id : 11, {_}: + meet2 ?30 ?31 =?= meet2 ?31 ?30 + [31, 30] by commutativity_of_meet2 ?30 ?31 +13000: Id : 12, {_}: + meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35) + [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35 +12998: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +12999: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +12998: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +13000: Id : 13, {_}: + join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38) + =>= + meet2 ?37 (join ?38 ?39) + [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39 +13000: Id : 14, {_}: + meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42) + =>= + join ?41 (meet2 ?42 ?43) + [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43 +13000: Goal: +13000: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal +13000: Order: +13000: lpo +13000: Leaf order: +13000: join 19 2 0 +13000: meet2 14 2 1 0,3 +13000: meet 14 2 1 0,2 +13000: b 2 0 2 2,2 +13000: a 2 0 2 1,2 +12998: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +12998: Id : 7, {_}: + join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +12998: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +12998: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +12998: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28 +12998: Id : 11, {_}: + meet2 ?30 ?31 =?= meet2 ?31 ?30 + [31, 30] by commutativity_of_meet2 ?30 ?31 +12998: Id : 12, {_}: + meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35) + [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35 +12998: Id : 13, {_}: + join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38) + =>= + meet2 ?37 (join ?38 ?39) + [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39 +12998: Id : 14, {_}: + meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42) + =>= + join ?41 (meet2 ?42 ?43) + [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43 +12998: Goal: +12998: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal +12998: Order: +12998: nrkbo +12998: Leaf order: +12998: join 19 2 0 +12998: meet2 14 2 1 0,3 +12998: meet 14 2 1 0,2 +12998: b 2 0 2 2,2 +12998: a 2 0 2 1,2 +12999: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28 +12999: Id : 11, {_}: + meet2 ?30 ?31 =?= meet2 ?31 ?30 + [31, 30] by commutativity_of_meet2 ?30 ?31 +12999: Id : 12, {_}: + meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35) + [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35 +12999: Id : 13, {_}: + join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38) + =>= + meet2 ?37 (join ?38 ?39) + [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39 +12999: Id : 14, {_}: + meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42) + =>= + join ?41 (meet2 ?42 ?43) + [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43 +12999: Goal: +12999: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal +12999: Order: +12999: kbo +12999: Leaf order: +12999: join 19 2 0 +12999: meet2 14 2 1 0,3 +12999: meet 14 2 1 0,2 +12999: b 2 0 2 2,2 +12999: a 2 0 2 1,2 +% SZS status Timeout for LAT024-1.p +NO CLASH, using fixed ground order +13029: Facts: +13029: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13029: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13029: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13029: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13029: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13029: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13029: Id : 8, {_}: + join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18 + [20, 19, 18] by tnl_1 ?18 ?19 ?20 +13029: Id : 9, {_}: + meet ?22 (join ?23 (join ?22 ?24)) =>= ?22 + [24, 23, 22] by tnl_2 ?22 ?23 ?24 +13029: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26 +13029: Id : 11, {_}: + meet2 ?28 (join ?28 ?29) =>= ?28 + [29, 28] by absorption1_2 ?28 ?29 +13029: Id : 12, {_}: + join ?31 (meet2 ?31 ?32) =>= ?31 + [32, 31] by absorption2_2 ?31 ?32 +13029: Id : 13, {_}: + meet2 ?34 ?35 =?= meet2 ?35 ?34 + [35, 34] by commutativity_of_meet2 ?34 ?35 +13029: Id : 14, {_}: + join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37 + [39, 38, 37] by tnl_1_2 ?37 ?38 ?39 +13029: Id : 15, {_}: + meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41 + [43, 42, 41] by tnl_2_2 ?41 ?42 ?43 +13029: Goal: +13029: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal +13029: Order: +13029: nrkbo +13029: Leaf order: +13029: join 13 2 0 +13029: meet2 9 2 1 0,3 +13029: meet 9 2 1 0,2 +13029: b 2 0 2 2,2 +13029: a 2 0 2 1,2 +NO CLASH, using fixed ground order +13030: Facts: +13030: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13030: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13030: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13030: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13030: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13030: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13030: Id : 8, {_}: + join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18 + [20, 19, 18] by tnl_1 ?18 ?19 ?20 +13030: Id : 9, {_}: + meet ?22 (join ?23 (join ?22 ?24)) =>= ?22 + [24, 23, 22] by tnl_2 ?22 ?23 ?24 +13030: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26 +13030: Id : 11, {_}: + meet2 ?28 (join ?28 ?29) =>= ?28 + [29, 28] by absorption1_2 ?28 ?29 +13030: Id : 12, {_}: + join ?31 (meet2 ?31 ?32) =>= ?31 + [32, 31] by absorption2_2 ?31 ?32 +13030: Id : 13, {_}: + meet2 ?34 ?35 =?= meet2 ?35 ?34 + [35, 34] by commutativity_of_meet2 ?34 ?35 +13030: Id : 14, {_}: + join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37 + [39, 38, 37] by tnl_1_2 ?37 ?38 ?39 +13030: Id : 15, {_}: + meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41 + [43, 42, 41] by tnl_2_2 ?41 ?42 ?43 +13030: Goal: +13030: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal +13030: Order: +13030: kbo +13030: Leaf order: +13030: join 13 2 0 +13030: meet2 9 2 1 0,3 +13030: meet 9 2 1 0,2 +13030: b 2 0 2 2,2 +13030: a 2 0 2 1,2 +NO CLASH, using fixed ground order +13031: Facts: +13031: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13031: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13031: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13031: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13031: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13031: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13031: Id : 8, {_}: + join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18 + [20, 19, 18] by tnl_1 ?18 ?19 ?20 +13031: Id : 9, {_}: + meet ?22 (join ?23 (join ?22 ?24)) =>= ?22 + [24, 23, 22] by tnl_2 ?22 ?23 ?24 +13031: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26 +13031: Id : 11, {_}: + meet2 ?28 (join ?28 ?29) =>= ?28 + [29, 28] by absorption1_2 ?28 ?29 +13031: Id : 12, {_}: + join ?31 (meet2 ?31 ?32) =>= ?31 + [32, 31] by absorption2_2 ?31 ?32 +13031: Id : 13, {_}: + meet2 ?34 ?35 =?= meet2 ?35 ?34 + [35, 34] by commutativity_of_meet2 ?34 ?35 +13031: Id : 14, {_}: + join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37 + [39, 38, 37] by tnl_1_2 ?37 ?38 ?39 +13031: Id : 15, {_}: + meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41 + [43, 42, 41] by tnl_2_2 ?41 ?42 ?43 +13031: Goal: +13031: Id : 1, {_}: meet a b =>= meet2 a b [] by prove_meets_equal +13031: Order: +13031: lpo +13031: Leaf order: +13031: join 13 2 0 +13031: meet2 9 2 1 0,3 +13031: meet 9 2 1 0,2 +13031: b 2 0 2 2,2 +13031: a 2 0 2 1,2 +% SZS status Timeout for LAT025-1.p +CLASH, statistics insufficient +13057: Facts: +13057: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13057: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13057: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13057: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13057: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13057: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13057: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13057: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13057: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13057: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13057: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13057: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13057: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13057: Id : 15, {_}: + join ?38 (meet ?39 (join ?38 ?40)) + =>= + meet (join ?38 ?39) (join ?38 ?40) + [40, 39, 38] by modular_law ?38 ?39 ?40 +13057: Goal: +13057: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +13057: Order: +13057: nrkbo +13057: Leaf order: +13057: n0 1 0 0 +13057: n1 1 0 0 +13057: complement 10 1 0 +13057: meet 17 2 3 0,2 +13057: join 18 2 2 0,2,2 +13057: c 2 0 2 2,2,2 +13057: b 2 0 2 1,2,2 +13057: a 3 0 3 1,2 +CLASH, statistics insufficient +13058: Facts: +13058: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13058: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13058: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13058: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13058: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13058: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13058: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13058: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13058: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13058: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13058: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13058: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13058: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13058: Id : 15, {_}: + join ?38 (meet ?39 (join ?38 ?40)) + =>= + meet (join ?38 ?39) (join ?38 ?40) + [40, 39, 38] by modular_law ?38 ?39 ?40 +13058: Goal: +13058: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +13058: Order: +13058: kbo +13058: Leaf order: +13058: n0 1 0 0 +13058: n1 1 0 0 +13058: complement 10 1 0 +13058: meet 17 2 3 0,2 +13058: join 18 2 2 0,2,2 +13058: c 2 0 2 2,2,2 +13058: b 2 0 2 1,2,2 +13058: a 3 0 3 1,2 +CLASH, statistics insufficient +13059: Facts: +13059: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13059: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13059: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13059: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13059: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13059: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13059: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13059: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13059: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13059: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13059: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13059: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13059: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13059: Id : 15, {_}: + join ?38 (meet ?39 (join ?38 ?40)) + =>= + meet (join ?38 ?39) (join ?38 ?40) + [40, 39, 38] by modular_law ?38 ?39 ?40 +13059: Goal: +13059: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +13059: Order: +13059: lpo +13059: Leaf order: +13059: n0 1 0 0 +13059: n1 1 0 0 +13059: complement 10 1 0 +13059: meet 17 2 3 0,2 +13059: join 18 2 2 0,2,2 +13059: c 2 0 2 2,2,2 +13059: b 2 0 2 1,2,2 +13059: a 3 0 3 1,2 +% SZS status Timeout for LAT046-1.p +NO CLASH, using fixed ground order +13087: Facts: +NO CLASH, using fixed ground order +13088: Facts: +13088: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13088: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13088: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13088: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13088: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13088: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13088: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13088: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13088: Goal: +13088: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modularity +13088: Order: +13088: kbo +13088: Leaf order: +13088: meet 11 2 2 0,2,2 +13088: join 13 2 4 0,2 +13088: c 2 0 2 2,2,2,2 +13088: b 2 0 2 1,2,2 +13088: a 4 0 4 1,2 +13087: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13087: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13087: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13087: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13087: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13087: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13087: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13087: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13087: Goal: +13087: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modularity +13087: Order: +13087: nrkbo +13087: Leaf order: +13087: meet 11 2 2 0,2,2 +13087: join 13 2 4 0,2 +13087: c 2 0 2 2,2,2,2 +13087: b 2 0 2 1,2,2 +13087: a 4 0 4 1,2 +NO CLASH, using fixed ground order +13089: Facts: +13089: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13089: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13089: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13089: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13089: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13089: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13089: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13089: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13089: Goal: +13089: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modularity +13089: Order: +13089: lpo +13089: Leaf order: +13089: meet 11 2 2 0,2,2 +13089: join 13 2 4 0,2 +13089: c 2 0 2 2,2,2,2 +13089: b 2 0 2 1,2,2 +13089: a 4 0 4 1,2 +% SZS status Timeout for LAT047-1.p +NO CLASH, using fixed ground order +13105: Facts: +13105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13105: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13105: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13105: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13105: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13105: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13105: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13105: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13105: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13105: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13105: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by weak_orthomodular_law ?38 ?39 +13105: Goal: +13105: Id : 1, {_}: + join a (meet (complement a) (join a b)) =>= join a b + [] by prove_orthomodular_law +13105: Order: +13105: nrkbo +13105: Leaf order: +13105: n0 1 0 0 +13105: n1 2 0 0 +13105: meet 15 2 1 0,2,2 +13105: join 18 2 3 0,2 +13105: b 2 0 2 2,2,2,2 +13105: complement 13 1 1 0,1,2,2 +13105: a 4 0 4 1,2 +NO CLASH, using fixed ground order +13106: Facts: +13106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13106: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13106: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13106: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13106: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13106: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13106: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13106: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13106: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13106: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13106: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by weak_orthomodular_law ?38 ?39 +13106: Goal: +13106: Id : 1, {_}: + join a (meet (complement a) (join a b)) =>= join a b + [] by prove_orthomodular_law +13106: Order: +13106: kbo +13106: Leaf order: +13106: n0 1 0 0 +13106: n1 2 0 0 +13106: meet 15 2 1 0,2,2 +13106: join 18 2 3 0,2 +13106: b 2 0 2 2,2,2,2 +13106: complement 13 1 1 0,1,2,2 +13106: a 4 0 4 1,2 +NO CLASH, using fixed ground order +13107: Facts: +13107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13107: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13107: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13107: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13107: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13107: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13107: Id : 11, {_}: + complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13107: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13107: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13107: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13107: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by weak_orthomodular_law ?38 ?39 +13107: Goal: +13107: Id : 1, {_}: + join a (meet (complement a) (join a b)) =>= join a b + [] by prove_orthomodular_law +13107: Order: +13107: lpo +13107: Leaf order: +13107: n0 1 0 0 +13107: n1 2 0 0 +13107: meet 15 2 1 0,2,2 +13107: join 18 2 3 0,2 +13107: b 2 0 2 2,2,2,2 +13107: complement 13 1 1 0,1,2,2 +13107: a 4 0 4 1,2 +% SZS status Timeout for LAT048-1.p +NO CLASH, using fixed ground order +13228: Facts: +13228: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13228: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13228: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13228: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13228: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13228: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13228: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13228: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13228: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13228: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13228: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13228: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13228: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13228: Goal: +13228: Id : 1, {_}: + join (meet (complement a) (join a b)) + (join (complement b) (meet a b)) + =>= + n1 + [] by prove_weak_orthomodular_law +13228: Order: +13228: nrkbo +13228: Leaf order: +13228: n0 1 0 0 +13228: n1 2 0 1 3 +13228: meet 14 2 2 0,1,2 +13228: join 15 2 3 0,2 +13228: b 3 0 3 2,2,1,2 +13228: complement 12 1 2 0,1,1,2 +13228: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +13229: Facts: +13229: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13229: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13229: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13229: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13229: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13229: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13229: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13229: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13229: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13229: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13229: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13229: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13229: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13229: Goal: +13229: Id : 1, {_}: + join (meet (complement a) (join a b)) + (join (complement b) (meet a b)) + =>= + n1 + [] by prove_weak_orthomodular_law +13229: Order: +13229: kbo +13229: Leaf order: +13229: n0 1 0 0 +13229: n1 2 0 1 3 +13229: meet 14 2 2 0,1,2 +13229: join 15 2 3 0,2 +13229: b 3 0 3 2,2,1,2 +13229: complement 12 1 2 0,1,1,2 +13229: a 3 0 3 1,1,1,2 +NO CLASH, using fixed ground order +13230: Facts: +13230: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13230: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13230: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13230: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13230: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13230: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13230: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13230: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13230: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13230: Id : 11, {_}: + complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13230: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13230: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13230: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13230: Goal: +13230: Id : 1, {_}: + join (meet (complement a) (join a b)) + (join (complement b) (meet a b)) + =>= + n1 + [] by prove_weak_orthomodular_law +13230: Order: +13230: lpo +13230: Leaf order: +13230: n0 1 0 0 +13230: n1 2 0 1 3 +13230: meet 14 2 2 0,1,2 +13230: join 15 2 3 0,2 +13230: b 3 0 3 2,2,1,2 +13230: complement 12 1 2 0,1,1,2 +13230: a 3 0 3 1,1,1,2 +% SZS status Timeout for LAT049-1.p +CLASH, statistics insufficient +13579: Facts: +13579: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13579: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13579: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13579: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13579: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13579: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13579: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13579: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13579: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13579: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13579: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13579: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13579: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13579: Id : 15, {_}: + join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39 + [39, 38] by orthomodular_law ?38 ?39 +13579: Goal: +13579: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modular_law +13579: Order: +13579: nrkbo +13579: Leaf order: +13579: n0 1 0 0 +13579: n1 1 0 0 +13579: complement 11 1 0 +13579: meet 15 2 2 0,2,2 +13579: join 19 2 4 0,2 +13579: c 2 0 2 2,2,2,2 +13579: b 2 0 2 1,2,2 +13579: a 4 0 4 1,2 +CLASH, statistics insufficient +13580: Facts: +13580: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13580: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13580: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13580: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13580: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13580: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13580: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13580: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13580: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13580: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13580: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13580: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13580: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13580: Id : 15, {_}: + join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39 + [39, 38] by orthomodular_law ?38 ?39 +13580: Goal: +13580: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modular_law +13580: Order: +13580: kbo +13580: Leaf order: +13580: n0 1 0 0 +13580: n1 1 0 0 +13580: complement 11 1 0 +13580: meet 15 2 2 0,2,2 +13580: join 19 2 4 0,2 +13580: c 2 0 2 2,2,2,2 +13580: b 2 0 2 1,2,2 +13580: a 4 0 4 1,2 +CLASH, statistics insufficient +13582: Facts: +13582: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13582: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13582: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13582: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13582: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13582: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13582: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13582: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13582: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13582: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13582: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13582: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13582: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13582: Id : 15, {_}: + join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39 + [39, 38] by orthomodular_law ?38 ?39 +13582: Goal: +13582: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modular_law +13582: Order: +13582: lpo +13582: Leaf order: +13582: n0 1 0 0 +13582: n1 1 0 0 +13582: complement 11 1 0 +13582: meet 15 2 2 0,2,2 +13582: join 19 2 4 0,2 +13582: c 2 0 2 2,2,2,2 +13582: b 2 0 2 1,2,2 +13582: a 4 0 4 1,2 +% SZS status Timeout for LAT050-1.p +CLASH, statistics insufficient +13811: Facts: +13811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13811: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13811: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13811: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13811: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13811: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +13811: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +13811: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +13811: Goal: +13811: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +13811: Order: +13811: nrkbo +13811: Leaf order: +13811: n0 1 0 0 +13811: n1 1 0 0 +13811: meet 11 2 1 0,3 +13811: complement 7 1 3 0,2 +13811: join 11 2 1 0,1,2 +13811: b 2 0 2 2,1,2 +13811: a 2 0 2 1,1,2 +CLASH, statistics insufficient +13812: Facts: +13812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13812: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13812: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13812: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13812: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13812: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +13812: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +13812: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +13812: Goal: +13812: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +13812: Order: +13812: kbo +13812: Leaf order: +13812: n0 1 0 0 +13812: n1 1 0 0 +13812: meet 11 2 1 0,3 +13812: complement 7 1 3 0,2 +13812: join 11 2 1 0,1,2 +13812: b 2 0 2 2,1,2 +13812: a 2 0 2 1,1,2 +CLASH, statistics insufficient +13813: Facts: +13813: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13813: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13813: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13813: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13813: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13813: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13813: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13813: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13813: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +13813: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +13813: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +13813: Goal: +13813: Id : 1, {_}: + complement (join a b) =>= meet (complement a) (complement b) + [] by prove_compatibility_law +13813: Order: +13813: lpo +13813: Leaf order: +13813: n0 1 0 0 +13813: n1 1 0 0 +13813: meet 11 2 1 0,3 +13813: complement 7 1 3 0,2 +13813: join 11 2 1 0,1,2 +13813: b 2 0 2 2,1,2 +13813: a 2 0 2 1,1,2 +% SZS status Timeout for LAT051-1.p +CLASH, statistics insufficient +13839: Facts: +13839: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13839: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13839: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13839: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13839: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13839: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13839: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13839: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13839: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +13839: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +13839: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +13839: Id : 13, {_}: + join ?32 (meet ?33 (join ?32 ?34)) + =>= + meet (join ?32 ?33) (join ?32 ?34) + [34, 33, 32] by modular_law ?32 ?33 ?34 +13839: Goal: +13839: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +13839: Order: +13839: nrkbo +13839: Leaf order: +13839: n0 1 0 0 +13839: n1 1 0 0 +13839: meet 13 2 1 0,3 +13839: complement 7 1 3 0,2 +13839: join 15 2 1 0,1,2 +13839: b 2 0 2 2,1,2 +13839: a 2 0 2 1,1,2 +CLASH, statistics insufficient +13840: Facts: +13840: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13840: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13840: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13840: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13840: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13840: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13840: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13840: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13840: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +13840: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +13840: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +13840: Id : 13, {_}: + join ?32 (meet ?33 (join ?32 ?34)) + =>= + meet (join ?32 ?33) (join ?32 ?34) + [34, 33, 32] by modular_law ?32 ?33 ?34 +13840: Goal: +13840: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +13840: Order: +13840: kbo +13840: Leaf order: +13840: n0 1 0 0 +13840: n1 1 0 0 +13840: meet 13 2 1 0,3 +13840: complement 7 1 3 0,2 +13840: join 15 2 1 0,1,2 +13840: b 2 0 2 2,1,2 +13840: a 2 0 2 1,1,2 +CLASH, statistics insufficient +13841: Facts: +13841: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13841: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13841: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13841: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13841: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13841: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13841: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13841: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13841: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +13841: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +13841: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +13841: Id : 13, {_}: + join ?32 (meet ?33 (join ?32 ?34)) + =>= + meet (join ?32 ?33) (join ?32 ?34) + [34, 33, 32] by modular_law ?32 ?33 ?34 +13841: Goal: +13841: Id : 1, {_}: + complement (join a b) =>= meet (complement a) (complement b) + [] by prove_compatibility_law +13841: Order: +13841: lpo +13841: Leaf order: +13841: n0 1 0 0 +13841: n1 1 0 0 +13841: meet 13 2 1 0,3 +13841: complement 7 1 3 0,2 +13841: join 15 2 1 0,1,2 +13841: b 2 0 2 2,1,2 +13841: a 2 0 2 1,1,2 +% SZS status Timeout for LAT052-1.p +CLASH, statistics insufficient +13871: Facts: +13871: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13871: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13871: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13871: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13871: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13871: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13871: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13871: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13871: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13871: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13871: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13871: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13871: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13871: Goal: +13871: Id : 1, {_}: + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a (meet (complement b) (complement a)))))) + =<= + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a + (meet (complement b) + (join (complement a) (meet (complement b) a))))))) + [] by prove_this +13871: Order: +13871: nrkbo +13871: Leaf order: +13871: n0 1 0 0 +13871: n1 1 0 0 +13871: join 19 2 7 0,2 +13871: meet 19 2 7 0,2,2 +13871: complement 21 1 11 0,1,2,2 +13871: b 7 0 7 1,1,2,2 +13871: a 9 0 9 1,2 +CLASH, statistics insufficient +13872: Facts: +13872: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13872: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13872: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13872: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13872: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13872: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13872: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13872: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13872: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13872: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13872: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13872: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13872: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13872: Goal: +13872: Id : 1, {_}: + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a (meet (complement b) (complement a)))))) + =<= + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a + (meet (complement b) + (join (complement a) (meet (complement b) a))))))) + [] by prove_this +13872: Order: +13872: kbo +13872: Leaf order: +13872: n0 1 0 0 +13872: n1 1 0 0 +13872: join 19 2 7 0,2 +13872: meet 19 2 7 0,2,2 +13872: complement 21 1 11 0,1,2,2 +13872: b 7 0 7 1,1,2,2 +13872: a 9 0 9 1,2 +CLASH, statistics insufficient +13873: Facts: +13873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13873: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13873: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13873: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13873: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13873: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +13873: Id : 11, {_}: + complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +13873: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +13873: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +13873: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +13873: Goal: +13873: Id : 1, {_}: + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a (meet (complement b) (complement a)))))) + =<= + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a + (meet (complement b) + (join (complement a) (meet (complement b) a))))))) + [] by prove_this +13873: Order: +13873: lpo +13873: Leaf order: +13873: n0 1 0 0 +13873: n1 1 0 0 +13873: join 19 2 7 0,2 +13873: meet 19 2 7 0,2,2 +13873: complement 21 1 11 0,1,2,2 +13873: b 7 0 7 1,1,2,2 +13873: a 9 0 9 1,2 +% SZS status Timeout for LAT054-1.p +CLASH, statistics insufficient +13890: Facts: +13890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13890: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13890: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13890: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13890: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13890: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +13890: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +13890: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +13890: Goal: +13890: Id : 1, {_}: + meet (join a (complement b)) + (join (join (meet a b) (meet (complement a) b)) + (meet (complement a) (complement b))) + =>= + join (meet a b) (meet (complement a) (complement b)) + [] by prove_e51 +13890: Order: +13890: nrkbo +13890: Leaf order: +13890: n0 1 0 0 +13890: n1 1 0 0 +13890: meet 17 2 6 0,2 +13890: join 15 2 4 0,1,2 +13890: complement 11 1 6 0,2,1,2 +13890: b 6 0 6 1,2,1,2 +13890: a 6 0 6 1,1,2 +CLASH, statistics insufficient +13891: Facts: +13891: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13891: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13891: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13891: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13891: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13891: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13891: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13891: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13891: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +13891: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +13891: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +13891: Goal: +13891: Id : 1, {_}: + meet (join a (complement b)) + (join (join (meet a b) (meet (complement a) b)) + (meet (complement a) (complement b))) + =>= + join (meet a b) (meet (complement a) (complement b)) + [] by prove_e51 +13891: Order: +13891: kbo +13891: Leaf order: +13891: n0 1 0 0 +13891: n1 1 0 0 +13891: meet 17 2 6 0,2 +13891: join 15 2 4 0,1,2 +13891: complement 11 1 6 0,2,1,2 +13891: b 6 0 6 1,2,1,2 +13891: a 6 0 6 1,1,2 +CLASH, statistics insufficient +13892: Facts: +13892: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13892: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13892: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13892: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13892: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13892: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13892: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13892: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13892: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +13892: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +13892: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +13892: Goal: +13892: Id : 1, {_}: + meet (join a (complement b)) + (join (join (meet a b) (meet (complement a) b)) + (meet (complement a) (complement b))) + =>= + join (meet a b) (meet (complement a) (complement b)) + [] by prove_e51 +13892: Order: +13892: lpo +13892: Leaf order: +13892: n0 1 0 0 +13892: n1 1 0 0 +13892: meet 17 2 6 0,2 +13892: join 15 2 4 0,1,2 +13892: complement 11 1 6 0,2,1,2 +13892: b 6 0 6 1,2,1,2 +13892: a 6 0 6 1,1,2 +% SZS status Timeout for LAT062-1.p +CLASH, statistics insufficient +13921: Facts: +13921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13921: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13921: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13921: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13921: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13921: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +13921: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +13921: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +13921: Goal: +CLASH, statistics insufficient +CLASH, statistics insufficient +13921: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_e62 +13921: Order: +13921: nrkbo +13921: Leaf order: +13921: n0 1 0 0 +13921: n1 1 0 0 +13921: join 14 2 3 0,2,2 +13921: meet 16 2 5 0,2 +13921: complement 7 1 2 0,1,2,2,2,2 +13921: b 3 0 3 1,2,2 +13921: a 7 0 7 1,2 +13923: Facts: +13923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13923: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13923: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13923: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13923: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13923: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +13923: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +13923: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +13923: Goal: +13923: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_e62 +13923: Order: +13923: lpo +13923: Leaf order: +13923: n0 1 0 0 +13923: n1 1 0 0 +13923: join 14 2 3 0,2,2 +13923: meet 16 2 5 0,2 +13923: complement 7 1 2 0,1,2,2,2,2 +13923: b 3 0 3 1,2,2 +13923: a 7 0 7 1,2 +13922: Facts: +13922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13922: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13922: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13922: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13922: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13922: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +13922: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +13922: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +13922: Goal: +13922: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_e62 +13922: Order: +13922: kbo +13922: Leaf order: +13922: n0 1 0 0 +13922: n1 1 0 0 +13922: join 14 2 3 0,2,2 +13922: meet 16 2 5 0,2 +13922: complement 7 1 2 0,1,2,2,2,2 +13922: b 3 0 3 1,2,2 +13922: a 7 0 7 1,2 +% SZS status Timeout for LAT063-1.p +NO CLASH, using fixed ground order +13955: Facts: +13955: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13955: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13955: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13955: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13955: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13955: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13955: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13955: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13955: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28)))) + [28, 27, 26] by equation_H2 ?26 ?27 ?28 +13955: Goal: +13955: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +13955: Order: +13955: nrkbo +13955: Leaf order: +13955: join 17 2 4 0,2,2 +13955: meet 21 2 6 0,2 +13955: c 3 0 3 2,2,2,2 +13955: b 4 0 4 1,2,2 +13955: a 5 0 5 1,2 +NO CLASH, using fixed ground order +13956: Facts: +13956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13956: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13956: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13956: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13956: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13956: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28)))) + [28, 27, 26] by equation_H2 ?26 ?27 ?28 +13956: Goal: +13956: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +13956: Order: +13956: kbo +13956: Leaf order: +13956: join 17 2 4 0,2,2 +13956: meet 21 2 6 0,2 +13956: c 3 0 3 2,2,2,2 +13956: b 4 0 4 1,2,2 +13956: a 5 0 5 1,2 +NO CLASH, using fixed ground order +13957: Facts: +13957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13957: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13957: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13957: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13957: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13957: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28)))) + [28, 27, 26] by equation_H2 ?26 ?27 ?28 +13957: Goal: +13957: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +13957: Order: +13957: lpo +13957: Leaf order: +13957: join 17 2 4 0,2,2 +13957: meet 21 2 6 0,2 +13957: c 3 0 3 2,2,2,2 +13957: b 4 0 4 1,2,2 +13957: a 5 0 5 1,2 +% SZS status Timeout for LAT098-1.p +NO CLASH, using fixed ground order +13999: Facts: +13999: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13999: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13999: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13999: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13999: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13999: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13999: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13999: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13999: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +13999: Goal: +13999: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +13999: Order: +13999: nrkbo +13999: Leaf order: +13999: meet 20 2 5 0,2 +13999: join 18 2 5 0,2,2 +13999: d 3 0 3 2,2,2,2,2 +13999: c 2 0 2 1,2,2,2,2 +13999: b 3 0 3 1,2,2 +13999: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14000: Facts: +14000: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14000: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14000: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14000: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14000: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14000: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14000: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14000: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14000: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +14000: Goal: +14000: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +14000: Order: +14000: kbo +14000: Leaf order: +14000: meet 20 2 5 0,2 +14000: join 18 2 5 0,2,2 +14000: d 3 0 3 2,2,2,2,2 +14000: c 2 0 2 1,2,2,2,2 +14000: b 3 0 3 1,2,2 +14000: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14001: Facts: +14001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14001: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14001: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14001: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14001: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14001: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14001: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14001: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +14001: Goal: +14001: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +14001: Order: +14001: lpo +14001: Leaf order: +14001: meet 20 2 5 0,2 +14001: join 18 2 5 0,2,2 +14001: d 3 0 3 2,2,2,2,2 +14001: c 2 0 2 1,2,2,2,2 +14001: b 3 0 3 1,2,2 +14001: a 4 0 4 1,2 +% SZS status Timeout for LAT100-1.p +NO CLASH, using fixed ground order +14017: Facts: +14017: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14017: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14017: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14017: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14017: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14017: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14017: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14017: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14017: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +14017: Goal: +14017: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +14017: Order: +14017: nrkbo +14017: Leaf order: +14017: join 16 2 3 0,2,2 +14017: meet 20 2 5 0,2 +14017: c 3 0 3 2,2,2,2 +14017: b 3 0 3 1,2,2 +14017: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14018: Facts: +14018: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14018: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14018: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14018: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14018: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14018: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14018: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14018: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14018: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +14018: Goal: +14018: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +14018: Order: +14018: kbo +14018: Leaf order: +14018: join 16 2 3 0,2,2 +14018: meet 20 2 5 0,2 +14018: c 3 0 3 2,2,2,2 +14018: b 3 0 3 1,2,2 +14018: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14019: Facts: +14019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14019: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14019: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14019: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14019: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14019: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +14019: Goal: +14019: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +14019: Order: +14019: lpo +14019: Leaf order: +14019: join 16 2 3 0,2,2 +14019: meet 20 2 5 0,2 +14019: c 3 0 3 2,2,2,2 +14019: b 3 0 3 1,2,2 +14019: a 4 0 4 1,2 +% SZS status Timeout for LAT101-1.p +NO CLASH, using fixed ground order +14050: Facts: +14050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14050: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14050: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14050: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14050: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14050: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +14050: Goal: +14050: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +14050: Order: +14050: nrkbo +14050: Leaf order: +14050: meet 20 2 5 0,2 +14050: join 18 2 5 0,2,2 +14050: d 3 0 3 2,2,2,2,2 +14050: c 2 0 2 1,2,2,2,2 +14050: b 3 0 3 1,2,2 +14050: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14051: Facts: +14051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14051: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14051: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14051: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14051: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14051: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +14051: Goal: +14051: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +14051: Order: +14051: kbo +14051: Leaf order: +14051: meet 20 2 5 0,2 +14051: join 18 2 5 0,2,2 +14051: d 3 0 3 2,2,2,2,2 +14051: c 2 0 2 1,2,2,2,2 +14051: b 3 0 3 1,2,2 +14051: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14052: Facts: +14052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14052: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14052: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14052: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14052: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14052: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +14052: Goal: +14052: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +14052: Order: +14052: lpo +14052: Leaf order: +14052: meet 20 2 5 0,2 +14052: join 18 2 5 0,2,2 +14052: d 3 0 3 2,2,2,2,2 +14052: c 2 0 2 1,2,2,2,2 +14052: b 3 0 3 1,2,2 +14052: a 4 0 4 1,2 +% SZS status Timeout for LAT102-1.p +NO CLASH, using fixed ground order +14140: Facts: +14140: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14140: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14140: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14140: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14140: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14140: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14140: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14140: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14140: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28)))) + [28, 27, 26] by equation_H10 ?26 ?27 ?28 +14140: Goal: +14140: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +14140: Order: +14140: nrkbo +14140: Leaf order: +14140: join 16 2 4 0,2,2 +14140: meet 20 2 6 0,2 +14140: c 3 0 3 2,2,2,2 +14140: b 3 0 3 1,2,2 +14140: a 6 0 6 1,2 +NO CLASH, using fixed ground order +14141: Facts: +14141: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14141: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14141: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14141: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14141: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14141: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14141: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14141: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14141: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28)))) + [28, 27, 26] by equation_H10 ?26 ?27 ?28 +14141: Goal: +14141: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +14141: Order: +14141: kbo +14141: Leaf order: +14141: join 16 2 4 0,2,2 +14141: meet 20 2 6 0,2 +14141: c 3 0 3 2,2,2,2 +14141: b 3 0 3 1,2,2 +14141: a 6 0 6 1,2 +NO CLASH, using fixed ground order +14142: Facts: +14142: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14142: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14142: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14142: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14142: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14142: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14142: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14142: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14142: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =?= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28)))) + [28, 27, 26] by equation_H10 ?26 ?27 ?28 +14142: Goal: +14142: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +14142: Order: +14142: lpo +14142: Leaf order: +14142: join 16 2 4 0,2,2 +14142: meet 20 2 6 0,2 +14142: c 3 0 3 2,2,2,2 +14142: b 3 0 3 1,2,2 +14142: a 6 0 6 1,2 +% SZS status Timeout for LAT103-1.p +NO CLASH, using fixed ground order +14175: Facts: +14175: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14175: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14175: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14175: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14175: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14175: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14175: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14175: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14175: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +14175: Goal: +14175: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +14175: Order: +14175: kbo +14175: Leaf order: +14175: join 17 2 4 0,2,2 +14175: meet 21 2 6 0,2 +14175: c 3 0 3 2,2,2,2 +14175: b 4 0 4 1,2,2 +14175: a 5 0 5 1,2 +NO CLASH, using fixed ground order +14176: Facts: +14176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14176: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14176: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14176: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14176: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14176: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +14176: Goal: +14176: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +14176: Order: +14176: lpo +14176: Leaf order: +14176: join 17 2 4 0,2,2 +14176: meet 21 2 6 0,2 +14176: c 3 0 3 2,2,2,2 +14176: b 4 0 4 1,2,2 +14176: a 5 0 5 1,2 +NO CLASH, using fixed ground order +14174: Facts: +14174: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14174: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14174: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14174: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14174: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14174: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14174: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14174: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14174: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +14174: Goal: +14174: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +14174: Order: +14174: nrkbo +14174: Leaf order: +14174: join 17 2 4 0,2,2 +14174: meet 21 2 6 0,2 +14174: c 3 0 3 2,2,2,2 +14174: b 4 0 4 1,2,2 +14174: a 5 0 5 1,2 +% SZS status Timeout for LAT104-1.p +NO CLASH, using fixed ground order +14193: Facts: +14193: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14193: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14193: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14193: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14193: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14193: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14193: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14193: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14193: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +14193: Goal: +14193: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +14193: Order: +14193: nrkbo +14193: Leaf order: +14193: join 16 2 3 0,2,2 +14193: meet 20 2 5 0,2 +14193: c 3 0 3 2,2,2,2 +14193: b 3 0 3 1,2,2 +14193: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14194: Facts: +14194: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14194: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14194: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14194: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14194: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14194: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14194: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14194: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14194: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +14194: Goal: +14194: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +14194: Order: +14194: kbo +14194: Leaf order: +14194: join 16 2 3 0,2,2 +14194: meet 20 2 5 0,2 +14194: c 3 0 3 2,2,2,2 +14194: b 3 0 3 1,2,2 +14194: a 4 0 4 1,2 +NO CLASH, using fixed ground order +14195: Facts: +14195: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14195: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14195: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14195: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14195: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14195: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14195: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14195: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14195: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +14195: Goal: +14195: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +14195: Order: +14195: lpo +14195: Leaf order: +14195: join 16 2 3 0,2,2 +14195: meet 20 2 5 0,2 +14195: c 3 0 3 2,2,2,2 +14195: b 3 0 3 1,2,2 +14195: a 4 0 4 1,2 +% SZS status Timeout for LAT105-1.p +NO CLASH, using fixed ground order +14223: Facts: +14223: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14223: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14223: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14223: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14223: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14223: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14223: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14223: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14223: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +14223: Goal: +14223: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +14223: Order: +14223: nrkbo +14223: Leaf order: +14223: join 17 2 4 0,2,2 +14223: meet 21 2 6 0,2 +14223: c 3 0 3 2,2,2,2 +14223: b 4 0 4 1,2,2 +14223: a 5 0 5 1,2 +NO CLASH, using fixed ground order +14224: Facts: +14224: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14224: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14224: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14224: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14224: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14224: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14224: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14224: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14224: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +14224: Goal: +14224: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +14224: Order: +14224: kbo +14224: Leaf order: +NO CLASH, using fixed ground order +14225: Facts: +14225: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14225: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14225: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14225: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14225: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14225: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14225: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14225: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14225: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +14225: Goal: +14225: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +14225: Order: +14225: lpo +14225: Leaf order: +14225: join 17 2 4 0,2,2 +14225: meet 21 2 6 0,2 +14225: c 3 0 3 2,2,2,2 +14225: b 4 0 4 1,2,2 +14225: a 5 0 5 1,2 +14224: join 17 2 4 0,2,2 +14224: meet 21 2 6 0,2 +14224: c 3 0 3 2,2,2,2 +14224: b 4 0 4 1,2,2 +14224: a 5 0 5 1,2 +% SZS status Timeout for LAT106-1.p +NO CLASH, using fixed ground order +14371: Facts: +14371: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14371: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14371: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14371: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14371: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14371: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14371: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14371: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14371: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +14371: Goal: +14371: Id : 1, {_}: + meet a (join (meet a b) (meet a c)) + =<= + meet a (join (meet b (join a (meet b c))) (meet c (join a b))) + [] by prove_H17 +14371: Order: +14371: nrkbo +14371: Leaf order: +14371: join 17 2 4 0,2,2 +14371: c 3 0 3 2,2,2,2 +14371: meet 22 2 7 0,2 +14371: b 4 0 4 2,1,2,2 +14371: a 6 0 6 1,2 +NO CLASH, using fixed ground order +14372: Facts: +14372: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14372: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14372: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14372: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14372: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14372: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14372: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14372: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14372: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +14372: Goal: +14372: Id : 1, {_}: + meet a (join (meet a b) (meet a c)) + =<= + meet a (join (meet b (join a (meet b c))) (meet c (join a b))) + [] by prove_H17 +14372: Order: +14372: kbo +14372: Leaf order: +14372: join 17 2 4 0,2,2 +14372: c 3 0 3 2,2,2,2 +14372: meet 22 2 7 0,2 +14372: b 4 0 4 2,1,2,2 +14372: a 6 0 6 1,2 +NO CLASH, using fixed ground order +14373: Facts: +14373: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14373: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14373: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14373: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14373: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14373: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14373: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14373: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14373: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +14373: Goal: +14373: Id : 1, {_}: + meet a (join (meet a b) (meet a c)) + =>= + meet a (join (meet b (join a (meet b c))) (meet c (join a b))) + [] by prove_H17 +14373: Order: +14373: lpo +14373: Leaf order: +14373: join 17 2 4 0,2,2 +14373: c 3 0 3 2,2,2,2 +14373: meet 22 2 7 0,2 +14373: b 4 0 4 2,1,2,2 +14373: a 6 0 6 1,2 +% SZS status Timeout for LAT107-1.p +NO CLASH, using fixed ground order +15801: Facts: +15801: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +15801: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +15801: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +15801: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +15801: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +15801: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +15801: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +15801: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +15801: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29 +15801: Goal: +15801: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +15801: Order: +15801: nrkbo +15801: Leaf order: +15801: meet 21 2 5 0,2 +15801: join 17 2 5 0,2,2 +15801: d 2 0 2 2,2,2,2,2 +15801: c 3 0 3 1,2,2,2 +15801: b 3 0 3 1,2,2 +15801: a 4 0 4 1,2 +NO CLASH, using fixed ground order +15804: Facts: +15804: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +15804: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +15804: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +15804: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +15804: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +15804: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +15804: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +15804: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +15804: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29 +15804: Goal: +15804: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +15804: Order: +15804: kbo +15804: Leaf order: +15804: meet 21 2 5 0,2 +15804: join 17 2 5 0,2,2 +15804: d 2 0 2 2,2,2,2,2 +15804: c 3 0 3 1,2,2,2 +15804: b 3 0 3 1,2,2 +15804: a 4 0 4 1,2 +NO CLASH, using fixed ground order +15805: Facts: +15805: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +15805: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +15805: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +15805: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +15805: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +15805: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +15805: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +15805: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +15805: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29 +15805: Goal: +15805: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +15805: Order: +15805: lpo +15805: Leaf order: +15805: meet 21 2 5 0,2 +15805: join 17 2 5 0,2,2 +15805: d 2 0 2 2,2,2,2,2 +15805: c 3 0 3 1,2,2,2 +15805: b 3 0 3 1,2,2 +15805: a 4 0 4 1,2 +% SZS status Timeout for LAT108-1.p +NO CLASH, using fixed ground order +17324: Facts: +17324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17324: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17324: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17324: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17324: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17324: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +17324: Goal: +17324: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +17324: Order: +17324: lpo +17324: Leaf order: +17324: meet 19 2 5 0,2 +17324: join 19 2 5 0,2,2 +17324: d 2 0 2 2,2,2,2,2 +17324: c 3 0 3 1,2,2,2 +17324: b 3 0 3 1,2,2 +17324: a 4 0 4 1,2 +NO CLASH, using fixed ground order +17322: Facts: +17322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17322: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17322: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17322: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17322: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17322: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +17322: Goal: +17322: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +17322: Order: +17322: nrkbo +17322: Leaf order: +17322: meet 19 2 5 0,2 +17322: join 19 2 5 0,2,2 +17322: d 2 0 2 2,2,2,2,2 +17322: c 3 0 3 1,2,2,2 +17322: b 3 0 3 1,2,2 +17322: a 4 0 4 1,2 +NO CLASH, using fixed ground order +17323: Facts: +17323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17323: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17323: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17323: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17323: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17323: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +17323: Goal: +17323: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +17323: Order: +17323: kbo +17323: Leaf order: +17323: meet 19 2 5 0,2 +17323: join 19 2 5 0,2,2 +17323: d 2 0 2 2,2,2,2,2 +17323: c 3 0 3 1,2,2,2 +17323: b 3 0 3 1,2,2 +17323: a 4 0 4 1,2 +% SZS status Timeout for LAT109-1.p +NO CLASH, using fixed ground order +19002: Facts: +19002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19002: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19002: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19002: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19002: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19002: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19002: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19002: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29 +19002: Goal: +19002: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +19002: Order: +19002: nrkbo +19002: Leaf order: +19002: meet 21 2 5 0,2 +19002: join 17 2 5 0,2,2 +19002: d 2 0 2 2,2,2,2,2 +19002: c 3 0 3 1,2,2,2 +19002: b 3 0 3 1,2,2 +19002: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19008: Facts: +19008: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19008: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19008: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19008: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19008: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19008: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19008: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19008: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19008: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29 +19008: Goal: +19008: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +19008: Order: +19008: kbo +19008: Leaf order: +19008: meet 21 2 5 0,2 +19008: join 17 2 5 0,2,2 +19008: d 2 0 2 2,2,2,2,2 +19008: c 3 0 3 1,2,2,2 +19008: b 3 0 3 1,2,2 +19008: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19009: Facts: +19009: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19009: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19009: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19009: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19009: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19009: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19009: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19009: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19009: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29 +19009: Goal: +19009: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +19009: Order: +19009: lpo +19009: Leaf order: +19009: meet 21 2 5 0,2 +19009: join 17 2 5 0,2,2 +19009: d 2 0 2 2,2,2,2,2 +19009: c 3 0 3 1,2,2,2 +19009: b 3 0 3 1,2,2 +19009: a 4 0 4 1,2 +% SZS status Timeout for LAT111-1.p +NO CLASH, using fixed ground order +19496: Facts: +19496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19496: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19496: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19496: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19496: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19496: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29 +19496: Goal: +19496: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +19496: Order: +19496: nrkbo +19496: Leaf order: +19496: meet 21 2 5 0,2 +19496: join 17 2 5 0,2,2 +19496: d 2 0 2 2,2,2,2,2 +19496: c 3 0 3 1,2,2,2 +19496: b 3 0 3 1,2,2 +19496: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19497: Facts: +19497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19497: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19497: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19497: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19497: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19497: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29 +19497: Goal: +19497: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +19497: Order: +19497: kbo +19497: Leaf order: +19497: meet 21 2 5 0,2 +19497: join 17 2 5 0,2,2 +19497: d 2 0 2 2,2,2,2,2 +19497: c 3 0 3 1,2,2,2 +19497: b 3 0 3 1,2,2 +19497: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19498: Facts: +19498: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19498: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19498: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19498: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19498: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19498: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19498: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19498: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19498: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29 +19498: Goal: +19498: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +19498: Order: +19498: lpo +19498: Leaf order: +19498: meet 21 2 5 0,2 +19498: join 17 2 5 0,2,2 +19498: d 2 0 2 2,2,2,2,2 +19498: c 3 0 3 1,2,2,2 +19498: b 3 0 3 1,2,2 +19498: a 4 0 4 1,2 +% SZS status Timeout for LAT112-1.p +NO CLASH, using fixed ground order +19529: Facts: +19529: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19529: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19529: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19529: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19529: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19529: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19529: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19529: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19529: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +19529: Goal: +19529: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +19529: Order: +19529: nrkbo +19529: Leaf order: +19529: meet 19 2 5 0,2 +19529: join 19 2 5 0,2,2 +19529: d 2 0 2 2,2,2,2,2 +19529: c 3 0 3 1,2,2,2 +19529: b 3 0 3 1,2,2 +19529: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19530: Facts: +19530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19530: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19530: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19530: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19530: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19530: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +19530: Goal: +19530: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +19530: Order: +19530: kbo +19530: Leaf order: +19530: meet 19 2 5 0,2 +19530: join 19 2 5 0,2,2 +19530: d 2 0 2 2,2,2,2,2 +19530: c 3 0 3 1,2,2,2 +19530: b 3 0 3 1,2,2 +19530: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19531: Facts: +19531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19531: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19531: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19531: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19531: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19531: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +19531: Goal: +19531: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +19531: Order: +19531: lpo +19531: Leaf order: +19531: meet 19 2 5 0,2 +19531: join 19 2 5 0,2,2 +19531: d 2 0 2 2,2,2,2,2 +19531: c 3 0 3 1,2,2,2 +19531: b 3 0 3 1,2,2 +19531: a 4 0 4 1,2 +% SZS status Timeout for LAT113-1.p +NO CLASH, using fixed ground order +19568: Facts: +19568: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19568: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19568: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19568: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19568: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19568: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19568: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19568: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19568: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19568: Goal: +19568: Id : 1, {_}: + join (meet a b) (meet a (join b c)) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H56 +19568: Order: +19568: kbo +19568: Leaf order: +19568: join 19 2 5 0,2 +19568: c 2 0 2 2,2,2,2 +19568: meet 17 2 5 0,1,2 +19568: b 5 0 5 2,1,2 +19568: a 5 0 5 1,1,2 +NO CLASH, using fixed ground order +19567: Facts: +19567: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19567: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19567: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19567: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19567: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19567: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19567: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19567: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19567: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19567: Goal: +19567: Id : 1, {_}: + join (meet a b) (meet a (join b c)) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H56 +19567: Order: +19567: nrkbo +19567: Leaf order: +19567: join 19 2 5 0,2 +19567: c 2 0 2 2,2,2,2 +19567: meet 17 2 5 0,1,2 +19567: b 5 0 5 2,1,2 +19567: a 5 0 5 1,1,2 +NO CLASH, using fixed ground order +19569: Facts: +19569: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19569: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19569: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19569: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19569: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19569: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19569: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19569: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19569: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19569: Goal: +19569: Id : 1, {_}: + join (meet a b) (meet a (join b c)) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H56 +19569: Order: +19569: lpo +19569: Leaf order: +19569: join 19 2 5 0,2 +19569: c 2 0 2 2,2,2,2 +19569: meet 17 2 5 0,1,2 +19569: b 5 0 5 2,1,2 +19569: a 5 0 5 1,1,2 +% SZS status Timeout for LAT114-1.p +NO CLASH, using fixed ground order +19631: Facts: +19631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19631: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19631: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19631: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19631: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19631: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19631: Goal: +19631: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +19631: Order: +19631: nrkbo +19631: Leaf order: +19631: meet 17 2 5 0,2 +19631: d 2 0 2 2,2,2,2 +19631: join 19 2 5 0,1,2,2 +19631: c 2 0 2 2,1,2,2 +19631: b 5 0 5 1,1,2,2 +19631: a 3 0 3 1,2 +NO CLASH, using fixed ground order +19632: Facts: +19632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19632: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19632: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19632: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19632: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19632: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19632: Goal: +19632: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +19632: Order: +19632: kbo +19632: Leaf order: +19632: meet 17 2 5 0,2 +19632: d 2 0 2 2,2,2,2 +19632: join 19 2 5 0,1,2,2 +19632: c 2 0 2 2,1,2,2 +19632: b 5 0 5 1,1,2,2 +19632: a 3 0 3 1,2 +NO CLASH, using fixed ground order +19633: Facts: +19633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19633: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19633: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19633: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19633: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19633: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19633: Goal: +19633: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +19633: Order: +19633: lpo +19633: Leaf order: +19633: meet 17 2 5 0,2 +19633: d 2 0 2 2,2,2,2 +19633: join 19 2 5 0,1,2,2 +19633: c 2 0 2 2,1,2,2 +19633: b 5 0 5 1,1,2,2 +19633: a 3 0 3 1,2 +% SZS status Timeout for LAT115-1.p +NO CLASH, using fixed ground order +19650: Facts: +19650: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19650: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19650: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19650: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19650: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19650: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +NO CLASH, using fixed ground order +19651: Facts: +19651: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19651: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19651: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19651: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19651: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19651: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19651: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19651: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19651: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19651: Goal: +19651: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b c) (join d (meet a b)))) + [] by prove_H60 +19651: Order: +19651: kbo +19651: Leaf order: +19651: meet 17 2 5 0,2 +19651: d 2 0 2 2,2,2,2 +19651: join 19 2 5 0,1,2,2 +19651: c 2 0 2 2,1,2,2 +19651: b 5 0 5 1,1,2,2 +19651: a 3 0 3 1,2 +19650: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19650: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19650: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19650: Goal: +19650: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b c) (join d (meet a b)))) + [] by prove_H60 +19650: Order: +19650: nrkbo +19650: Leaf order: +19650: meet 17 2 5 0,2 +19650: d 2 0 2 2,2,2,2 +19650: join 19 2 5 0,1,2,2 +19650: c 2 0 2 2,1,2,2 +19650: b 5 0 5 1,1,2,2 +19650: a 3 0 3 1,2 +NO CLASH, using fixed ground order +19652: Facts: +19652: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19652: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19652: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19652: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19652: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19652: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19652: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19652: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19652: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +19652: Goal: +19652: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b c) (join d (meet a b)))) + [] by prove_H60 +19652: Order: +19652: lpo +19652: Leaf order: +19652: meet 17 2 5 0,2 +19652: d 2 0 2 2,2,2,2 +19652: join 19 2 5 0,1,2,2 +19652: c 2 0 2 2,1,2,2 +19652: b 5 0 5 1,1,2,2 +19652: a 3 0 3 1,2 +% SZS status Timeout for LAT116-1.p +NO CLASH, using fixed ground order +19680: Facts: +19680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19680: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19680: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19680: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19680: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19680: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))) + [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29 +19680: Goal: +19680: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19680: Order: +19680: nrkbo +19680: Leaf order: +19680: meet 20 2 5 0,2 +19680: join 16 2 4 0,2,2 +19680: c 3 0 3 2,2,2 +19680: b 3 0 3 1,2,2 +19680: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19681: Facts: +19681: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19681: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19681: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19681: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19681: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19681: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19681: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19681: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19681: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))) + [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29 +19681: Goal: +19681: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19681: Order: +19681: kbo +19681: Leaf order: +19681: meet 20 2 5 0,2 +19681: join 16 2 4 0,2,2 +19681: c 3 0 3 2,2,2 +19681: b 3 0 3 1,2,2 +19681: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19682: Facts: +19682: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19682: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19682: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19682: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19682: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19682: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19682: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19682: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19682: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))) + [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29 +19682: Goal: +19682: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19682: Order: +19682: lpo +19682: Leaf order: +19682: meet 20 2 5 0,2 +19682: join 16 2 4 0,2,2 +19682: c 3 0 3 2,2,2 +19682: b 3 0 3 1,2,2 +19682: a 5 0 5 1,2 +% SZS status Timeout for LAT117-1.p +NO CLASH, using fixed ground order +19698: Facts: +19698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19698: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19698: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19698: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19698: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19698: Id : 10, {_}: + meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27))) + =>= + join (meet ?26 ?27) (meet ?26 ?28) + [28, 27, 26] by equation_H82 ?26 ?27 ?28 +19698: Goal: +19698: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +19698: Order: +19698: nrkbo +19698: Leaf order: +19698: join 17 2 4 0,2,2 +19698: meet 20 2 6 0,2 +19698: c 3 0 3 2,2,2,2 +19698: b 4 0 4 1,2,2 +19698: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19699: Facts: +19699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19699: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19699: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19699: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19699: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19699: Id : 10, {_}: + meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27))) + =>= + join (meet ?26 ?27) (meet ?26 ?28) + [28, 27, 26] by equation_H82 ?26 ?27 ?28 +19699: Goal: +19699: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +19699: Order: +19699: kbo +19699: Leaf order: +19699: join 17 2 4 0,2,2 +19699: meet 20 2 6 0,2 +19699: c 3 0 3 2,2,2,2 +19699: b 4 0 4 1,2,2 +19699: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19700: Facts: +19700: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19700: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19700: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19700: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19700: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19700: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19700: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19700: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19700: Id : 10, {_}: + meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27))) + =>= + join (meet ?26 ?27) (meet ?26 ?28) + [28, 27, 26] by equation_H82 ?26 ?27 ?28 +19700: Goal: +19700: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +19700: Order: +19700: lpo +19700: Leaf order: +19700: join 17 2 4 0,2,2 +19700: meet 20 2 6 0,2 +19700: c 3 0 3 2,2,2,2 +19700: b 4 0 4 1,2,2 +19700: a 5 0 5 1,2 +% SZS status Timeout for LAT119-1.p +NO CLASH, using fixed ground order +19732: Facts: +19732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19732: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19732: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19732: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19732: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19732: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28)))) + [28, 27, 26] by equation_H10_dual ?26 ?27 ?28 +19732: Goal: +19732: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +19732: Order: +19732: nrkbo +19732: Leaf order: +19732: meet 16 2 4 0,2 +19732: join 18 2 4 0,2,2 +19732: c 2 0 2 2,2,2 +19732: b 4 0 4 1,2,2 +19732: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19733: Facts: +19733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19733: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19733: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19733: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19733: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19733: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28)))) + [28, 27, 26] by equation_H10_dual ?26 ?27 ?28 +19733: Goal: +19733: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +19733: Order: +19733: kbo +19733: Leaf order: +19733: meet 16 2 4 0,2 +19733: join 18 2 4 0,2,2 +19733: c 2 0 2 2,2,2 +19733: b 4 0 4 1,2,2 +19733: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19734: Facts: +19734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19734: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19734: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19734: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19734: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19734: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28)))) + [28, 27, 26] by equation_H10_dual ?26 ?27 ?28 +19734: Goal: +19734: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +19734: Order: +19734: lpo +19734: Leaf order: +19734: meet 16 2 4 0,2 +19734: join 18 2 4 0,2,2 +19734: c 2 0 2 2,2,2 +19734: b 4 0 4 1,2,2 +19734: a 4 0 4 1,2 +% SZS status Timeout for LAT120-1.p +NO CLASH, using fixed ground order +19750: Facts: +19750: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19750: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19750: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19750: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19750: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19750: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19750: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19750: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19750: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +19750: Goal: +19750: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19750: Order: +19750: nrkbo +19750: Leaf order: +19750: meet 16 2 3 0,2,2 +19750: join 20 2 5 0,2 +19750: c 3 0 3 2,2,2,2 +19750: b 3 0 3 1,2,2 +19750: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19751: Facts: +19751: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19751: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19751: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19751: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19751: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19751: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19751: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19751: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19751: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +19751: Goal: +19751: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19751: Order: +19751: kbo +19751: Leaf order: +19751: meet 16 2 3 0,2,2 +19751: join 20 2 5 0,2 +19751: c 3 0 3 2,2,2,2 +19751: b 3 0 3 1,2,2 +19751: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19752: Facts: +19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19752: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19752: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19752: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19752: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19752: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +19752: Goal: +19752: Id : 1, {_}: + join a (meet b (join a c)) + =>= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19752: Order: +19752: lpo +19752: Leaf order: +19752: meet 16 2 3 0,2,2 +19752: join 20 2 5 0,2 +19752: c 3 0 3 2,2,2,2 +19752: b 3 0 3 1,2,2 +19752: a 4 0 4 1,2 +% SZS status Timeout for LAT121-1.p +NO CLASH, using fixed ground order +19779: Facts: +19779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19779: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19779: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19779: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19779: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19779: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +19779: Goal: +19779: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19779: Order: +19779: nrkbo +19779: Leaf order: +19779: meet 16 2 3 0,2,2 +19779: join 20 2 5 0,2 +19779: c 3 0 3 2,2,2,2 +19779: b 3 0 3 1,2,2 +19779: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19780: Facts: +19780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19780: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19780: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19780: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19780: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19780: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +19780: Goal: +19780: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19780: Order: +19780: kbo +19780: Leaf order: +19780: meet 16 2 3 0,2,2 +19780: join 20 2 5 0,2 +19780: c 3 0 3 2,2,2,2 +19780: b 3 0 3 1,2,2 +19780: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19781: Facts: +19781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19781: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19781: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19781: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19781: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19781: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +19781: Goal: +19781: Id : 1, {_}: + join a (meet b (join a c)) + =>= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19781: Order: +19781: lpo +19781: Leaf order: +19781: meet 16 2 3 0,2,2 +19781: join 20 2 5 0,2 +19781: c 3 0 3 2,2,2,2 +19781: b 3 0 3 1,2,2 +19781: a 4 0 4 1,2 +% SZS status Timeout for LAT122-1.p +NO CLASH, using fixed ground order +19798: Facts: +19798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19798: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19798: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19798: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19798: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19798: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?28 (join ?26 ?27))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H22_dual ?26 ?27 ?28 +19798: Goal: +19798: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19798: Order: +19798: nrkbo +19798: Leaf order: +19798: meet 16 2 3 0,2,2 +19798: join 20 2 5 0,2 +19798: c 3 0 3 2,2,2,2 +19798: b 3 0 3 1,2,2 +19798: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19799: Facts: +19799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19799: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19799: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19799: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19799: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19799: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?28 (join ?26 ?27))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H22_dual ?26 ?27 ?28 +19799: Goal: +19799: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19799: Order: +19799: kbo +19799: Leaf order: +19799: meet 16 2 3 0,2,2 +19799: join 20 2 5 0,2 +19799: c 3 0 3 2,2,2,2 +19799: b 3 0 3 1,2,2 +19799: a 4 0 4 1,2 +NO CLASH, using fixed ground order +19800: Facts: +19800: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19800: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19800: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19800: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19800: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19800: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19800: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19800: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19800: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?28 (join ?26 ?27))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H22_dual ?26 ?27 ?28 +19800: Goal: +19800: Id : 1, {_}: + join a (meet b (join a c)) + =>= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +19800: Order: +19800: lpo +19800: Leaf order: +19800: meet 16 2 3 0,2,2 +19800: join 20 2 5 0,2 +19800: c 3 0 3 2,2,2,2 +19800: b 3 0 3 1,2,2 +19800: a 4 0 4 1,2 +% SZS status Timeout for LAT123-1.p +NO CLASH, using fixed ground order +19842: Facts: +19842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19842: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19842: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19842: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19842: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19842: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 (join ?28 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29 +19842: Goal: +19842: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19842: Order: +19842: nrkbo +19842: Leaf order: +19842: meet 17 2 5 0,2 +19842: join 20 2 4 0,2,2 +19842: c 3 0 3 2,2,2 +19842: b 3 0 3 1,2,2 +19842: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19843: Facts: +19843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19843: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19843: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19843: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19843: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19843: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 (join ?28 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29 +19843: Goal: +19843: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19843: Order: +19843: kbo +19843: Leaf order: +19843: meet 17 2 5 0,2 +19843: join 20 2 4 0,2,2 +19843: c 3 0 3 2,2,2 +19843: b 3 0 3 1,2,2 +19843: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19844: Facts: +19844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19844: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19844: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19844: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19844: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19844: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 (join ?28 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29 +19844: Goal: +19844: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19844: Order: +19844: lpo +19844: Leaf order: +19844: meet 17 2 5 0,2 +19844: join 20 2 4 0,2,2 +19844: c 3 0 3 2,2,2 +19844: b 3 0 3 1,2,2 +19844: a 5 0 5 1,2 +% SZS status Timeout for LAT124-1.p +NO CLASH, using fixed ground order +19863: Facts: +19863: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19863: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19863: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19863: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19863: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19863: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19863: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19863: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19863: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 ?29)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29 +19863: Goal: +19863: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19863: Order: +19863: nrkbo +19863: Leaf order: +19863: meet 18 2 5 0,2 +19863: join 18 2 4 0,2,2 +19863: c 3 0 3 2,2,2 +19863: b 3 0 3 1,2,2 +19863: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19864: Facts: +19864: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19864: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19864: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19864: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19864: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19864: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19864: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19864: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19864: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 ?29)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29 +19864: Goal: +19864: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19864: Order: +19864: kbo +19864: Leaf order: +19864: meet 18 2 5 0,2 +19864: join 18 2 4 0,2,2 +19864: c 3 0 3 2,2,2 +19864: b 3 0 3 1,2,2 +19864: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19865: Facts: +19865: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19865: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19865: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19865: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19865: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19865: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19865: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19865: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19865: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 ?29)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29 +19865: Goal: +19865: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19865: Order: +19865: lpo +19865: Leaf order: +19865: meet 18 2 5 0,2 +19865: join 18 2 4 0,2,2 +19865: c 3 0 3 2,2,2 +19865: b 3 0 3 1,2,2 +19865: a 5 0 5 1,2 +% SZS status Timeout for LAT125-1.p +NO CLASH, using fixed ground order +19895: Facts: +19895: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19895: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19895: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19895: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19895: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19895: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19895: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19895: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19895: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28)))) + [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29 +19895: Goal: +19895: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19895: Order: +19895: kbo +19895: Leaf order: +19895: meet 18 2 5 0,2 +19895: join 18 2 4 0,2,2 +19895: c 3 0 3 2,2,2 +19895: b 3 0 3 1,2,2 +19895: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19894: Facts: +19894: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19894: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19894: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19894: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19894: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19894: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19894: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19894: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19894: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28)))) + [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29 +19894: Goal: +19894: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19894: Order: +19894: nrkbo +19894: Leaf order: +19894: meet 18 2 5 0,2 +19894: join 18 2 4 0,2,2 +19894: c 3 0 3 2,2,2 +19894: b 3 0 3 1,2,2 +19894: a 5 0 5 1,2 +NO CLASH, using fixed ground order +19896: Facts: +19896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19896: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19896: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19896: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19896: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19896: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28)))) + [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29 +19896: Goal: +19896: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +19896: Order: +19896: lpo +19896: Leaf order: +19896: meet 18 2 5 0,2 +19896: join 18 2 4 0,2,2 +19896: c 3 0 3 2,2,2 +19896: b 3 0 3 1,2,2 +19896: a 5 0 5 1,2 +% SZS status Timeout for LAT126-1.p +NO CLASH, using fixed ground order +19924: Facts: +19924: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19924: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19924: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19924: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19924: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19924: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19924: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19924: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19924: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27)))) + [28, 27, 26] by equation_H55_dual ?26 ?27 ?28 +19924: Goal: +19924: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +19924: Order: +19924: nrkbo +19924: Leaf order: +19924: join 16 2 4 0,2,2 +19924: meet 20 2 6 0,2 +19924: c 3 0 3 2,2,2,2 +19924: b 3 0 3 1,2,2 +19924: a 6 0 6 1,2 +NO CLASH, using fixed ground order +19925: Facts: +19925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19925: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19925: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19925: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19925: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19925: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27)))) + [28, 27, 26] by equation_H55_dual ?26 ?27 ?28 +19925: Goal: +19925: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +19925: Order: +19925: kbo +19925: Leaf order: +19925: join 16 2 4 0,2,2 +19925: meet 20 2 6 0,2 +19925: c 3 0 3 2,2,2,2 +19925: b 3 0 3 1,2,2 +19925: a 6 0 6 1,2 +NO CLASH, using fixed ground order +19926: Facts: +19926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19926: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19926: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19926: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19926: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19926: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =?= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27)))) + [28, 27, 26] by equation_H55_dual ?26 ?27 ?28 +19926: Goal: +19926: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +19926: Order: +19926: lpo +19926: Leaf order: +19926: join 16 2 4 0,2,2 +19926: meet 20 2 6 0,2 +19926: c 3 0 3 2,2,2,2 +19926: b 3 0 3 1,2,2 +19926: a 6 0 6 1,2 +% SZS status Timeout for LAT127-1.p +NO CLASH, using fixed ground order +20053: Facts: +20053: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20053: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20053: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20053: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20053: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20053: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20053: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20053: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20053: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +20053: Goal: +20053: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +20053: Order: +20053: nrkbo +20053: Leaf order: +20053: join 17 2 4 0,2,2 +20053: meet 19 2 6 0,2 +20053: c 3 0 3 2,2,2,2 +20053: b 4 0 4 1,2,2 +20053: a 5 0 5 1,2 +NO CLASH, using fixed ground order +20054: Facts: +20054: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20054: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20054: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20054: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20054: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20054: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20054: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20054: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20054: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +20054: Goal: +20054: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +20054: Order: +20054: kbo +20054: Leaf order: +20054: join 17 2 4 0,2,2 +20054: meet 19 2 6 0,2 +20054: c 3 0 3 2,2,2,2 +20054: b 4 0 4 1,2,2 +20054: a 5 0 5 1,2 +NO CLASH, using fixed ground order +20055: Facts: +20055: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20055: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20055: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20055: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20055: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20055: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20055: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20055: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20055: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +20055: Goal: +20055: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +20055: Order: +20055: lpo +20055: Leaf order: +20055: join 17 2 4 0,2,2 +20055: meet 19 2 6 0,2 +20055: c 3 0 3 2,2,2,2 +20055: b 4 0 4 1,2,2 +20055: a 5 0 5 1,2 +% SZS status Timeout for LAT128-1.p +NO CLASH, using fixed ground order +20071: Facts: +20071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20071: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20071: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20071: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20071: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20071: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +20071: Goal: +20071: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +20071: Order: +20071: nrkbo +20071: Leaf order: +20071: join 16 2 3 0,2,2 +20071: meet 18 2 5 0,2 +20071: c 3 0 3 2,2,2,2 +20071: b 3 0 3 1,2,2 +20071: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20072: Facts: +20072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20072: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20072: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20072: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20072: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20072: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +20072: Goal: +20072: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +20072: Order: +20072: kbo +20072: Leaf order: +20072: join 16 2 3 0,2,2 +20072: meet 18 2 5 0,2 +20072: c 3 0 3 2,2,2,2 +20072: b 3 0 3 1,2,2 +20072: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20073: Facts: +20073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20073: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20073: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20073: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20073: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20073: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +20073: Goal: +20073: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +20073: Order: +20073: lpo +20073: Leaf order: +20073: join 16 2 3 0,2,2 +20073: meet 18 2 5 0,2 +20073: c 3 0 3 2,2,2,2 +20073: b 3 0 3 1,2,2 +20073: a 4 0 4 1,2 +% SZS status Timeout for LAT129-1.p +NO CLASH, using fixed ground order +20105: Facts: +20105: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20105: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20105: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20105: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20105: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20105: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20105: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20105: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20105: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +20105: Goal: +20105: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet a c)))) + [] by prove_H39 +20105: Order: +20105: nrkbo +20105: Leaf order: +20105: meet 17 2 5 0,2 +20105: join 17 2 4 0,2,2 +20105: d 2 0 2 2,2,2,2,2 +20105: c 3 0 3 1,2,2,2 +20105: b 2 0 2 1,2,2 +20105: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20106: Facts: +20106: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20106: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20106: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20106: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20106: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20106: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20106: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20106: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20106: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +20106: Goal: +20106: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet a c)))) + [] by prove_H39 +20106: Order: +20106: kbo +20106: Leaf order: +20106: meet 17 2 5 0,2 +20106: join 17 2 4 0,2,2 +20106: d 2 0 2 2,2,2,2,2 +20106: c 3 0 3 1,2,2,2 +20106: b 2 0 2 1,2,2 +20106: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20107: Facts: +20107: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20107: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20107: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20107: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20107: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20107: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20107: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20107: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20107: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +20107: Goal: +20107: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join d (meet a c)))) + [] by prove_H39 +20107: Order: +20107: lpo +20107: Leaf order: +20107: meet 17 2 5 0,2 +20107: join 17 2 4 0,2,2 +20107: d 2 0 2 2,2,2,2,2 +20107: c 3 0 3 1,2,2,2 +20107: b 2 0 2 1,2,2 +20107: a 4 0 4 1,2 +% SZS status Timeout for LAT130-1.p +NO CLASH, using fixed ground order +20123: Facts: +20123: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20123: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20123: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20123: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20123: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20123: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20123: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20123: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20123: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +20123: Goal: +20123: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +20123: Order: +20123: nrkbo +20123: Leaf order: +20123: meet 17 2 5 0,2 +20123: join 18 2 5 0,2,2 +20123: d 2 0 2 2,2,2,2,2 +20123: c 3 0 3 1,2,2,2 +20123: b 3 0 3 1,2,2 +20123: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20124: Facts: +20124: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20124: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20124: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20124: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20124: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20124: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20124: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20124: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20124: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +20124: Goal: +20124: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +20124: Order: +20124: kbo +20124: Leaf order: +20124: meet 17 2 5 0,2 +20124: join 18 2 5 0,2,2 +20124: d 2 0 2 2,2,2,2,2 +20124: c 3 0 3 1,2,2,2 +20124: b 3 0 3 1,2,2 +20124: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20125: Facts: +20125: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20125: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20125: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20125: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20125: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20125: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20125: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20125: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20125: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +20125: Goal: +20125: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +20125: Order: +20125: lpo +20125: Leaf order: +20125: meet 17 2 5 0,2 +20125: join 18 2 5 0,2,2 +20125: d 2 0 2 2,2,2,2,2 +20125: c 3 0 3 1,2,2,2 +20125: b 3 0 3 1,2,2 +20125: a 4 0 4 1,2 +% SZS status Timeout for LAT131-1.p +NO CLASH, using fixed ground order +20152: Facts: +20152: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20152: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20152: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20152: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20152: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20152: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20152: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20152: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20152: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + meet (join ?26 (meet ?28 (join ?26 ?27))) + (join ?26 (meet ?27 (join ?26 ?28))) + [28, 27, 26] by equation_H69_dual ?26 ?27 ?28 +20152: Goal: +20152: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +20152: Order: +20152: nrkbo +20152: Leaf order: +20152: meet 18 2 5 0,2 +20152: join 19 2 5 0,2,2 +20152: d 2 0 2 2,2,2,2,2 +20152: c 3 0 3 1,2,2,2 +20152: b 3 0 3 1,2,2 +20152: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20153: Facts: +20153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20153: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20153: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20153: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20153: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20153: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + meet (join ?26 (meet ?28 (join ?26 ?27))) + (join ?26 (meet ?27 (join ?26 ?28))) + [28, 27, 26] by equation_H69_dual ?26 ?27 ?28 +20153: Goal: +20153: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +20153: Order: +20153: kbo +20153: Leaf order: +20153: meet 18 2 5 0,2 +20153: join 19 2 5 0,2,2 +20153: d 2 0 2 2,2,2,2,2 +20153: c 3 0 3 1,2,2,2 +20153: b 3 0 3 1,2,2 +20153: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20154: Facts: +20154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20154: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20154: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20154: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20154: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20154: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + meet (join ?26 (meet ?28 (join ?26 ?27))) + (join ?26 (meet ?27 (join ?26 ?28))) + [28, 27, 26] by equation_H69_dual ?26 ?27 ?28 +20154: Goal: +20154: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +20154: Order: +20154: lpo +20154: Leaf order: +20154: meet 18 2 5 0,2 +20154: join 19 2 5 0,2,2 +20154: d 2 0 2 2,2,2,2,2 +20154: c 3 0 3 1,2,2,2 +20154: b 3 0 3 1,2,2 +20154: a 4 0 4 1,2 +% SZS status Timeout for LAT132-1.p +NO CLASH, using fixed ground order +20170: Facts: +20170: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20170: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20170: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20170: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20170: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20170: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20170: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20170: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20170: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +20170: Goal: +20170: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet (join a (meet b (join a c))) (join c (meet a b))) + [] by prove_H6_dual +20170: Order: +20170: nrkbo +20170: Leaf order: +20170: meet 16 2 4 0,2,2 +20170: join 20 2 6 0,2 +20170: c 3 0 3 2,2,2,2 +20170: b 3 0 3 1,2,2 +20170: a 6 0 6 1,2 +NO CLASH, using fixed ground order +20171: Facts: +20171: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20171: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20171: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20171: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20171: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20171: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20171: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20171: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20171: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +20171: Goal: +20171: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet (join a (meet b (join a c))) (join c (meet a b))) + [] by prove_H6_dual +20171: Order: +20171: kbo +20171: Leaf order: +20171: meet 16 2 4 0,2,2 +20171: join 20 2 6 0,2 +20171: c 3 0 3 2,2,2,2 +20171: b 3 0 3 1,2,2 +20171: a 6 0 6 1,2 +NO CLASH, using fixed ground order +20172: Facts: +20172: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20172: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20172: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20172: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20172: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20172: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20172: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20172: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20172: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +20172: Goal: +20172: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet (join a (meet b (join a c))) (join c (meet a b))) + [] by prove_H6_dual +20172: Order: +20172: lpo +20172: Leaf order: +20172: meet 16 2 4 0,2,2 +20172: join 20 2 6 0,2 +20172: c 3 0 3 2,2,2,2 +20172: b 3 0 3 1,2,2 +20172: a 6 0 6 1,2 +% SZS status Timeout for LAT133-1.p +NO CLASH, using fixed ground order +20205: Facts: +20205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20205: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20205: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20205: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20205: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20205: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28)) + [28, 27, 26] by equation_H61 ?26 ?27 ?28 +20205: Goal: +20205: Id : 1, {_}: + meet (join a b) (join a c) + =<= + join a (meet (join b (meet c (join a b))) (join c (meet a b))) + [] by prove_H22_dual +20205: Order: +20205: kbo +20205: Leaf order: +20205: meet 16 2 4 0,2 +20205: c 3 0 3 2,2,2 +20205: join 20 2 6 0,1,2 +20205: b 4 0 4 2,1,2 +20205: a 5 0 5 1,1,2 +NO CLASH, using fixed ground order +20204: Facts: +20204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20204: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20204: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20204: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20204: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20204: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28)) + [28, 27, 26] by equation_H61 ?26 ?27 ?28 +20204: Goal: +20204: Id : 1, {_}: + meet (join a b) (join a c) + =<= + join a (meet (join b (meet c (join a b))) (join c (meet a b))) + [] by prove_H22_dual +20204: Order: +20204: nrkbo +20204: Leaf order: +20204: meet 16 2 4 0,2 +20204: c 3 0 3 2,2,2 +20204: join 20 2 6 0,1,2 +20204: b 4 0 4 2,1,2 +20204: a 5 0 5 1,1,2 +NO CLASH, using fixed ground order +20206: Facts: +20206: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20206: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20206: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20206: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20206: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20206: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20206: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20206: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20206: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28)) + [28, 27, 26] by equation_H61 ?26 ?27 ?28 +20206: Goal: +20206: Id : 1, {_}: + meet (join a b) (join a c) + =<= + join a (meet (join b (meet c (join a b))) (join c (meet a b))) + [] by prove_H22_dual +20206: Order: +20206: lpo +20206: Leaf order: +20206: meet 16 2 4 0,2 +20206: c 3 0 3 2,2,2 +20206: join 20 2 6 0,1,2 +20206: b 4 0 4 2,1,2 +20206: a 5 0 5 1,1,2 +% SZS status Timeout for LAT134-1.p +NO CLASH, using fixed ground order +20243: Facts: +20243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20243: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20243: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20243: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20243: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20243: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +20243: Goal: +20243: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +20243: Order: +20243: nrkbo +20243: Leaf order: +20243: join 17 2 5 0,2 +20243: meet 17 2 4 0,2,2 +20243: d 2 0 2 2,2,2,2,2 +20243: c 3 0 3 1,2,2,2 +20243: b 2 0 2 1,2,2 +20243: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20244: Facts: +20244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20244: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20244: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20244: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20244: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20244: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +20244: Goal: +20244: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +20244: Order: +20244: kbo +20244: Leaf order: +20244: join 17 2 5 0,2 +20244: meet 17 2 4 0,2,2 +20244: d 2 0 2 2,2,2,2,2 +20244: c 3 0 3 1,2,2,2 +20244: b 2 0 2 1,2,2 +20244: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20245: Facts: +20245: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20245: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20245: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20245: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20245: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20245: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20245: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20245: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20245: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +20245: Goal: +20245: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =>= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +20245: Order: +20245: lpo +20245: Leaf order: +20245: join 17 2 5 0,2 +20245: meet 17 2 4 0,2,2 +20245: d 2 0 2 2,2,2,2,2 +20245: c 3 0 3 1,2,2,2 +20245: b 2 0 2 1,2,2 +20245: a 4 0 4 1,2 +% SZS status Timeout for LAT135-1.p +NO CLASH, using fixed ground order +20272: Facts: +20272: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20272: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20272: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20272: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20272: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20272: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20272: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20272: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20272: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +20272: Goal: +20272: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +20272: Order: +20272: nrkbo +20272: Leaf order: +20272: join 18 2 5 0,2 +20272: meet 18 2 4 0,2,2 +20272: d 2 0 2 2,2,2,2,2 +20272: c 3 0 3 1,2,2,2 +20272: b 2 0 2 1,2,2 +20272: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20273: Facts: +20273: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20273: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20273: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20273: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20273: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20273: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20273: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20273: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20273: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +20273: Goal: +20273: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +20273: Order: +20273: kbo +20273: Leaf order: +20273: join 18 2 5 0,2 +20273: meet 18 2 4 0,2,2 +20273: d 2 0 2 2,2,2,2,2 +20273: c 3 0 3 1,2,2,2 +20273: b 2 0 2 1,2,2 +20273: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20274: Facts: +20274: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20274: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20274: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20274: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20274: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20274: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20274: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20274: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20274: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +20274: Goal: +20274: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =>= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +20274: Order: +20274: lpo +20274: Leaf order: +20274: join 18 2 5 0,2 +20274: meet 18 2 4 0,2,2 +20274: d 2 0 2 2,2,2,2,2 +20274: c 3 0 3 1,2,2,2 +20274: b 2 0 2 1,2,2 +20274: a 4 0 4 1,2 +% SZS status Timeout for LAT136-1.p +NO CLASH, using fixed ground order +20301: Facts: +20301: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20301: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20301: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20301: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20301: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20301: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20301: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20301: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20301: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +20301: Goal: +20301: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join c (meet a b))))) + [] by prove_H40_dual +20301: Order: +20301: nrkbo +20301: Leaf order: +20301: join 18 2 5 0,2 +20301: meet 19 2 5 0,2,2 +20301: d 2 0 2 2,2,2,2,2 +20301: c 3 0 3 1,2,2,2 +20301: b 3 0 3 1,2,2 +20301: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20302: Facts: +20302: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20302: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20302: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20302: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20302: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20302: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20302: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20302: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20302: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +20302: Goal: +20302: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join c (meet a b))))) + [] by prove_H40_dual +20302: Order: +20302: kbo +20302: Leaf order: +20302: join 18 2 5 0,2 +20302: meet 19 2 5 0,2,2 +20302: d 2 0 2 2,2,2,2,2 +20302: c 3 0 3 1,2,2,2 +20302: b 3 0 3 1,2,2 +20302: a 4 0 4 1,2 +NO CLASH, using fixed ground order +20303: Facts: +20303: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20303: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20303: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20303: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20303: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20303: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20303: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20303: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20303: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +20303: Goal: +20303: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join c (meet a b))))) + [] by prove_H40_dual +20303: Order: +20303: lpo +20303: Leaf order: +20303: join 18 2 5 0,2 +20303: meet 19 2 5 0,2,2 +20303: d 2 0 2 2,2,2,2,2 +20303: c 3 0 3 1,2,2,2 +20303: b 3 0 3 1,2,2 +20303: a 4 0 4 1,2 +% SZS status Timeout for LAT137-1.p +NO CLASH, using fixed ground order +20331: Facts: +20331: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20331: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20331: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20331: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20331: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20331: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20331: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20331: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20331: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28)) + [28, 27, 26] by equation_H61_dual ?26 ?27 ?28 +20331: Goal: +20331: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +20331: Order: +20331: nrkbo +20331: Leaf order: +20331: join 16 2 4 0,2,2 +20331: meet 20 2 6 0,2 +20331: c 3 0 3 2,2,2,2 +20331: b 3 0 3 1,2,2 +20331: a 6 0 6 1,2 +NO CLASH, using fixed ground order +20332: Facts: +20332: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20332: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20332: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20332: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20332: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20332: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20332: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20332: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20332: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28)) + [28, 27, 26] by equation_H61_dual ?26 ?27 ?28 +20332: Goal: +20332: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +20332: Order: +20332: kbo +20332: Leaf order: +20332: join 16 2 4 0,2,2 +20332: meet 20 2 6 0,2 +20332: c 3 0 3 2,2,2,2 +20332: b 3 0 3 1,2,2 +20332: a 6 0 6 1,2 +NO CLASH, using fixed ground order +20333: Facts: +20333: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +20333: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +20333: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +20333: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +20333: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +20333: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +20333: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +20333: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +20333: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28)) + [28, 27, 26] by equation_H61_dual ?26 ?27 ?28 +20333: Goal: +20333: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +20333: Order: +20333: lpo +20333: Leaf order: +20333: join 16 2 4 0,2,2 +20333: meet 20 2 6 0,2 +20333: c 3 0 3 2,2,2,2 +20333: b 3 0 3 1,2,2 +20333: a 6 0 6 1,2 +% SZS status Timeout for LAT171-1.p +NO CLASH, using fixed ground order +20686: Facts: +20686: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20686: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20686: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20686: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20686: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent +20686: Goal: +20686: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma +20686: Order: +20686: nrkbo +20686: Leaf order: +20686: y 2 0 0 +20686: not 2 1 0 +20686: truth 4 0 1 3 +20686: implies 16 2 1 0,2 +20686: z 2 0 1 2,2 +20686: x 2 0 1 1,2 +NO CLASH, using fixed ground order +20687: Facts: +20687: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20687: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20687: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20687: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20687: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent +20687: Goal: +20687: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma +20687: Order: +20687: kbo +20687: Leaf order: +20687: y 2 0 0 +20687: not 2 1 0 +20687: truth 4 0 1 3 +20687: implies 16 2 1 0,2 +20687: z 2 0 1 2,2 +20687: x 2 0 1 1,2 +NO CLASH, using fixed ground order +20688: Facts: +20688: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20688: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20688: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20688: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20688: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent +20688: Goal: +20688: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma +20688: Order: +20688: lpo +20688: Leaf order: +20688: y 2 0 0 +20688: not 2 1 0 +20688: truth 4 0 1 3 +20688: implies 16 2 1 0,2 +20688: z 2 0 1 2,2 +20688: x 2 0 1 1,2 +% SZS status Timeout for LCL136-1.p +NO CLASH, using fixed ground order +20715: Facts: +20715: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20715: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20715: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20715: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20715: Goal: +20715: Id : 1, {_}: + implies (implies (implies x y) y) + (implies (implies y z) (implies x z)) + =>= + truth + [] by prove_wajsberg_lemma +20715: Order: +20715: nrkbo +20715: Leaf order: +20715: not 2 1 0 +20715: truth 4 0 1 3 +20715: z 2 0 2 2,1,2,2 +20715: implies 19 2 6 0,2 +20715: y 3 0 3 2,1,1,2 +20715: x 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +20716: Facts: +20716: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20716: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20716: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20716: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20716: Goal: +20716: Id : 1, {_}: + implies (implies (implies x y) y) + (implies (implies y z) (implies x z)) + =>= + truth + [] by prove_wajsberg_lemma +20716: Order: +20716: kbo +20716: Leaf order: +20716: not 2 1 0 +20716: truth 4 0 1 3 +20716: z 2 0 2 2,1,2,2 +20716: implies 19 2 6 0,2 +20716: y 3 0 3 2,1,1,2 +20716: x 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +20717: Facts: +20717: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20717: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20717: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20717: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20717: Goal: +20717: Id : 1, {_}: + implies (implies (implies x y) y) + (implies (implies y z) (implies x z)) + =>= + truth + [] by prove_wajsberg_lemma +20717: Order: +20717: lpo +20717: Leaf order: +20717: not 2 1 0 +20717: truth 4 0 1 3 +20717: z 2 0 2 2,1,2,2 +20717: implies 19 2 6 0,2 +20717: y 3 0 3 2,1,1,2 +20717: x 2 0 2 1,1,1,2 +% SZS status Timeout for LCL137-1.p +NO CLASH, using fixed ground order +20733: Facts: +20733: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20733: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20733: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20733: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20733: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +20733: Id : 7, {_}: + or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +20733: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +20733: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +20733: Id : 10, {_}: + and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +20733: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +20733: Goal: +20733: Id : 1, {_}: + not (or (and x (or x x)) (and x x)) + =<= + and (not x) (or (or (not x) (not x)) (and (not x) (not x))) + [] by prove_wajsberg_theorem +20733: Order: +20733: nrkbo +20733: Leaf order: +20733: implies 14 2 0 +20733: truth 3 0 0 +20733: not 12 1 6 0,2 +20733: and 11 2 4 0,1,1,2 +20733: or 12 2 4 0,1,2 +20733: x 10 0 10 1,1,1,2 +NO CLASH, using fixed ground order +20734: Facts: +20734: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20734: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20734: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20734: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20734: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +20734: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +20734: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +20734: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +20734: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +20734: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +20734: Goal: +NO CLASH, using fixed ground order +20735: Facts: +20735: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +20735: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +20735: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +20735: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +20735: Id : 6, {_}: + or ?14 ?15 =>= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +20735: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +20735: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +20735: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +20735: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +20735: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +20735: Goal: +20735: Id : 1, {_}: + not (or (and x (or x x)) (and x x)) + =<= + and (not x) (or (or (not x) (not x)) (and (not x) (not x))) + [] by prove_wajsberg_theorem +20735: Order: +20735: lpo +20735: Leaf order: +20735: implies 14 2 0 +20735: truth 3 0 0 +20735: not 12 1 6 0,2 +20735: and 11 2 4 0,1,1,2 +20735: or 12 2 4 0,1,2 +20735: x 10 0 10 1,1,1,2 +20734: Id : 1, {_}: + not (or (and x (or x x)) (and x x)) + =<= + and (not x) (or (or (not x) (not x)) (and (not x) (not x))) + [] by prove_wajsberg_theorem +20734: Order: +20734: kbo +20734: Leaf order: +20734: implies 14 2 0 +20734: truth 3 0 0 +20734: not 12 1 6 0,2 +20734: and 11 2 4 0,1,1,2 +20734: or 12 2 4 0,1,2 +20734: x 10 0 10 1,1,1,2 +% SZS status Timeout for LCL165-1.p +NO CLASH, using fixed ground order +20763: Facts: +20763: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20763: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20763: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20763: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20763: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20763: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20763: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20763: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20763: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20763: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20763: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20763: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20763: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20763: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20763: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20763: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20763: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20763: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20763: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20763: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20763: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20763: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20763: Goal: +20763: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +20763: Order: +20763: kbo +20763: Leaf order: +20763: commutator 1 2 0 +20763: additive_inverse 22 1 0 +20763: multiply 40 2 0 +20763: additive_identity 8 0 0 +20763: associator 4 3 3 0,2 +20763: add 26 2 2 0,3,2 +20763: v 2 0 2 2,3,2 +20763: u 2 0 2 1,3,2 +20763: y 3 0 3 2,2 +20763: x 3 0 3 1,2 +NO CLASH, using fixed ground order +20762: Facts: +20762: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20762: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20762: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20762: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20762: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20762: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20762: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20762: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20762: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20762: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20762: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20762: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20762: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20762: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20762: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20762: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20762: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20762: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20762: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20762: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20762: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20762: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20762: Goal: +20762: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +20762: Order: +20762: nrkbo +20762: Leaf order: +20762: commutator 1 2 0 +20762: additive_inverse 22 1 0 +20762: multiply 40 2 0 +20762: additive_identity 8 0 0 +20762: associator 4 3 3 0,2 +20762: add 26 2 2 0,3,2 +20762: v 2 0 2 2,3,2 +20762: u 2 0 2 1,3,2 +20762: y 3 0 3 2,2 +20762: x 3 0 3 1,2 +NO CLASH, using fixed ground order +20764: Facts: +20764: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20764: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20764: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20764: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20764: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20764: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20764: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20764: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20764: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20764: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20764: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20764: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20764: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20764: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20764: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20764: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20764: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20764: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20764: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20764: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20764: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20764: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20764: Goal: +20764: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +20764: Order: +20764: lpo +20764: Leaf order: +20764: commutator 1 2 0 +20764: additive_inverse 22 1 0 +20764: multiply 40 2 0 +20764: additive_identity 8 0 0 +20764: associator 4 3 3 0,2 +20764: add 26 2 2 0,3,2 +20764: v 2 0 2 2,3,2 +20764: u 2 0 2 1,3,2 +20764: y 3 0 3 2,2 +20764: x 3 0 3 1,2 +% SZS status Timeout for RNG019-7.p +NO CLASH, using fixed ground order +20780: Facts: +20780: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20780: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20780: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20780: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20780: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20780: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20780: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20780: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20780: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20780: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20780: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20780: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20780: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20780: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20780: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20780: Goal: +20780: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +20780: Order: +20780: nrkbo +20780: Leaf order: +20780: commutator 1 2 0 +20780: additive_inverse 6 1 0 +20780: multiply 22 2 0 +20780: additive_identity 8 0 0 +20780: associator 4 3 3 0,2 +20780: y 3 0 3 3,2 +20780: add 18 2 2 0,2,2 +20780: v 2 0 2 2,2,2 +20780: u 2 0 2 1,2,2 +20780: x 3 0 3 1,2 +NO CLASH, using fixed ground order +20781: Facts: +20781: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20781: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20781: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20781: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20781: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20781: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20781: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20781: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20781: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20781: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20781: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20781: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20781: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20781: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20781: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20781: Goal: +20781: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +20781: Order: +20781: kbo +20781: Leaf order: +20781: commutator 1 2 0 +20781: additive_inverse 6 1 0 +20781: multiply 22 2 0 +20781: additive_identity 8 0 0 +20781: associator 4 3 3 0,2 +20781: y 3 0 3 3,2 +20781: add 18 2 2 0,2,2 +20781: v 2 0 2 2,2,2 +20781: u 2 0 2 1,2,2 +20781: x 3 0 3 1,2 +NO CLASH, using fixed ground order +20782: Facts: +20782: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20782: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20782: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20782: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20782: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20782: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20782: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20782: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20782: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20782: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20782: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20782: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20782: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20782: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20782: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20782: Goal: +20782: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +20782: Order: +20782: lpo +20782: Leaf order: +20782: commutator 1 2 0 +20782: additive_inverse 6 1 0 +20782: multiply 22 2 0 +20782: additive_identity 8 0 0 +20782: associator 4 3 3 0,2 +20782: y 3 0 3 3,2 +20782: add 18 2 2 0,2,2 +20782: v 2 0 2 2,2,2 +20782: u 2 0 2 1,2,2 +20782: x 3 0 3 1,2 +% SZS status Timeout for RNG020-6.p +NO CLASH, using fixed ground order +20815: Facts: +20815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20815: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20815: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20815: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20815: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20815: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20815: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20815: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20815: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20815: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20815: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20815: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20815: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +NO CLASH, using fixed ground order +20816: Facts: +20816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20816: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20816: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20816: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +NO CLASH, using fixed ground order +20817: Facts: +20817: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20817: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20816: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20817: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20816: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20817: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20817: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20816: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20817: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20817: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20816: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20817: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20816: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20815: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20816: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20815: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20816: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20816: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20815: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20816: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20815: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20816: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20815: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20816: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20815: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20816: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20815: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20815: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20815: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20815: Goal: +20815: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +20815: Order: +20815: nrkbo +20815: Leaf order: +20815: commutator 1 2 0 +20815: additive_inverse 22 1 0 +20815: multiply 40 2 0 +20815: additive_identity 8 0 0 +20815: associator 4 3 3 0,2 +20815: y 3 0 3 3,2 +20815: add 26 2 2 0,2,2 +20815: v 2 0 2 2,2,2 +20815: u 2 0 2 1,2,2 +20815: x 3 0 3 1,2 +20817: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20816: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20816: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20816: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20816: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20816: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20816: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20816: Goal: +20816: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +20816: Order: +20816: kbo +20816: Leaf order: +20816: commutator 1 2 0 +20816: additive_inverse 22 1 0 +20816: multiply 40 2 0 +20816: additive_identity 8 0 0 +20816: associator 4 3 3 0,2 +20816: y 3 0 3 3,2 +20816: add 26 2 2 0,2,2 +20816: v 2 0 2 2,2,2 +20816: u 2 0 2 1,2,2 +20816: x 3 0 3 1,2 +20817: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20817: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20817: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20817: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20817: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20817: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20817: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20817: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20817: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20817: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20817: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20817: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20817: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20817: Goal: +20817: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +20817: Order: +20817: lpo +20817: Leaf order: +20817: commutator 1 2 0 +20817: additive_inverse 22 1 0 +20817: multiply 40 2 0 +20817: additive_identity 8 0 0 +20817: associator 4 3 3 0,2 +20817: y 3 0 3 3,2 +20817: add 26 2 2 0,2,2 +20817: v 2 0 2 2,2,2 +20817: u 2 0 2 1,2,2 +20817: x 3 0 3 1,2 +% SZS status Timeout for RNG020-7.p +NO CLASH, using fixed ground order +20843: Facts: +20843: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20843: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20843: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20843: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20843: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20843: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20843: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20843: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20843: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20843: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20843: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20843: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20843: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20843: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20843: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20843: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20843: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20843: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20843: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20843: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20843: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20843: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20843: Goal: +20843: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +20843: Order: +20843: kbo +20843: Leaf order: +20843: commutator 1 2 0 +20843: additive_inverse 22 1 0 +20843: multiply 40 2 0 +20843: additive_identity 8 0 0 +20843: associator 4 3 3 0,2 +20843: y 3 0 3 3,2 +20843: x 3 0 3 2,2 +20843: add 26 2 2 0,1,2 +20843: v 2 0 2 2,1,2 +20843: u 2 0 2 1,1,2 +NO CLASH, using fixed ground order +20842: Facts: +20842: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20842: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20842: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20842: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20842: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20842: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20842: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20842: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20842: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20842: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20842: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20842: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20842: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20842: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20842: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20842: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20842: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20842: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20842: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20842: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20842: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20842: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20842: Goal: +20842: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +20842: Order: +20842: nrkbo +20842: Leaf order: +20842: commutator 1 2 0 +20842: additive_inverse 22 1 0 +20842: multiply 40 2 0 +20842: additive_identity 8 0 0 +20842: associator 4 3 3 0,2 +20842: y 3 0 3 3,2 +20842: x 3 0 3 2,2 +20842: add 26 2 2 0,1,2 +20842: v 2 0 2 2,1,2 +20842: u 2 0 2 1,1,2 +NO CLASH, using fixed ground order +20844: Facts: +20844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20844: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20844: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20844: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20844: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20844: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20844: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20844: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20844: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20844: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20844: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20844: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20844: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20844: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20844: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20844: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +20844: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +20844: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +20844: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +20844: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +20844: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +20844: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +20844: Goal: +20844: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +20844: Order: +20844: lpo +20844: Leaf order: +20844: commutator 1 2 0 +20844: additive_inverse 22 1 0 +20844: multiply 40 2 0 +20844: additive_identity 8 0 0 +20844: associator 4 3 3 0,2 +20844: y 3 0 3 3,2 +20844: x 3 0 3 2,2 +20844: add 26 2 2 0,1,2 +20844: v 2 0 2 2,1,2 +20844: u 2 0 2 1,1,2 +% SZS status Timeout for RNG021-7.p +NO CLASH, using fixed ground order +20871: Facts: +20871: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20871: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20871: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20871: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20871: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20871: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20871: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20871: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20871: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20871: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20871: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20871: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20871: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20871: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20871: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20871: Goal: +20871: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +20871: Order: +20871: nrkbo +20871: Leaf order: +20871: commutator 1 2 0 +20871: additive_inverse 6 1 0 +20871: multiply 22 2 0 +20871: additive_identity 9 0 1 3 +20871: add 17 2 1 0,2 +20871: associator 3 3 2 0,1,2 +20871: z 2 0 2 3,1,2 +20871: y 2 0 2 2,1,2 +20871: x 2 0 2 1,1,2 +NO CLASH, using fixed ground order +20872: Facts: +20872: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20872: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20872: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20872: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20872: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20872: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20872: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20872: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20872: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20872: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20872: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20872: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20872: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20872: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20872: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20872: Goal: +20872: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +20872: Order: +20872: kbo +20872: Leaf order: +20872: commutator 1 2 0 +20872: additive_inverse 6 1 0 +20872: multiply 22 2 0 +20872: additive_identity 9 0 1 3 +20872: add 17 2 1 0,2 +20872: associator 3 3 2 0,1,2 +20872: z 2 0 2 3,1,2 +20872: y 2 0 2 2,1,2 +20872: x 2 0 2 1,1,2 +NO CLASH, using fixed ground order +20873: Facts: +20873: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20873: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20873: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20873: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20873: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20873: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20873: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20873: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20873: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20873: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20873: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20873: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20873: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20873: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20873: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20873: Goal: +20873: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +20873: Order: +20873: lpo +20873: Leaf order: +20873: commutator 1 2 0 +20873: additive_inverse 6 1 0 +20873: multiply 22 2 0 +20873: additive_identity 9 0 1 3 +20873: add 17 2 1 0,2 +20873: associator 3 3 2 0,1,2 +20873: z 2 0 2 3,1,2 +20873: y 2 0 2 2,1,2 +20873: x 2 0 2 1,1,2 +% SZS status Timeout for RNG025-4.p +NO CLASH, using fixed ground order +20890: Facts: +20890: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +20890: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +20890: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +20890: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +20890: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +20890: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +20890: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +20890: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +20890: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +20890: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +20890: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +20890: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20890: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20890: Id : 15, {_}: + associator ?37 ?38 (add ?39 ?40) + =<= + add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40) + [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40 +20890: Id : 16, {_}: + associator ?42 (add ?43 ?44) ?45 + =<= + add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45) + [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45 +20890: Id : 17, {_}: + associator (add ?47 ?48) ?49 ?50 + =<= + add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50) + [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50 +NO CLASH, using fixed ground order +20891: Facts: +20891: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +20891: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +20891: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +20891: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +20891: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +20891: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +20891: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +20891: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +NO CLASH, using fixed ground order +20892: Facts: +20892: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +20892: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +20892: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +20892: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +20892: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +20892: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +20892: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +20892: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +20892: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +20891: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +20890: Id : 18, {_}: + commutator ?52 ?53 + =<= + add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53)) + [53, 52] by commutator ?52 ?53 +20890: Goal: +20892: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +20890: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +20890: Order: +20890: nrkbo +20890: Leaf order: +20892: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +20892: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20892: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20892: Id : 15, {_}: + associator ?37 ?38 (add ?39 ?40) + =>= + add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40) + [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40 +20892: Id : 16, {_}: + associator ?42 (add ?43 ?44) ?45 + =>= + add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45) + [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45 +20892: Id : 17, {_}: + associator (add ?47 ?48) ?49 ?50 + =>= + add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50) + [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50 +20892: Id : 18, {_}: + commutator ?52 ?53 + =<= + add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53)) + [53, 52] by commutator ?52 ?53 +20892: Goal: +20892: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +20892: Order: +20892: lpo +20892: Leaf order: +20892: commutator 1 2 0 +20892: additive_inverse 5 1 0 +20892: multiply 18 2 0 +20892: additive_identity 9 0 1 3 +20892: add 22 2 1 0,2 +20892: associator 11 3 2 0,1,2 +20892: c 2 0 2 3,1,2 +20892: b 2 0 2 2,1,2 +20892: a 2 0 2 1,1,2 +20891: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +20890: commutator 1 2 0 +20890: additive_inverse 5 1 0 +20890: multiply 18 2 0 +20890: additive_identity 9 0 1 3 +20890: add 22 2 1 0,2 +20890: associator 11 3 2 0,1,2 +20890: c 2 0 2 3,1,2 +20890: b 2 0 2 2,1,2 +20890: a 2 0 2 1,1,2 +20891: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +20891: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20891: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20891: Id : 15, {_}: + associator ?37 ?38 (add ?39 ?40) + =<= + add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40) + [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40 +20891: Id : 16, {_}: + associator ?42 (add ?43 ?44) ?45 + =<= + add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45) + [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45 +20891: Id : 17, {_}: + associator (add ?47 ?48) ?49 ?50 + =<= + add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50) + [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50 +20891: Id : 18, {_}: + commutator ?52 ?53 + =<= + add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53)) + [53, 52] by commutator ?52 ?53 +20891: Goal: +20891: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +20891: Order: +20891: kbo +20891: Leaf order: +20891: commutator 1 2 0 +20891: additive_inverse 5 1 0 +20891: multiply 18 2 0 +20891: additive_identity 9 0 1 3 +20891: add 22 2 1 0,2 +20891: associator 11 3 2 0,1,2 +20891: c 2 0 2 3,1,2 +20891: b 2 0 2 2,1,2 +20891: a 2 0 2 1,1,2 +% SZS status Timeout for RNG025-8.p +NO CLASH, using fixed ground order +20920: Facts: +20920: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +20920: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =<= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +20920: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =<= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +20920: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +20920: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +20920: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +20920: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +20920: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +20920: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +20920: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +20920: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +20920: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +20920: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +20920: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +20920: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +20920: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +20920: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +20920: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +20920: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +20920: Id : 21, {_}: + multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60) + [60, 59] by left_alternative ?59 ?60 +20920: Id : 22, {_}: + associator ?62 ?63 (add ?64 ?65) + =<= + add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65) + [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65 +20920: Id : 23, {_}: + associator ?67 (add ?68 ?69) ?70 + =<= + add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70) + [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70 +20920: Id : 24, {_}: + associator (add ?72 ?73) ?74 ?75 + =<= + add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75) + [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75 +20920: Id : 25, {_}: + commutator ?77 ?78 + =<= + add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78)) + [78, 77] by commutator ?77 ?78 +20920: Goal: +20920: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +20920: Order: +20920: nrkbo +20920: Leaf order: +20920: commutator 1 2 0 +20920: multiply 36 2 0 add +20920: additive_inverse 21 1 0 +20920: additive_identity 9 0 1 3 +20920: add 30 2 1 0,2 +20920: associator 11 3 2 0,1,2 +20920: c 2 0 2 3,1,2 +20920: b 2 0 2 2,1,2 +20920: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +20921: Facts: +20921: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +20921: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =<= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +20921: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =<= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +20921: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +20921: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +20921: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +20921: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +20921: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +20921: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +20921: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +20921: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +20921: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +20921: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +20921: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +20921: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +20921: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +20921: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +20921: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +20921: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +20921: Id : 21, {_}: + multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60) + [60, 59] by left_alternative ?59 ?60 +20921: Id : 22, {_}: + associator ?62 ?63 (add ?64 ?65) + =<= + add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65) + [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65 +20921: Id : 23, {_}: + associator ?67 (add ?68 ?69) ?70 + =<= + add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70) + [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70 +20921: Id : 24, {_}: + associator (add ?72 ?73) ?74 ?75 + =<= + add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75) + [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75 +20921: Id : 25, {_}: + commutator ?77 ?78 + =<= + add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78)) + [78, 77] by commutator ?77 ?78 +20921: Goal: +20921: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +20921: Order: +20921: kbo +20921: Leaf order: +20921: commutator 1 2 0 +20921: multiply 36 2 0 add +20921: additive_inverse 21 1 0 +20921: additive_identity 9 0 1 3 +20921: add 30 2 1 0,2 +20921: associator 11 3 2 0,1,2 +20921: c 2 0 2 3,1,2 +20921: b 2 0 2 2,1,2 +20921: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +20922: Facts: +20922: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +20922: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =<= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +20922: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =<= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +20922: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +20922: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +20922: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +20922: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +20922: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +20922: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +20922: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +20922: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +20922: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +20922: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +20922: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +20922: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +20922: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +20922: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +20922: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +20922: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +20922: Id : 21, {_}: + multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60) + [60, 59] by left_alternative ?59 ?60 +20922: Id : 22, {_}: + associator ?62 ?63 (add ?64 ?65) + =>= + add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65) + [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65 +20922: Id : 23, {_}: + associator ?67 (add ?68 ?69) ?70 + =>= + add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70) + [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70 +20922: Id : 24, {_}: + associator (add ?72 ?73) ?74 ?75 + =>= + add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75) + [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75 +20922: Id : 25, {_}: + commutator ?77 ?78 + =<= + add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78)) + [78, 77] by commutator ?77 ?78 +20922: Goal: +20922: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +20922: Order: +20922: lpo +20922: Leaf order: +20922: commutator 1 2 0 +20922: multiply 36 2 0 add +20922: additive_inverse 21 1 0 +20922: additive_identity 9 0 1 3 +20922: add 30 2 1 0,2 +20922: associator 11 3 2 0,1,2 +20922: c 2 0 2 3,1,2 +20922: b 2 0 2 2,1,2 +20922: a 2 0 2 1,1,2 +% SZS status Timeout for RNG025-9.p +NO CLASH, using fixed ground order +20954: Facts: +20954: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +20954: Id : 3, {_}: + multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) + [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +20954: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +20954: Id : 5, {_}: + pixley ?11 ?12 ?13 + =<= + add (multiply ?11 (inverse ?12)) + (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) + [13, 12, 11] by pixley_defn ?11 ?12 ?13 +20954: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +20954: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +20954: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +20954: Goal: +20954: Id : 1, {_}: + add a (multiply b c) =<= multiply (add a b) (add a c) + [] by prove_add_multiply_property +20954: Order: +20954: nrkbo +20954: Leaf order: +20954: pixley 4 3 0 +20954: n1 1 0 0 +20954: inverse 3 1 0 +20954: add 9 2 3 0,2 +20954: multiply 9 2 2 0,2,2 +20954: c 2 0 2 2,2,2 +20954: b 2 0 2 1,2,2 +20954: a 3 0 3 1,2 +NO CLASH, using fixed ground order +20955: Facts: +20955: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +20955: Id : 3, {_}: + multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) + [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +20955: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +20955: Id : 5, {_}: + pixley ?11 ?12 ?13 + =<= + add (multiply ?11 (inverse ?12)) + (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) + [13, 12, 11] by pixley_defn ?11 ?12 ?13 +20955: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +20955: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +20955: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +20955: Goal: +20955: Id : 1, {_}: + add a (multiply b c) =<= multiply (add a b) (add a c) + [] by prove_add_multiply_property +20955: Order: +20955: kbo +20955: Leaf order: +20955: pixley 4 3 0 +20955: n1 1 0 0 +20955: inverse 3 1 0 +20955: add 9 2 3 0,2 +20955: multiply 9 2 2 0,2,2 +20955: c 2 0 2 2,2,2 +20955: b 2 0 2 1,2,2 +20955: a 3 0 3 1,2 +NO CLASH, using fixed ground order +20956: Facts: +20956: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +20956: Id : 3, {_}: + multiply ?5 (add ?6 ?7) =?= add (multiply ?6 ?5) (multiply ?7 ?5) + [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +20956: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +20956: Id : 5, {_}: + pixley ?11 ?12 ?13 + =<= + add (multiply ?11 (inverse ?12)) + (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) + [13, 12, 11] by pixley_defn ?11 ?12 ?13 +20956: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +20956: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +20956: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +20956: Goal: +20956: Id : 1, {_}: + add a (multiply b c) =<= multiply (add a b) (add a c) + [] by prove_add_multiply_property +20956: Order: +20956: lpo +20956: Leaf order: +20956: pixley 4 3 0 +20956: n1 1 0 0 +20956: inverse 3 1 0 +20956: add 9 2 3 0,2 +20956: multiply 9 2 2 0,2,2 +20956: c 2 0 2 2,2,2 +20956: b 2 0 2 1,2,2 +20956: a 3 0 3 1,2 +Statistics : +Max weight : 22 +Found proof, 38.942991s +% SZS status Unsatisfiable for BOO023-1.p +% SZS output start CNFRefutation for BOO023-1.p +Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35 +Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13 +Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3 +Id : 485, {_}: multiply (pixley ?939 ?940 ?941) (multiply ?941 (add ?939 (inverse ?940))) =>= multiply ?941 (add ?939 (inverse ?940)) [941, 940, 939] by Super 2 with 19 at 1,2 +Id : 505, {_}: multiply ?1017 (multiply ?1018 (add ?1017 (inverse ?1018))) =>= multiply ?1018 (add ?1017 (inverse ?1018)) [1018, 1017] by Super 485 with 7 at 1,2 +Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3 +Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3 +Id : 413, {_}: ?825 =<= add (multiply ?826 (inverse ?826)) (multiply ?825 n1) [826, 825] by Demod 22 with 6 at 2 +Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2 +Id : 428, {_}: ?870 =<= add (inverse n1) (multiply ?870 n1) [870] by Super 413 with 16 at 1,3 +Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3 +Id : 548, {_}: ?1062 =<= add (inverse n1) (multiply ?1062 n1) [1062] by Super 413 with 16 at 1,3 +Id : 593, {_}: add ?1120 n1 =?= add (inverse n1) n1 [1120] by Super 548 with 2 at 2,3 +Id : 553, {_}: add ?1072 n1 =?= add (inverse n1) n1 [1072] by Super 548 with 2 at 2,3 +Id : 607, {_}: add ?1148 n1 =?= add ?1149 n1 [1149, 1148] by Super 593 with 553 at 3 +Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3 +Id : 408, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2 +Id : 412, {_}: multiply (multiply ?822 n1) (add ?823 ?822) =<= add (multiply ?823 (multiply ?822 n1)) (multiply ?822 n1) [823, 822] by Super 13 with 408 at 2,2,2 +Id : 274, {_}: multiply (multiply ?502 (add ?503 ?504)) (multiply ?504 ?502) =>= multiply ?504 ?502 [504, 503, 502] by Super 2 with 3 at 1,2 +Id : 284, {_}: multiply (multiply ?542 n1) (multiply (inverse ?543) ?542) =>= multiply (inverse ?543) ?542 [543, 542] by Super 274 with 4 at 2,1,2 +Id : 173, {_}: multiply (inverse ?334) (add ?335 n1) =<= add (multiply ?335 (inverse ?334)) (inverse ?334) [335, 334] by Super 3 with 16 at 2,3 +Id : 1514, {_}: multiply ?2669 (multiply ?2670 (add ?2669 (inverse ?2670))) =>= multiply ?2670 (add ?2669 (inverse ?2670)) [2670, 2669] by Super 485 with 7 at 1,2 +Id : 672, {_}: multiply (multiply ?1271 n1) (multiply (inverse ?1272) ?1271) =>= multiply (inverse ?1272) ?1271 [1272, 1271] by Super 274 with 4 at 2,1,2 +Id : 688, {_}: multiply n1 (multiply (inverse ?1320) (add ?1321 n1)) =>= multiply (inverse ?1320) (add ?1321 n1) [1321, 1320] by Super 672 with 2 at 1,2 +Id : 199, {_}: multiply (inverse ?371) (add ?372 n1) =<= add (multiply ?372 (inverse ?371)) (inverse ?371) [372, 371] by Super 3 with 16 at 2,3 +Id : 210, {_}: multiply (inverse ?404) (add (add ?405 (inverse ?404)) n1) =>= add (inverse ?404) (inverse ?404) [405, 404] by Super 199 with 2 at 1,3 +Id : 966, {_}: add (inverse ?404) (multiply n1 (inverse ?404)) =>= add (inverse ?404) (inverse ?404) [404] by Demod 210 with 14 at 2 +Id : 174, {_}: multiply (inverse ?337) (add n1 ?338) =<= add (inverse ?337) (multiply ?338 (inverse ?337)) [338, 337] by Super 3 with 16 at 1,3 +Id : 967, {_}: multiply (inverse ?404) (add n1 n1) =?= add (inverse ?404) (inverse ?404) [404] by Demod 966 with 174 at 2 +Id : 982, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) (add n1 n1) [1904] by Super 688 with 967 at 2,2 +Id : 1530, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 1514 with 982 at 2,2 +Id : 1554, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 1530 with 967 at 2,2 +Id : 1555, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 1554 with 982 at 3 +Id : 1556, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 1555 with 967 at 3 +Id : 1568, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 1556 at 2,3 +Id : 1597, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1568 with 8 at 2 +Id : 1814, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 1597 at 2,2 +Id : 1906, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 1814 with 173 at 3 +Id : 1990, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3163 n1) [3163] by Super 1906 with 607 at 2,3 +Id : 2009, {_}: multiply (inverse n1) (inverse n1) =>= add (inverse n1) (inverse n1) [] by Super 1990 with 967 at 3 +Id : 2048, {_}: multiply (inverse n1) (add (inverse n1) n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Super 173 with 2009 at 1,3 +Id : 1928, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Super 1906 with 607 at 2,3 +Id : 2040, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 1928 with 2009 at 2 +Id : 2082, {_}: add (inverse n1) (inverse n1) =<= add (add (inverse n1) (inverse n1)) (inverse n1) [] by Demod 2048 with 2040 at 2 +Id : 2135, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Super 14 with 2082 at 2,2 +Id : 2186, {_}: add (inverse n1) (inverse n1) =<= add (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 2135 with 1556 at 2 +Id : 2187, {_}: add (inverse n1) (inverse n1) =<= multiply (inverse n1) (add n1 (inverse n1)) [] by Demod 2186 with 174 at 3 +Id : 2188, {_}: add (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2187 with 4 at 2,3 +Id : 2041, {_}: inverse n1 =<= add (add (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 1597 with 2009 at 1,3 +Id : 2225, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (add (inverse n1) (inverse n1)) [] by Demod 2041 with 2188 at 1,3 +Id : 2226, {_}: inverse n1 =<= add (multiply (inverse n1) n1) (multiply (inverse n1) n1) [] by Demod 2225 with 2188 at 2,3 +Id : 2235, {_}: inverse n1 =<= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 2226 with 3 at 3 +Id : 2236, {_}: inverse n1 =<= multiply (inverse n1) (add n1 n1) [] by Demod 2235 with 982 at 3 +Id : 2237, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 2236 with 967 at 3 +Id : 2238, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 2237 with 2188 at 3 +Id : 2244, {_}: add (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2188 with 2238 at 3 +Id : 2259, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= add (multiply ?3306 (inverse n1)) (inverse n1) [3306] by Super 13 with 2244 at 2,2,2 +Id : 2294, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= multiply (inverse n1) (add ?3306 n1) [3306] by Demod 2259 with 173 at 3 +Id : 2232, {_}: multiply (inverse n1) n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2040 with 2188 at 2 +Id : 2243, {_}: inverse n1 =<= multiply (inverse n1) (add ?3128 n1) [3128] by Demod 2232 with 2238 at 2 +Id : 2295, {_}: multiply (inverse n1) (add ?3306 (inverse n1)) =>= inverse n1 [3306] by Demod 2294 with 2243 at 3 +Id : 2419, {_}: multiply (multiply (add ?3405 (inverse n1)) n1) (inverse n1) =>= multiply (inverse n1) (add ?3405 (inverse n1)) [3405] by Super 284 with 2295 at 2,2 +Id : 3205, {_}: multiply (multiply (add ?4259 (inverse n1)) n1) (inverse n1) =>= inverse n1 [4259] by Demod 2419 with 2295 at 3 +Id : 3222, {_}: multiply (multiply n1 n1) (inverse n1) =>= inverse n1 [] by Super 3205 with 4 at 1,1,2 +Id : 3294, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= add (inverse n1) (multiply ?4332 (inverse n1)) [4332] by Super 3 with 3222 at 1,3 +Id : 3323, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4332) =>= multiply (inverse n1) (add n1 ?4332) [4332] by Demod 3294 with 174 at 3 +Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3 +Id : 2249, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Super 24 with 2244 at 1,2,2,3 +Id : 2310, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (add (inverse n1) (inverse n1))) [3289] by Demod 2249 with 2244 at 1,2 +Id : 2311, {_}: pixley (inverse n1) n1 ?3289 =<= add (inverse n1) (multiply ?3289 (inverse n1)) [3289] by Demod 2310 with 2244 at 2,2,3 +Id : 2312, {_}: pixley (inverse n1) n1 ?3289 =<= multiply (inverse n1) (add n1 ?3289) [3289] by Demod 2311 with 174 at 3 +Id : 3528, {_}: multiply (inverse n1) (add (multiply n1 n1) ?4508) =>= pixley (inverse n1) n1 ?4508 [4508] by Demod 3323 with 2312 at 3 +Id : 3542, {_}: multiply (inverse n1) (multiply n1 (add n1 ?4535)) =>= pixley (inverse n1) n1 (multiply ?4535 n1) [4535] by Super 3528 with 3 at 2,2 +Id : 2258, {_}: pixley (inverse n1) n1 ?3304 =<= add (multiply (inverse n1) (inverse n1)) (multiply ?3304 (inverse n1)) [3304] by Super 19 with 2244 at 2,2,3 +Id : 2766, {_}: pixley (inverse n1) n1 ?3924 =<= multiply (inverse n1) (add (inverse n1) ?3924) [3924] by Demod 2258 with 3 at 3 +Id : 2784, {_}: pixley (inverse n1) n1 (multiply ?3959 n1) =>= multiply (inverse n1) ?3959 [3959] by Super 2766 with 428 at 2,3 +Id : 4047, {_}: multiply (inverse n1) (multiply n1 (add n1 ?5164)) =>= multiply (inverse n1) ?5164 [5164] by Demod 3542 with 2784 at 3 +Id : 4052, {_}: multiply (inverse n1) (multiply n1 n1) =>= multiply (inverse n1) (inverse n1) [] by Super 4047 with 4 at 2,2,2 +Id : 2233, {_}: multiply (inverse n1) (inverse n1) =>= multiply (inverse n1) n1 [] by Demod 2009 with 2188 at 3 +Id : 2242, {_}: multiply (inverse n1) (inverse n1) =>= inverse n1 [] by Demod 2233 with 2238 at 3 +Id : 4088, {_}: multiply (inverse n1) (multiply n1 n1) =>= inverse n1 [] by Demod 4052 with 2242 at 3 +Id : 4118, {_}: multiply (multiply n1 n1) (add (inverse n1) n1) =>= add (inverse n1) (multiply n1 n1) [] by Super 412 with 4088 at 1,3 +Id : 1137, {_}: multiply (multiply ?2152 n1) (add ?2152 ?2153) =<= add (multiply ?2152 n1) (multiply ?2153 (multiply ?2152 n1)) [2153, 2152] by Super 14 with 408 at 1,2,2 +Id : 411, {_}: multiply ?820 (multiply ?820 n1) =>= multiply ?820 n1 [820] by Super 2 with 408 at 1,2 +Id : 1151, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= add (multiply ?2193 n1) (multiply ?2193 n1) [2193] by Super 1137 with 411 at 2,3 +Id : 1282, {_}: multiply (multiply ?2412 n1) (add ?2412 ?2412) =>= multiply n1 (add ?2412 ?2412) [2412] by Demod 1151 with 3 at 3 +Id : 1286, {_}: multiply (multiply n1 n1) (add ?2420 n1) =>= multiply n1 (add n1 n1) [2420] by Super 1282 with 607 at 2,2 +Id : 4147, {_}: multiply n1 (add n1 n1) =<= add (inverse n1) (multiply n1 n1) [] by Demod 4118 with 1286 at 2 +Id : 4148, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3 +Id : 4590, {_}: multiply (add n1 n1) (add n1 ?5598) =>= add n1 (multiply ?5598 (add n1 n1)) [5598] by Super 3 with 4148 at 1,3 +Id : 4186, {_}: multiply n1 (add n1 n1) =>= n1 [] by Demod 4147 with 428 at 3 +Id : 4194, {_}: multiply n1 (add ?5284 n1) =>= n1 [5284] by Super 4186 with 607 at 2,2 +Id : 4313, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 4194 at 2 +Id : 4601, {_}: multiply (add n1 n1) n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Super 4590 with 4313 at 2,2 +Id : 4648, {_}: n1 =<= add n1 (multiply (multiply n1 n1) (add n1 n1)) [] by Demod 4601 with 2 at 2 +Id : 1187, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= multiply n1 (add ?2193 ?2193) [2193] by Demod 1151 with 3 at 3 +Id : 4649, {_}: n1 =<= add n1 (multiply n1 (add n1 n1)) [] by Demod 4648 with 1187 at 2,3 +Id : 4650, {_}: n1 =<= add n1 n1 [] by Demod 4649 with 4194 at 2,3 +Id : 4692, {_}: add ?5677 n1 =>= n1 [5677] by Super 607 with 4650 at 3 +Id : 5124, {_}: multiply ?6342 n1 =<= add ?6342 (multiply n1 ?6342) [6342] by Super 14 with 4692 at 2,2 +Id : 4670, {_}: multiply n1 (add (inverse ?1904) (inverse ?1904)) =>= multiply (inverse ?1904) n1 [1904] by Demod 982 with 4650 at 2,3 +Id : 4669, {_}: multiply (inverse ?404) n1 =<= add (inverse ?404) (inverse ?404) [404] by Demod 967 with 4650 at 2,2 +Id : 4674, {_}: multiply n1 (multiply (inverse ?1904) n1) =>= multiply (inverse ?1904) n1 [1904] by Demod 4670 with 4669 at 2,2 +Id : 5136, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= add (multiply (inverse ?6367) n1) (multiply (inverse ?6367) n1) [6367] by Super 5124 with 4674 at 2,3 +Id : 5182, {_}: multiply (multiply (inverse ?6367) n1) n1 =<= multiply n1 (add (inverse ?6367) (inverse ?6367)) [6367] by Demod 5136 with 3 at 3 +Id : 5183, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply n1 (multiply (inverse ?6367) n1) [6367] by Demod 5182 with 4669 at 2,3 +Id : 5184, {_}: multiply (multiply (inverse ?6367) n1) n1 =>= multiply (inverse ?6367) n1 [6367] by Demod 5183 with 4674 at 3 +Id : 5206, {_}: multiply (inverse ?6424) n1 =<= add (inverse n1) (multiply (inverse ?6424) n1) [6424] by Super 428 with 5184 at 2,3 +Id : 5244, {_}: multiply (inverse ?6424) n1 =>= inverse ?6424 [6424] by Demod 5206 with 428 at 3 +Id : 5308, {_}: inverse ?6512 =<= add (inverse n1) (inverse ?6512) [6512] by Super 428 with 5244 at 2,3 +Id : 5370, {_}: pixley (inverse n1) ?6557 ?6558 =<= add (multiply (inverse n1) (inverse ?6557)) (multiply ?6558 (inverse ?6557)) [6558, 6557] by Super 19 with 5308 at 2,2,3 +Id : 7459, {_}: pixley (inverse n1) ?8766 ?8767 =<= multiply (inverse ?8766) (add (inverse n1) ?8767) [8767, 8766] by Demod 5370 with 3 at 3 +Id : 5371, {_}: inverse (inverse n1) =>= n1 [] by Super 4 with 5308 at 2 +Id : 7482, {_}: pixley (inverse n1) (inverse n1) ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Super 7459 with 5371 at 1,3 +Id : 7542, {_}: ?8832 =<= multiply n1 (add (inverse n1) ?8832) [8832] by Demod 7482 with 6 at 2 +Id : 5466, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 (inverse (inverse n1))) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Super 19 with 5371 at 2,2,2,3 +Id : 5516, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 (add ?6672 n1)) [6673, 6672] by Demod 5466 with 5371 at 2,1,3 +Id : 5517, {_}: pixley ?6672 (inverse n1) ?6673 =<= add (multiply ?6672 n1) (multiply ?6673 n1) [6673, 6672] by Demod 5516 with 4692 at 2,2,3 +Id : 5854, {_}: pixley ?6987 (inverse n1) ?6988 =<= multiply n1 (add ?6987 ?6988) [6988, 6987] by Demod 5517 with 3 at 3 +Id : 5871, {_}: pixley (inverse n1) (inverse n1) (multiply ?7040 n1) =>= multiply n1 ?7040 [7040] by Super 5854 with 428 at 2,3 +Id : 5916, {_}: multiply ?7040 n1 =?= multiply n1 ?7040 [7040] by Demod 5871 with 6 at 2 +Id : 5518, {_}: pixley ?6672 (inverse n1) ?6673 =<= multiply n1 (add ?6672 ?6673) [6673, 6672] by Demod 5517 with 3 at 3 +Id : 5837, {_}: multiply ?6926 (pixley ?6926 (inverse n1) (inverse n1)) =>= multiply n1 (add ?6926 (inverse n1)) [6926] by Super 505 with 5518 at 2,2 +Id : 5906, {_}: multiply ?6926 ?6926 =?= multiply n1 (add ?6926 (inverse n1)) [6926] by Demod 5837 with 7 at 2,2 +Id : 5907, {_}: multiply ?6926 ?6926 =?= pixley ?6926 (inverse n1) (inverse n1) [6926] by Demod 5906 with 5518 at 3 +Id : 5908, {_}: multiply ?6926 ?6926 =>= ?6926 [6926] by Demod 5907 with 7 at 3 +Id : 7131, {_}: multiply ?8481 (add ?8482 ?8481) =>= add (multiply ?8482 ?8481) ?8481 [8482, 8481] by Super 3 with 5908 at 2,3 +Id : 5066, {_}: multiply ?6275 n1 =<= add ?6275 (multiply n1 ?6275) [6275] by Super 14 with 4692 at 2,2 +Id : 6609, {_}: multiply ?7988 n1 =<= add ?7988 (multiply ?7988 n1) [7988] by Super 5066 with 5916 at 2,3 +Id : 7156, {_}: multiply (multiply ?8553 n1) (multiply ?8553 n1) =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Super 7131 with 6609 at 2,2 +Id : 7254, {_}: multiply ?8553 n1 =<= add (multiply ?8553 (multiply ?8553 n1)) (multiply ?8553 n1) [8553] by Demod 7156 with 5908 at 2 +Id : 7255, {_}: multiply ?8553 n1 =<= multiply (multiply ?8553 n1) (add ?8553 ?8553) [8553] by Demod 7254 with 412 at 3 +Id : 5833, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= pixley ?2193 (inverse n1) ?2193 [2193] by Demod 1187 with 5518 at 3 +Id : 5835, {_}: multiply (multiply ?2193 n1) (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5833 with 8 at 3 +Id : 7256, {_}: multiply ?8553 n1 =>= ?8553 [8553] by Demod 7255 with 5835 at 3 +Id : 7273, {_}: ?7040 =<= multiply n1 ?7040 [7040] by Demod 5916 with 7256 at 2 +Id : 7543, {_}: ?8832 =<= add (inverse n1) ?8832 [8832] by Demod 7542 with 7273 at 3 +Id : 7582, {_}: multiply (inverse n1) (multiply ?8919 (inverse ?8919)) =?= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Super 505 with 7543 at 2,2,2 +Id : 5473, {_}: multiply ?6687 (multiply (inverse n1) (add ?6687 n1)) =?= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Super 505 with 5371 at 2,2,2,2 +Id : 5499, {_}: multiply ?6687 (multiply (inverse n1) n1) =<= multiply (inverse n1) (add ?6687 (inverse (inverse n1))) [6687] by Demod 5473 with 4692 at 2,2,2 +Id : 5500, {_}: multiply ?6687 (multiply (inverse n1) n1) =?= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5499 with 5371 at 2,2,3 +Id : 5501, {_}: multiply ?6687 (inverse n1) =<= multiply (inverse n1) (add ?6687 n1) [6687] by Demod 5500 with 5244 at 2,2 +Id : 5502, {_}: multiply ?6687 (inverse n1) =?= multiply (inverse n1) n1 [6687] by Demod 5501 with 4692 at 2,3 +Id : 5503, {_}: multiply ?6687 (inverse n1) =>= inverse n1 [6687] by Demod 5502 with 5244 at 3 +Id : 5615, {_}: multiply (inverse n1) (add n1 ?6752) =>= add (inverse n1) (inverse n1) [6752] by Super 174 with 5503 at 2,3 +Id : 5636, {_}: pixley (inverse n1) n1 ?6752 =?= add (inverse n1) (inverse n1) [6752] by Demod 5615 with 2312 at 2 +Id : 5285, {_}: inverse ?404 =<= add (inverse ?404) (inverse ?404) [404] by Demod 4669 with 5244 at 2 +Id : 5637, {_}: pixley (inverse n1) n1 ?6752 =>= inverse n1 [6752] by Demod 5636 with 5285 at 3 +Id : 5782, {_}: inverse n1 =<= multiply (inverse n1) ?3959 [3959] by Demod 2784 with 5637 at 2 +Id : 7613, {_}: inverse n1 =<= multiply ?8919 (add (inverse n1) (inverse ?8919)) [8919] by Demod 7582 with 5782 at 2 +Id : 7614, {_}: inverse n1 =<= multiply ?8919 (inverse ?8919) [8919] by Demod 7613 with 7543 at 2,3 +Id : 7674, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =?= add (inverse n1) (multiply ?8985 (inverse ?8984)) [8985, 8984] by Super 3 with 7614 at 1,3 +Id : 7731, {_}: multiply (inverse ?8984) (add ?8984 ?8985) =>= multiply ?8985 (inverse ?8984) [8985, 8984] by Demod 7674 with 7543 at 3 +Id : 289, {_}: multiply (multiply ?563 (multiply (inverse ?564) (add ?565 n1))) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [565, 564, 563] by Super 274 with 173 at 2,1,2 +Id : 8394, {_}: multiply (multiply ?563 (multiply (inverse ?564) n1)) (multiply (inverse ?564) ?563) =>= multiply (inverse ?564) ?563 [564, 563] by Demod 289 with 4692 at 2,2,1,2 +Id : 8406, {_}: multiply (multiply ?9773 (inverse ?9774)) (multiply (inverse ?9774) ?9773) =>= multiply (inverse ?9774) ?9773 [9774, 9773] by Demod 8394 with 7256 at 2,1,2 +Id : 8444, {_}: multiply (inverse n1) (multiply (inverse ?9877) ?9877) =>= multiply (inverse ?9877) ?9877 [9877] by Super 8406 with 7614 at 1,2 +Id : 8534, {_}: inverse n1 =<= multiply (inverse ?9877) ?9877 [9877] by Demod 8444 with 5782 at 2 +Id : 8551, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= add (multiply ?9926 ?9925) (inverse n1) [9926, 9925] by Super 3 with 8534 at 2,3 +Id : 367, {_}: multiply ?731 (add (add ?732 ?731) ?733) =>= add ?731 (multiply ?733 ?731) [733, 732, 731] by Super 12 with 2 at 1,3 +Id : 379, {_}: multiply ?780 n1 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Super 367 with 4 at 2,2 +Id : 7285, {_}: ?780 =<= add ?780 (multiply (inverse (add ?781 ?780)) ?780) [781, 780] by Demod 379 with 7256 at 2 +Id : 7585, {_}: ?8927 =<= add ?8927 (multiply (inverse ?8927) ?8927) [8927] by Super 7285 with 7543 at 1,1,2,3 +Id : 8670, {_}: ?8927 =<= add ?8927 (inverse n1) [8927] by Demod 7585 with 8534 at 2,3 +Id : 9041, {_}: multiply ?9925 (add ?9926 (inverse ?9925)) =>= multiply ?9926 ?9925 [9926, 9925] by Demod 8551 with 8670 at 3 +Id : 172, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 (add n1 (inverse ?331))) [332, 331] by Super 19 with 16 at 1,3 +Id : 9053, {_}: pixley n1 ?10412 ?10412 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Super 172 with 9041 at 2,3 +Id : 9135, {_}: n1 =<= add (inverse ?10412) (multiply n1 ?10412) [10412] by Demod 9053 with 7 at 2 +Id : 9136, {_}: n1 =<= add (inverse ?10412) ?10412 [10412] by Demod 9135 with 7273 at 2,3 +Id : 9201, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =<= add (multiply (inverse (inverse ?10589)) (inverse ?10589)) (multiply ?10590 n1) [10590, 10589] by Super 19 with 9136 at 2,2,3 +Id : 9238, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =?= add (inverse n1) (multiply ?10590 n1) [10590, 10589] by Demod 9201 with 8534 at 1,3 +Id : 9239, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= add (inverse n1) ?10590 [10590, 10589] by Demod 9238 with 7256 at 2,3 +Id : 9240, {_}: pixley (inverse (inverse ?10589)) ?10589 ?10590 =>= ?10590 [10590, 10589] by Demod 9239 with 7543 at 3 +Id : 10446, {_}: ?12102 =<= inverse (inverse ?12102) [12102] by Super 7 with 9240 at 2 +Id : 10555, {_}: multiply (inverse ?12273) (add ?12274 ?12273) =>= multiply ?12274 (inverse ?12273) [12274, 12273] by Super 9041 with 10446 at 2,2,2 +Id : 11456, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 (inverse (inverse ?13532)) =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Super 24 with 10555 at 2,3 +Id : 11548, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =<= add (inverse ?13532) (multiply (add ?13531 (inverse ?13532)) (inverse (inverse ?13532))) [13532, 13531] by Demod 11456 with 10446 at 3,2 +Id : 8892, {_}: multiply (inverse ?10244) (add ?10244 ?10245) =>= multiply ?10245 (inverse ?10244) [10245, 10244] by Demod 7674 with 7543 at 3 +Id : 7580, {_}: multiply ?8914 (add ?8915 ?8914) =?= add (multiply (inverse n1) ?8914) ?8914 [8915, 8914] by Super 13 with 7543 at 2,2 +Id : 5958, {_}: multiply ?7147 (add ?7148 ?7147) =>= add (multiply ?7148 ?7147) ?7147 [7148, 7147] by Super 3 with 5908 at 2,3 +Id : 7619, {_}: add (multiply ?8915 ?8914) ?8914 =?= add (multiply (inverse n1) ?8914) ?8914 [8914, 8915] by Demod 7580 with 5958 at 2 +Id : 7620, {_}: add (multiply ?8915 ?8914) ?8914 =>= add (inverse n1) ?8914 [8914, 8915] by Demod 7619 with 5782 at 1,3 +Id : 7775, {_}: add (multiply ?9114 ?9115) ?9115 =>= ?9115 [9115, 9114] by Demod 7620 with 7543 at 3 +Id : 7621, {_}: add (multiply ?8915 ?8914) ?8914 =>= ?8914 [8914, 8915] by Demod 7620 with 7543 at 3 +Id : 7749, {_}: multiply ?7147 (add ?7148 ?7147) =>= ?7147 [7148, 7147] by Demod 5958 with 7621 at 3 +Id : 7792, {_}: add ?9167 (add ?9168 ?9167) =>= add ?9168 ?9167 [9168, 9167] by Super 7775 with 7749 at 1,2 +Id : 8900, {_}: multiply (inverse ?10265) (add ?10266 ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10266, 10265] by Super 8892 with 7792 at 2,2 +Id : 11444, {_}: multiply ?10266 (inverse ?10265) =<= multiply (add ?10266 ?10265) (inverse ?10265) [10265, 10266] by Demod 8900 with 10555 at 2 +Id : 11549, {_}: pixley (add ?13531 (inverse ?13532)) ?13532 ?13532 =?= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11548 with 11444 at 2,3 +Id : 11550, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 (inverse (inverse ?13532))) [13532, 13531] by Demod 11549 with 7 at 2 +Id : 11551, {_}: add ?13531 (inverse ?13532) =<= add (inverse ?13532) (multiply ?13531 ?13532) [13532, 13531] by Demod 11550 with 10446 at 2,2,3 +Id : 11841, {_}: multiply (inverse (inverse ?13951)) (add ?13952 (inverse ?13951)) =>= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13952, 13951] by Super 7731 with 11551 at 2,2 +Id : 11918, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) (inverse (inverse ?13951)) [13951, 13952] by Demod 11841 with 10555 at 2 +Id : 11919, {_}: multiply ?13952 (inverse (inverse ?13951)) =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11918 with 10446 at 2,3 +Id : 11920, {_}: multiply ?13952 ?13951 =<= multiply (multiply ?13952 ?13951) ?13951 [13951, 13952] by Demod 11919 with 10446 at 2,2 +Id : 12244, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= add (multiply ?14435 ?14434) (multiply ?14436 ?14434) [14436, 14435, 14434] by Super 3 with 11920 at 2,3 +Id : 29011, {_}: multiply ?35505 (add ?35506 (multiply ?35507 ?35505)) =>= multiply ?35505 (add ?35506 ?35507) [35507, 35506, 35505] by Demod 12244 with 3 at 3 +Id : 29060, {_}: multiply ?35715 (add ?35716 (inverse n1)) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Super 29011 with 8534 at 2,2,2 +Id : 11860, {_}: add ?14021 (inverse ?14022) =<= add (inverse ?14022) (multiply ?14021 ?14022) [14022, 14021] by Demod 11550 with 10446 at 2,2,3 +Id : 11890, {_}: add n1 (inverse ?14122) =<= add (inverse ?14122) ?14122 [14122] by Super 11860 with 7273 at 2,3 +Id : 11943, {_}: add n1 (inverse ?14122) =>= n1 [14122] by Demod 11890 with 9136 at 3 +Id : 11977, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) (multiply ?332 n1) [332, 331] by Demod 172 with 11943 at 2,2,3 +Id : 11984, {_}: pixley n1 ?331 ?332 =<= add (inverse ?331) ?332 [332, 331] by Demod 11977 with 7256 at 2,3 +Id : 11991, {_}: add ?13531 (inverse ?13532) =<= pixley n1 ?13532 (multiply ?13531 ?13532) [13532, 13531] by Demod 11551 with 11984 at 3 +Id : 12023, {_}: add n1 (inverse ?14257) =>= n1 [14257] by Demod 11890 with 9136 at 3 +Id : 12028, {_}: add n1 ?14267 =>= n1 [14267] by Super 12023 with 10446 at 2,2 +Id : 12137, {_}: multiply ?14331 (add n1 ?14332) =?= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Super 14 with 12028 at 1,2,2 +Id : 12188, {_}: multiply ?14331 n1 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12137 with 12028 at 2,2 +Id : 12598, {_}: ?14940 =<= add ?14940 (multiply ?14941 ?14940) [14941, 14940] by Demod 12188 with 7256 at 2 +Id : 409, {_}: multiply (multiply ?814 n1) (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Super 14 with 408 at 1,2,2 +Id : 7278, {_}: multiply ?814 (add ?814 ?815) =<= add (multiply ?814 n1) (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 409 with 7256 at 1,2 +Id : 7279, {_}: multiply ?814 (add ?814 ?815) =<= add ?814 (multiply ?815 (multiply ?814 n1)) [815, 814] by Demod 7278 with 7256 at 1,3 +Id : 7280, {_}: multiply ?814 (add ?814 ?815) =>= add ?814 (multiply ?815 ?814) [815, 814] by Demod 7279 with 7256 at 2,2,3 +Id : 12189, {_}: ?14331 =<= add ?14331 (multiply ?14332 ?14331) [14332, 14331] by Demod 12188 with 7256 at 2 +Id : 12573, {_}: multiply ?814 (add ?814 ?815) =>= ?814 [815, 814] by Demod 7280 with 12189 at 3 +Id : 12624, {_}: add ?15025 ?15026 =<= add (add ?15025 ?15026) ?15025 [15026, 15025] by Super 12598 with 12573 at 2,3 +Id : 12720, {_}: multiply ?15175 (add (inverse ?15175) ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Super 9041 with 12624 at 2,2 +Id : 12767, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (add (inverse ?15175) ?15176) ?15175 [15176, 15175] by Demod 12720 with 11984 at 2,2 +Id : 12768, {_}: multiply ?15175 (pixley n1 ?15175 ?15176) =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15176, 15175] by Demod 12767 with 11984 at 1,3 +Id : 8552, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= add (inverse n1) (multiply ?9929 ?9928) [9929, 9928] by Super 3 with 8534 at 1,3 +Id : 8614, {_}: multiply ?9928 (add (inverse ?9928) ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8552 with 7543 at 3 +Id : 11985, {_}: multiply ?9928 (pixley n1 ?9928 ?9929) =>= multiply ?9929 ?9928 [9929, 9928] by Demod 8614 with 11984 at 2,2 +Id : 12769, {_}: multiply ?15176 ?15175 =<= multiply (pixley n1 ?15175 ?15176) ?15175 [15175, 15176] by Demod 12768 with 11985 at 2 +Id : 15132, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= pixley n1 ?18424 (multiply ?18425 ?18424) [18425, 18424] by Super 11991 with 12769 at 3,3 +Id : 15170, {_}: add (pixley n1 ?18424 ?18425) (inverse ?18424) =>= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15132 with 11991 at 3 +Id : 12729, {_}: add ?15203 ?15204 =<= add (add ?15203 ?15204) ?15203 [15204, 15203] by Super 12598 with 12573 at 2,3 +Id : 12745, {_}: add (inverse ?15249) ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Super 12729 with 11984 at 1,3 +Id : 12826, {_}: pixley n1 ?15249 ?15250 =<= add (pixley n1 ?15249 ?15250) (inverse ?15249) [15250, 15249] by Demod 12745 with 11984 at 2 +Id : 23185, {_}: pixley n1 ?18424 ?18425 =<= add ?18425 (inverse ?18424) [18425, 18424] by Demod 15170 with 12826 at 2 +Id : 29209, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (add ?35716 (inverse ?35715)) [35716, 35715] by Demod 29060 with 23185 at 2,2 +Id : 29210, {_}: multiply ?35715 (pixley n1 n1 ?35716) =?= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29209 with 23185 at 2,3 +Id : 29211, {_}: multiply ?35715 ?35716 =<= multiply ?35715 (pixley n1 ?35715 ?35716) [35716, 35715] by Demod 29210 with 6 at 2,2 +Id : 29212, {_}: multiply ?35715 ?35716 =?= multiply ?35716 ?35715 [35716, 35715] by Demod 29211 with 11985 at 3 +Id : 11904, {_}: add ?14161 (inverse (inverse ?14162)) =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Super 11860 with 10446 at 1,3 +Id : 11970, {_}: add ?14161 ?14162 =<= add ?14162 (multiply ?14161 (inverse ?14162)) [14162, 14161] by Demod 11904 with 10446 at 2,2 +Id : 15099, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18302 (multiply ?18303 (inverse ?18302)) [18303, 18302] by Super 11970 with 12769 at 2,3 +Id : 15201, {_}: add (pixley n1 (inverse ?18302) ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15099 with 11970 at 3 +Id : 10547, {_}: pixley n1 (inverse ?12250) ?12251 =<= add (inverse (inverse ?12250)) (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Super 172 with 10446 at 2,2,2,3 +Id : 10574, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 (add n1 ?12250)) [12251, 12250] by Demod 10547 with 10446 at 1,3 +Id : 17614, {_}: pixley n1 (inverse ?12250) ?12251 =<= add ?12250 (multiply ?12251 n1) [12251, 12250] by Demod 10574 with 12028 at 2,2,3 +Id : 17615, {_}: pixley n1 (inverse ?12250) ?12251 =>= add ?12250 ?12251 [12251, 12250] by Demod 17614 with 7256 at 2,3 +Id : 23377, {_}: add (add ?18302 ?18303) ?18302 =>= add ?18303 ?18302 [18303, 18302] by Demod 15201 with 17615 at 1,2 +Id : 23378, {_}: add ?18302 ?18303 =?= add ?18303 ?18302 [18303, 18302] by Demod 23377 with 12624 at 2 +Id : 363, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =<= add (multiply ?716 (add (add ?713 ?714) ?715)) (add ?714 (multiply ?715 ?714)) [716, 715, 714, 713] by Super 3 with 14 at 2,3 +Id : 33202, {_}: multiply (add (add ?713 ?714) ?715) (add ?716 ?714) =>= add (multiply ?716 (add (add ?713 ?714) ?715)) ?714 [716, 715, 714, 713] by Demod 363 with 12189 at 2,3 +Id : 33249, {_}: multiply (add (add ?41120 ?41121) ?41122) (add ?41123 ?41121) =>= add ?41121 (multiply ?41123 (add (add ?41120 ?41121) ?41122)) [41123, 41122, 41121, 41120] by Demod 33202 with 23378 at 3 +Id : 7276, {_}: multiply ?2193 (add ?2193 ?2193) =>= ?2193 [2193] by Demod 5835 with 7256 at 1,2 +Id : 7300, {_}: add (multiply ?2193 ?2193) ?2193 =>= ?2193 [2193] by Demod 7276 with 5958 at 2 +Id : 7301, {_}: add ?2193 ?2193 =>= ?2193 [2193] by Demod 7300 with 5908 at 1,2 +Id : 33300, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =<= add ?41375 (multiply ?41376 (add (add ?41374 ?41375) (add ?41374 ?41375))) [41376, 41375, 41374] by Super 33249 with 7301 at 1,2 +Id : 33433, {_}: multiply (add ?41374 ?41375) (add ?41376 ?41375) =>= add ?41375 (multiply ?41376 (add ?41374 ?41375)) [41376, 41375, 41374] by Demod 33300 with 7301 at 2,2,3 +Id : 42671, {_}: multiply ?52830 (add ?52831 ?52832) =<= add (multiply ?52830 ?52831) (multiply ?52832 ?52830) [52832, 52831, 52830] by Super 3 with 29212 at 1,3 +Id : 42679, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add (multiply (add ?52859 ?52860) ?52861) ?52860 [52861, 52860, 52859] by Super 42671 with 7749 at 2,3 +Id : 42859, {_}: multiply (add ?52859 ?52860) (add ?52861 ?52860) =>= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52861, 52860, 52859] by Demod 42679 with 23378 at 3 +Id : 58778, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =?= add ?52860 (multiply (add ?52859 ?52860) ?52861) [52859, 52861, 52860] by Demod 42859 with 33433 at 2 +Id : 42225, {_}: multiply ?51978 (add ?51979 ?51980) =<= add (multiply ?51979 ?51978) (multiply ?51978 ?51980) [51980, 51979, 51978] by Super 3 with 29212 at 2,3 +Id : 56980, {_}: multiply (add ?78761 ?78762) (add ?78762 ?78763) =>= add ?78762 (multiply (add ?78761 ?78762) ?78763) [78763, 78762, 78761] by Super 42225 with 7749 at 1,3 +Id : 57032, {_}: multiply (add ?78985 ?78986) (add ?78985 ?78987) =>= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Super 56980 with 23378 at 1,2 +Id : 42307, {_}: multiply (add ?52335 ?52336) (add ?52335 ?52337) =>= add ?52335 (multiply (add ?52335 ?52336) ?52337) [52337, 52336, 52335] by Super 42225 with 12573 at 1,3 +Id : 69246, {_}: add ?78985 (multiply (add ?78985 ?78986) ?78987) =?= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 57032 with 42307 at 2 +Id : 42691, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add (multiply (add ?52915 ?52916) ?52917) ?52915 [52917, 52916, 52915] by Super 42671 with 12573 at 2,3 +Id : 42878, {_}: multiply (add ?52915 ?52916) (add ?52917 ?52915) =>= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 42691 with 23378 at 3 +Id : 33277, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =<= add ?41259 (multiply ?41261 (add (add ?41259 ?41259) ?41260)) [41261, 41260, 41259] by Super 33249 with 7301 at 1,1,2 +Id : 33397, {_}: multiply (add ?41259 ?41260) (add ?41261 ?41259) =>= add ?41259 (multiply ?41261 (add ?41259 ?41260)) [41261, 41260, 41259] by Demod 33277 with 7301 at 1,2,2,3 +Id : 59822, {_}: add ?52915 (multiply ?52917 (add ?52915 ?52916)) =?= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52916, 52917, 52915] by Demod 42878 with 33397 at 2 +Id : 49363, {_}: multiply (add ?63432 ?63433) (add ?63433 ?63434) =>= add ?63433 (multiply ?63432 (add ?63433 ?63434)) [63434, 63433, 63432] by Super 29212 with 33397 at 3 +Id : 42295, {_}: multiply (add ?52279 ?52280) (add ?52280 ?52281) =>= add ?52280 (multiply (add ?52279 ?52280) ?52281) [52281, 52280, 52279] by Super 42225 with 7749 at 1,3 +Id : 65944, {_}: add ?95703 (multiply (add ?95704 ?95703) ?95705) =?= add ?95703 (multiply ?95704 (add ?95703 ?95705)) [95705, 95704, 95703] by Demod 49363 with 42295 at 2 +Id : 12345, {_}: multiply ?14434 (add ?14435 (multiply ?14436 ?14434)) =>= multiply ?14434 (add ?14435 ?14436) [14436, 14435, 14434] by Demod 12244 with 3 at 3 +Id : 66007, {_}: add ?95981 (multiply (add ?95982 ?95981) (multiply ?95983 ?95982)) =>= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95983, 95982, 95981] by Super 65944 with 12345 at 2,3 +Id : 12571, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= ?41 [43, 42, 41] by Demod 14 with 12189 at 3 +Id : 12574, {_}: multiply (multiply ?14855 ?14856) (add ?14856 ?14857) =>= multiply ?14855 ?14856 [14857, 14856, 14855] by Super 12571 with 12189 at 1,2,2 +Id : 32599, {_}: multiply (add ?39770 ?39771) (multiply ?39772 ?39770) =>= multiply ?39772 ?39770 [39772, 39771, 39770] by Super 29212 with 12574 at 3 +Id : 66421, {_}: add ?95981 (multiply ?95983 ?95982) =<= add ?95981 (multiply ?95982 (add ?95981 ?95983)) [95982, 95983, 95981] by Demod 66007 with 32599 at 2,2 +Id : 74546, {_}: add ?52915 (multiply ?52916 ?52917) =<= add ?52915 (multiply (add ?52915 ?52916) ?52917) [52917, 52916, 52915] by Demod 59822 with 66421 at 2 +Id : 74547, {_}: add ?78985 (multiply ?78986 ?78987) =<= add ?78985 (multiply (add ?78986 ?78985) ?78987) [78987, 78986, 78985] by Demod 69246 with 74546 at 2 +Id : 74549, {_}: add ?52860 (multiply ?52861 (add ?52859 ?52860)) =>= add ?52860 (multiply ?52859 ?52861) [52859, 52861, 52860] by Demod 58778 with 74547 at 3 +Id : 75087, {_}: add a (multiply c b) =?= add a (multiply c b) [] by Demod 57307 with 74549 at 3 +Id : 57307, {_}: add a (multiply c b) =<= add a (multiply b (add c a)) [] by Demod 57306 with 33433 at 3 +Id : 57306, {_}: add a (multiply c b) =<= multiply (add c a) (add b a) [] by Demod 57305 with 29212 at 3 +Id : 57305, {_}: add a (multiply c b) =<= multiply (add b a) (add c a) [] by Demod 57304 with 23378 at 2,3 +Id : 57304, {_}: add a (multiply c b) =<= multiply (add b a) (add a c) [] by Demod 57303 with 23378 at 1,3 +Id : 57303, {_}: add a (multiply c b) =<= multiply (add a b) (add a c) [] by Demod 1 with 29212 at 2,2 +Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property +% SZS output end CNFRefutation for BOO023-1.p +20955: solved BOO023-1.p in 19.273203 using kbo +20955: status Unsatisfiable for BOO023-1.p +NO CLASH, using fixed ground order +21165: Facts: +NO CLASH, using fixed ground order +21166: Facts: +21166: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +21166: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +21166: Id : 4, {_}: + multiply ?11 ?11 ?12 =>= ?11 + [12, 11] by ternary_multiply_2 ?11 ?12 +21166: Id : 5, {_}: + multiply (inverse ?14) ?14 ?15 =>= ?15 + [15, 14] by left_inverse ?14 ?15 +21166: Id : 6, {_}: + multiply ?17 ?18 (inverse ?18) =>= ?17 + [18, 17] by right_inverse ?17 ?18 +21166: Goal: +21166: Id : 1, {_}: + multiply (multiply a (inverse a) b) + (inverse (multiply (multiply c d e) f (multiply c d g))) + (multiply d (multiply g f e) c) + =>= + b + [] by prove_single_axiom +21166: Order: +21166: kbo +21166: Leaf order: +21166: g 2 0 2 3,3,1,2,2 +21166: f 2 0 2 2,1,2,2 +21166: e 2 0 2 3,1,1,2,2 +21166: d 3 0 3 2,1,1,2,2 +21166: c 3 0 3 1,1,1,2,2 +21166: multiply 16 3 7 0,2 +21166: b 2 0 2 3,1,2 +21166: inverse 4 1 2 0,2,1,2 +21166: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21167: Facts: +21167: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +21167: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +21167: Id : 4, {_}: + multiply ?11 ?11 ?12 =>= ?11 + [12, 11] by ternary_multiply_2 ?11 ?12 +21167: Id : 5, {_}: + multiply (inverse ?14) ?14 ?15 =>= ?15 + [15, 14] by left_inverse ?14 ?15 +21167: Id : 6, {_}: + multiply ?17 ?18 (inverse ?18) =>= ?17 + [18, 17] by right_inverse ?17 ?18 +21167: Goal: +21167: Id : 1, {_}: + multiply (multiply a (inverse a) b) + (inverse (multiply (multiply c d e) f (multiply c d g))) + (multiply d (multiply g f e) c) + =>= + b + [] by prove_single_axiom +21167: Order: +21167: lpo +21167: Leaf order: +21167: g 2 0 2 3,3,1,2,2 +21167: f 2 0 2 2,1,2,2 +21167: e 2 0 2 3,1,1,2,2 +21167: d 3 0 3 2,1,1,2,2 +21167: c 3 0 3 1,1,1,2,2 +21167: multiply 16 3 7 0,2 +21167: b 2 0 2 3,1,2 +21167: inverse 4 1 2 0,2,1,2 +21167: a 2 0 2 1,1,2 +21165: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +21165: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +21165: Id : 4, {_}: + multiply ?11 ?11 ?12 =>= ?11 + [12, 11] by ternary_multiply_2 ?11 ?12 +21165: Id : 5, {_}: + multiply (inverse ?14) ?14 ?15 =>= ?15 + [15, 14] by left_inverse ?14 ?15 +21165: Id : 6, {_}: + multiply ?17 ?18 (inverse ?18) =>= ?17 + [18, 17] by right_inverse ?17 ?18 +21165: Goal: +21165: Id : 1, {_}: + multiply (multiply a (inverse a) b) + (inverse (multiply (multiply c d e) f (multiply c d g))) + (multiply d (multiply g f e) c) + =>= + b + [] by prove_single_axiom +21165: Order: +21165: nrkbo +21165: Leaf order: +21165: g 2 0 2 3,3,1,2,2 +21165: f 2 0 2 2,1,2,2 +21165: e 2 0 2 3,1,1,2,2 +21165: d 3 0 3 2,1,1,2,2 +21165: c 3 0 3 1,1,1,2,2 +21165: multiply 16 3 7 0,2 +21165: b 2 0 2 3,1,2 +21165: inverse 4 1 2 0,2,1,2 +21165: a 2 0 2 1,1,2 +Statistics : +Max weight : 24 +Found proof, 10.936664s +% SZS status Unsatisfiable for BOO034-1.p +% SZS output start CNFRefutation for BOO034-1.p +Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15 +Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12 +Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18 +Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2 +Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2 +Id : 920, {_}: multiply (multiply ?2937 ?2938 ?2939) ?2937 ?2938 =?= multiply ?2939 ?2937 (multiply ?2937 ?2938 ?2938) [2939, 2938, 2937] by Super 12 with 13 at 3 +Id : 1359, {_}: multiply (multiply ?4051 ?4052 ?4053) ?4051 ?4052 =>= multiply ?4053 ?4051 ?4052 [4053, 4052, 4051] by Demod 920 with 3 at 3,3 +Id : 1364, {_}: multiply ?4070 ?4070 ?4071 =?= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Super 1359 with 6 at 1,2 +Id : 1413, {_}: ?4070 =<= multiply (inverse ?4071) ?4070 ?4071 [4071, 4070] by Demod 1364 with 4 at 2 +Id : 1453, {_}: multiply (multiply ?4288 ?4289 (inverse ?4289)) ?4290 ?4289 =>= multiply ?4288 ?4289 ?4290 [4290, 4289, 4288] by Super 12 with 1413 at 3,3 +Id : 1476, {_}: multiply ?4288 ?4290 ?4289 =?= multiply ?4288 ?4289 ?4290 [4289, 4290, 4288] by Demod 1453 with 6 at 1,2 +Id : 519, {_}: multiply (multiply ?1786 ?1787 ?1788) ?1789 ?1787 =?= multiply ?1786 ?1787 (multiply ?1788 ?1789 ?1787) [1789, 1788, 1787, 1786] by Super 2 with 3 at 3,2 +Id : 659, {_}: multiply (multiply ?2172 ?2173 ?2174) ?2174 ?2173 =>= multiply ?2172 ?2173 ?2174 [2174, 2173, 2172] by Super 519 with 4 at 3,3 +Id : 664, {_}: multiply ?2191 (inverse ?2192) ?2192 =?= multiply ?2191 ?2192 (inverse ?2192) [2192, 2191] by Super 659 with 6 at 1,2 +Id : 701, {_}: multiply ?2191 (inverse ?2192) ?2192 =>= ?2191 [2192, 2191] by Demod 664 with 6 at 3 +Id : 1371, {_}: multiply ?4106 ?4106 (inverse ?4107) =?= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Super 1359 with 701 at 1,2 +Id : 1415, {_}: ?4106 =<= multiply ?4107 ?4106 (inverse ?4107) [4107, 4106] by Demod 1371 with 4 at 2 +Id : 1522, {_}: multiply ?4441 ?4442 (multiply ?4443 ?4441 (inverse ?4441)) =>= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Super 13 with 1415 at 3,3 +Id : 1536, {_}: multiply ?4441 ?4442 ?4443 =?= multiply ?4443 ?4441 ?4442 [4443, 4442, 4441] by Demod 1522 with 6 at 3,2 +Id : 727, {_}: inverse (inverse ?2329) =>= ?2329 [2329] by Super 5 with 701 at 2 +Id : 761, {_}: multiply ?2420 (inverse ?2420) ?2421 =>= ?2421 [2421, 2420] by Super 5 with 727 at 1,2 +Id : 40424, {_}: b === b [] by Demod 40423 with 6 at 2 +Id : 40423, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g f e))) =>= b [] by Demod 40422 with 1476 at 3,1,3,2 +Id : 40422, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply g e f))) =>= b [] by Demod 40421 with 1536 at 3,1,3,2 +Id : 40421, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f g e))) =>= b [] by Demod 40420 with 1476 at 3,1,3,2 +Id : 40420, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply f e g))) =>= b [] by Demod 40419 with 1536 at 3,1,3,2 +Id : 40419, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e g f))) =>= b [] by Demod 40418 with 1476 at 3,1,3,2 +Id : 40418, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d c (multiply e f g))) =>= b [] by Demod 40417 with 1476 at 1,3,2 +Id : 40417, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40416 with 1476 at 2 +Id : 40416, {_}: multiply b (inverse (multiply d (multiply e f g) c)) (multiply d c (multiply g f e)) =>= b [] by Demod 40415 with 1536 at 2 +Id : 40415, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply d (multiply e f g) c)) =>= b [] by Demod 40414 with 1536 at 1,3,2 +Id : 40414, {_}: multiply (multiply d c (multiply g f e)) b (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40413 with 761 at 2,2 +Id : 40413, {_}: multiply (multiply d c (multiply g f e)) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40412 with 1476 at 1,2 +Id : 40412, {_}: multiply (multiply d (multiply g f e) c) (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 40411 with 1476 at 2 +Id : 40411, {_}: multiply (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) =>= b [] by Demod 40410 with 1536 at 2 +Id : 40410, {_}: multiply (multiply a (inverse a) b) (multiply d (multiply g f e) c) (inverse (multiply c d (multiply e f g))) =>= b [] by Demod 11 with 1476 at 2 +Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2 +Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom +% SZS output end CNFRefutation for BOO034-1.p +21165: solved BOO034-1.p in 10.220638 using nrkbo +21165: status Unsatisfiable for BOO034-1.p +CLASH, statistics insufficient +21378: Facts: +21378: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +21378: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +21378: Goal: +21378: Id : 1, {_}: + apply (apply ?1 (f ?1)) (g ?1) + =<= + apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1)) + [1] by prove_u_combinator ?1 +21378: Order: +21378: nrkbo +21378: Leaf order: +21378: k 1 0 0 +21378: s 1 0 0 +21378: g 3 1 3 0,2,2 +21378: apply 13 2 5 0,2 +21378: f 3 1 3 0,2,1,2 +CLASH, statistics insufficient +21379: Facts: +21379: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +21379: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +21379: Goal: +21379: Id : 1, {_}: + apply (apply ?1 (f ?1)) (g ?1) + =<= + apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1)) + [1] by prove_u_combinator ?1 +21379: Order: +21379: kbo +21379: Leaf order: +21379: k 1 0 0 +21379: s 1 0 0 +21379: g 3 1 3 0,2,2 +21379: apply 13 2 5 0,2 +21379: f 3 1 3 0,2,1,2 +CLASH, statistics insufficient +21380: Facts: +21380: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +21380: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +21380: Goal: +21380: Id : 1, {_}: + apply (apply ?1 (f ?1)) (g ?1) + =<= + apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1)) + [1] by prove_u_combinator ?1 +21380: Order: +21380: lpo +21380: Leaf order: +21380: k 1 0 0 +21380: s 1 0 0 +21380: g 3 1 3 0,2,2 +21380: apply 13 2 5 0,2 +21380: f 3 1 3 0,2,1,2 +% SZS status Timeout for COL004-1.p +NO CLASH, using fixed ground order +21607: Facts: +21607: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +21607: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +21607: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply (apply s (apply k s)) k)) + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + [] by strong_fixed_point +21607: Goal: +21607: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +21607: Order: +21607: nrkbo +21607: Leaf order: +21607: k 13 0 0 +21607: s 11 0 0 +21607: apply 32 2 3 0,2 +21607: fixed_pt 3 0 3 2,2 +21607: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +21608: Facts: +21608: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +21608: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +21608: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply (apply s (apply k s)) k)) + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + [] by strong_fixed_point +21608: Goal: +21608: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +21608: Order: +21608: kbo +21608: Leaf order: +21608: k 13 0 0 +21608: s 11 0 0 +21608: apply 32 2 3 0,2 +21608: fixed_pt 3 0 3 2,2 +21608: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +21609: Facts: +21609: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +21609: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +21609: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply (apply s (apply k s)) k)) + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + [] by strong_fixed_point +21609: Goal: +21609: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +21609: Order: +21609: lpo +21609: Leaf order: +21609: k 13 0 0 +21609: s 11 0 0 +21609: apply 32 2 3 0,2 +21609: fixed_pt 3 0 3 2,2 +21609: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL006-6.p +CLASH, statistics insufficient +21625: Facts: +21625: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +21625: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +21625: Id : 4, {_}: + apply (apply t ?11) ?12 =>= apply ?12 ?11 + [12, 11] by t_definition ?11 ?12 +21625: Goal: +21625: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +21625: Order: +21625: nrkbo +21625: Leaf order: +21625: t 1 0 0 +21625: b 1 0 0 +21625: s 1 0 0 +21625: apply 17 2 3 0,2 +21625: f 3 1 3 0,2,2 +CLASH, statistics insufficient +21626: Facts: +21626: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +21626: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +21626: Id : 4, {_}: + apply (apply t ?11) ?12 =>= apply ?12 ?11 + [12, 11] by t_definition ?11 ?12 +21626: Goal: +21626: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +21626: Order: +21626: kbo +21626: Leaf order: +21626: t 1 0 0 +21626: b 1 0 0 +21626: s 1 0 0 +21626: apply 17 2 3 0,2 +21626: f 3 1 3 0,2,2 +CLASH, statistics insufficient +21627: Facts: +21627: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +21627: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +21627: Id : 4, {_}: + apply (apply t ?11) ?12 =?= apply ?12 ?11 + [12, 11] by t_definition ?11 ?12 +21627: Goal: +21627: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +21627: Order: +21627: lpo +21627: Leaf order: +21627: t 1 0 0 +21627: b 1 0 0 +21627: s 1 0 0 +21627: apply 17 2 3 0,2 +21627: f 3 1 3 0,2,2 +% SZS status Timeout for COL036-1.p +CLASH, statistics insufficient +21654: Facts: +21654: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +CLASH, statistics insufficient +21655: Facts: +21655: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +21655: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +21655: Goal: +21655: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (g ?1)) (f ?1) + [1] by prove_f_combinator ?1 +21655: Order: +21655: kbo +21655: Leaf order: +21655: t 1 0 0 +21655: b 1 0 0 +21655: h 2 1 2 0,2,2 +21655: g 2 1 2 0,2,1,2 +21655: apply 13 2 5 0,2 +21655: f 2 1 2 0,2,1,1,2 +21654: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +21654: Goal: +21654: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (g ?1)) (f ?1) + [1] by prove_f_combinator ?1 +21654: Order: +21654: nrkbo +21654: Leaf order: +21654: t 1 0 0 +21654: b 1 0 0 +21654: h 2 1 2 0,2,2 +21654: g 2 1 2 0,2,1,2 +21654: apply 13 2 5 0,2 +21654: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +21656: Facts: +21656: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +21656: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +21656: Goal: +21656: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (g ?1)) (f ?1) + [1] by prove_f_combinator ?1 +21656: Order: +21656: lpo +21656: Leaf order: +21656: t 1 0 0 +21656: b 1 0 0 +21656: h 2 1 2 0,2,2 +21656: g 2 1 2 0,2,1,2 +21656: apply 13 2 5 0,2 +21656: f 2 1 2 0,2,1,1,2 +Goal subsumed +Statistics : +Max weight : 100 +Found proof, 5.123186s +% SZS status Unsatisfiable for COL063-1.p +% SZS output start CNFRefutation for COL063-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2 +Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2 +Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2 +Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1 +% SZS output end CNFRefutation for COL063-1.p +21654: solved COL063-1.p in 5.12832 using nrkbo +21654: status Unsatisfiable for COL063-1.p +NO CLASH, using fixed ground order +21661: Facts: +21661: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21661: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21661: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21661: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21661: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21661: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21661: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21661: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21661: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21661: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21661: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21661: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21661: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21661: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21661: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21661: Goal: +21661: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +21661: Order: +21661: nrkbo +21661: Leaf order: +21661: inverse 1 1 0 +21661: multiply 19 2 1 0,3 +21661: greatest_lower_bound 14 2 1 0,2,3 +21661: least_upper_bound 14 2 1 0,1,3 +21661: identity 4 0 2 2,1,3 +21661: a 3 0 3 2 +NO CLASH, using fixed ground order +21662: Facts: +21662: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21662: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21662: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21662: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21662: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21662: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21662: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21662: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21662: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21662: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21662: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21662: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21662: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21662: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21662: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21662: Goal: +21662: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +21662: Order: +21662: kbo +21662: Leaf order: +21662: inverse 1 1 0 +21662: multiply 19 2 1 0,3 +21662: greatest_lower_bound 14 2 1 0,2,3 +21662: least_upper_bound 14 2 1 0,1,3 +21662: identity 4 0 2 2,1,3 +21662: a 3 0 3 2 +NO CLASH, using fixed ground order +21663: Facts: +21663: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21663: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21663: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21663: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21663: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21663: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21663: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21663: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21663: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21663: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21663: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21663: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21663: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21663: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21663: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21663: Goal: +21663: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +21663: Order: +21663: lpo +21663: Leaf order: +21663: inverse 1 1 0 +21663: multiply 19 2 1 0,3 +21663: greatest_lower_bound 14 2 1 0,2,3 +21663: least_upper_bound 14 2 1 0,1,3 +21663: identity 4 0 2 2,1,3 +21663: a 3 0 3 2 +% SZS status Timeout for GRP167-3.p +NO CLASH, using fixed ground order +21683: Facts: +21683: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21683: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21683: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21683: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21683: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21683: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21683: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21683: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21683: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21683: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21683: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21683: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21683: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21683: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21683: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21683: Goal: +21683: Id : 1, {_}: + inverse (least_upper_bound a b) + =<= + greatest_lower_bound (inverse a) (inverse b) + [] by prove_p10 +21683: Order: +21683: nrkbo +21683: Leaf order: +21683: multiply 18 2 0 +21683: identity 2 0 0 +21683: greatest_lower_bound 14 2 1 0,3 +21683: inverse 4 1 3 0,2 +21683: least_upper_bound 14 2 1 0,1,2 +21683: b 2 0 2 2,1,2 +21683: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21684: Facts: +21684: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21684: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21684: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21684: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21684: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21684: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21684: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21684: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21684: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21684: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21684: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21684: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +NO CLASH, using fixed ground order +21685: Facts: +21685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21685: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21685: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21685: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21685: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21685: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21685: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21685: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21685: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21685: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21685: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21685: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21685: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21685: Goal: +21685: Id : 1, {_}: + inverse (least_upper_bound a b) + =>= + greatest_lower_bound (inverse a) (inverse b) + [] by prove_p10 +21685: Order: +21685: lpo +21685: Leaf order: +21685: multiply 18 2 0 +21685: identity 2 0 0 +21685: greatest_lower_bound 14 2 1 0,3 +21685: inverse 4 1 3 0,2 +21685: least_upper_bound 14 2 1 0,1,2 +21685: b 2 0 2 2,1,2 +21685: a 2 0 2 1,1,2 +21684: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21684: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21684: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21684: Goal: +21684: Id : 1, {_}: + inverse (least_upper_bound a b) + =<= + greatest_lower_bound (inverse a) (inverse b) + [] by prove_p10 +21684: Order: +21684: kbo +21684: Leaf order: +21684: multiply 18 2 0 +21684: identity 2 0 0 +21684: greatest_lower_bound 14 2 1 0,3 +21684: inverse 4 1 3 0,2 +21684: least_upper_bound 14 2 1 0,1,2 +21684: b 2 0 2 2,1,2 +21684: a 2 0 2 1,1,2 +% SZS status Timeout for GRP179-1.p +NO CLASH, using fixed ground order +21733: Facts: +21733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21733: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21733: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21733: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21733: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21733: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21733: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21733: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21733: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21733: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21733: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21733: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21733: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21733: Goal: +21733: Id : 1, {_}: + least_upper_bound (inverse a) identity + =<= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +21733: Order: +21733: kbo +21733: Leaf order: +21733: multiply 18 2 0 +21733: greatest_lower_bound 14 2 1 0,1,3 +21733: least_upper_bound 14 2 1 0,2 +21733: identity 4 0 2 2,2 +21733: inverse 3 1 2 0,1,2 +21733: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21732: Facts: +21732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21732: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21732: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21732: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21732: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21732: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21732: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21732: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21732: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21732: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21732: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21732: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21732: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21732: Goal: +21732: Id : 1, {_}: + least_upper_bound (inverse a) identity + =<= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +21732: Order: +21732: nrkbo +21732: Leaf order: +21732: multiply 18 2 0 +21732: greatest_lower_bound 14 2 1 0,1,3 +21732: least_upper_bound 14 2 1 0,2 +21732: identity 4 0 2 2,2 +21732: inverse 3 1 2 0,1,2 +21732: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21734: Facts: +21734: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21734: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21734: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21734: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21734: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21734: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21734: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21734: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21734: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21734: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21734: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21734: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21734: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21734: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21734: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21734: Goal: +21734: Id : 1, {_}: + least_upper_bound (inverse a) identity + =<= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +21734: Order: +21734: lpo +21734: Leaf order: +21734: multiply 18 2 0 +21734: greatest_lower_bound 14 2 1 0,1,3 +21734: least_upper_bound 14 2 1 0,2 +21734: identity 4 0 2 2,2 +21734: inverse 3 1 2 0,1,2 +21734: a 2 0 2 1,1,2 +% SZS status Timeout for GRP179-2.p +NO CLASH, using fixed ground order +21751: Facts: +21751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21751: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21751: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21751: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21751: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21751: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21751: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21751: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21751: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21751: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21751: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21751: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21751: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21751: Goal: +21751: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +21751: Order: +21751: nrkbo +21751: Leaf order: +21751: identity 2 0 0 +21751: least_upper_bound 14 2 1 0,3 +21751: multiply 20 2 2 0,2 +21751: inverse 2 1 1 0,1,2,2 +21751: greatest_lower_bound 14 2 1 0,1,1,2,2 +21751: b 3 0 3 2,1,1,2,2 +21751: a 3 0 3 1,2 +NO CLASH, using fixed ground order +21752: Facts: +21752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21752: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21752: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21752: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21752: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21752: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21752: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21752: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21752: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21752: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21752: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21752: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21752: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21752: Goal: +21752: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +21752: Order: +21752: kbo +21752: Leaf order: +21752: identity 2 0 0 +21752: least_upper_bound 14 2 1 0,3 +21752: multiply 20 2 2 0,2 +21752: inverse 2 1 1 0,1,2,2 +21752: greatest_lower_bound 14 2 1 0,1,1,2,2 +21752: b 3 0 3 2,1,1,2,2 +21752: a 3 0 3 1,2 +NO CLASH, using fixed ground order +21753: Facts: +21753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21753: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21753: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21753: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21753: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21753: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21753: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21753: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21753: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21753: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21753: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21753: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21753: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21753: Goal: +21753: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +21753: Order: +21753: lpo +21753: Leaf order: +21753: identity 2 0 0 +21753: least_upper_bound 14 2 1 0,3 +21753: multiply 20 2 2 0,2 +21753: inverse 2 1 1 0,1,2,2 +21753: greatest_lower_bound 14 2 1 0,1,1,2,2 +21753: b 3 0 3 2,1,1,2,2 +21753: a 3 0 3 1,2 +% SZS status Timeout for GRP180-1.p +NO CLASH, using fixed ground order +21783: Facts: +21783: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21783: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21783: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21783: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21783: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21783: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21783: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21783: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21783: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21783: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21783: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21783: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21783: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21783: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21783: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21783: Id : 17, {_}: inverse identity =>= identity [] by p20_1 +21783: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51 +21783: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20_3 ?53 ?54 +21783: Goal: +21783: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +21783: Order: +21783: nrkbo +21783: Leaf order: +21783: multiply 20 2 0 +21783: inverse 8 1 1 0,2,2 +21783: greatest_lower_bound 15 2 2 0,2 +21783: least_upper_bound 14 2 1 0,1,2 +21783: identity 7 0 3 2,1,2 +21783: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21785: Facts: +21785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21785: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21785: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21785: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21785: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21785: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21785: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21785: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21785: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21785: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21785: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21785: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21785: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21785: Id : 17, {_}: inverse identity =>= identity [] by p20_1 +21785: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51 +21785: Id : 19, {_}: + inverse (multiply ?53 ?54) =>= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20_3 ?53 ?54 +21785: Goal: +21785: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +21785: Order: +21785: lpo +21785: Leaf order: +21785: multiply 20 2 0 +21785: inverse 8 1 1 0,2,2 +21785: greatest_lower_bound 15 2 2 0,2 +21785: least_upper_bound 14 2 1 0,1,2 +21785: identity 7 0 3 2,1,2 +21785: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21784: Facts: +21784: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21784: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21784: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21784: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21784: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21784: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21784: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21784: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21784: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21784: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21784: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21784: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21784: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21784: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21784: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21784: Id : 17, {_}: inverse identity =>= identity [] by p20_1 +21784: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51 +21784: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20_3 ?53 ?54 +21784: Goal: +21784: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +21784: Order: +21784: kbo +21784: Leaf order: +21784: multiply 20 2 0 +21784: inverse 8 1 1 0,2,2 +21784: greatest_lower_bound 15 2 2 0,2 +21784: least_upper_bound 14 2 1 0,1,2 +21784: identity 7 0 3 2,1,2 +21784: a 2 0 2 1,1,2 +% SZS status Timeout for GRP183-2.p +NO CLASH, using fixed ground order +21802: Facts: +21802: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21802: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21802: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21802: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21802: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21802: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21802: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21802: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21802: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21802: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21802: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21802: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21802: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21802: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21802: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21802: Goal: +21802: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +21802: Order: +21802: nrkbo +21802: Leaf order: +21802: greatest_lower_bound 14 2 1 0,1,2,3 +21802: inverse 3 1 2 0,2,3 +21802: least_upper_bound 14 2 1 0,2 +21802: identity 3 0 1 2,2 +21802: multiply 20 2 2 0,1,2 +21802: b 2 0 2 2,1,2 +21802: a 3 0 3 1,1,2 +NO CLASH, using fixed ground order +21803: Facts: +21803: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21803: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21803: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21803: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21803: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21803: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21803: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21803: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21803: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21803: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21803: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21803: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21803: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21803: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21803: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21803: Goal: +21803: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +21803: Order: +21803: kbo +21803: Leaf order: +21803: greatest_lower_bound 14 2 1 0,1,2,3 +21803: inverse 3 1 2 0,2,3 +21803: least_upper_bound 14 2 1 0,2 +21803: identity 3 0 1 2,2 +21803: multiply 20 2 2 0,1,2 +21803: b 2 0 2 2,1,2 +21803: a 3 0 3 1,1,2 +NO CLASH, using fixed ground order +21804: Facts: +21804: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +21804: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +21804: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +21804: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +21804: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +21804: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +21804: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +21804: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +21804: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +21804: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +21804: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +21804: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +21804: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +21804: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +21804: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +21804: Goal: +21804: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +21804: Order: +21804: lpo +21804: Leaf order: +21804: greatest_lower_bound 14 2 1 0,1,2,3 +21804: inverse 3 1 2 0,2,3 +21804: least_upper_bound 14 2 1 0,2 +21804: identity 3 0 1 2,2 +21804: multiply 20 2 2 0,1,2 +21804: b 2 0 2 2,1,2 +21804: a 3 0 3 1,1,2 +% SZS status Timeout for GRP186-1.p +NO CLASH, using fixed ground order +21831: Facts: +21831: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +21831: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +21831: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +21831: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +21831: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +21831: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +21831: Id : 8, {_}: + join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +21831: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +21831: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +21831: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +21831: Goal: +21831: Id : 1, {_}: + join a + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (join (meet (complement a) b) + (meet (complement a) (complement b))))) + =>= + n1 + [] by prove_e2 +21831: Order: +21831: nrkbo +21831: Leaf order: +21831: n0 1 0 0 +21831: n1 2 0 1 3 +21831: meet 14 2 5 0,1,2,2 +21831: join 17 2 5 0,2 +21831: b 4 0 4 1,2,1,2,1,2,2 +21831: complement 15 1 6 0,1,1,2,2 +21831: a 7 0 7 1,2 +NO CLASH, using fixed ground order +21832: Facts: +21832: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +21832: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +21832: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +21832: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +21832: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +21832: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +21832: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +21832: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +21832: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +21832: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +21832: Goal: +21832: Id : 1, {_}: + join a + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (join (meet (complement a) b) + (meet (complement a) (complement b))))) + =>= + n1 + [] by prove_e2 +21832: Order: +21832: kbo +21832: Leaf order: +21832: n0 1 0 0 +21832: n1 2 0 1 3 +21832: meet 14 2 5 0,1,2,2 +21832: join 17 2 5 0,2 +21832: b 4 0 4 1,2,1,2,1,2,2 +21832: complement 15 1 6 0,1,1,2,2 +21832: a 7 0 7 1,2 +NO CLASH, using fixed ground order +21833: Facts: +21833: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +21833: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +21833: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +21833: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +21833: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +21833: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +21833: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +21833: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +21833: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +21833: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +21833: Goal: +21833: Id : 1, {_}: + join a + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (join (meet (complement a) b) + (meet (complement a) (complement b))))) + =>= + n1 + [] by prove_e2 +21833: Order: +21833: lpo +21833: Leaf order: +21833: n0 1 0 0 +21833: n1 2 0 1 3 +21833: meet 14 2 5 0,1,2,2 +21833: join 17 2 5 0,2 +21833: b 4 0 4 1,2,1,2,1,2,2 +21833: complement 15 1 6 0,1,1,2,2 +21833: a 7 0 7 1,2 +% SZS status Timeout for LAT017-1.p +NO CLASH, using fixed ground order +21853: Facts: +21853: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +21853: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +21853: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +21853: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +21853: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +21853: Id : 7, {_}: + join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +21853: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +21853: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +21853: Id : 10, {_}: + join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28) + =>= + meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28) + [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30 +21853: Goal: +21853: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +21853: Order: +21853: nrkbo +21853: Leaf order: +21853: meet 21 2 3 0,2 +21853: join 20 2 2 0,2,2 +21853: c 2 0 2 2,2,2 +21853: b 2 0 2 1,2,2 +21853: a 3 0 3 1,2 +NO CLASH, using fixed ground order +21854: Facts: +21854: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +21854: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +21854: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +21854: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +21854: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +21854: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +21854: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +21854: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +21854: Id : 10, {_}: + join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28) + =>= + meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28) + [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30 +21854: Goal: +21854: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +21854: Order: +21854: kbo +21854: Leaf order: +21854: meet 21 2 3 0,2 +21854: join 20 2 2 0,2,2 +21854: c 2 0 2 2,2,2 +21854: b 2 0 2 1,2,2 +21854: a 3 0 3 1,2 +NO CLASH, using fixed ground order +21855: Facts: +21855: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +21855: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +21855: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +21855: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +21855: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +21855: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +21855: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +21855: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +21855: Id : 10, {_}: + join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28) + =>= + meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28) + [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30 +21855: Goal: +21855: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +21855: Order: +21855: lpo +21855: Leaf order: +21855: meet 21 2 3 0,2 +21855: join 20 2 2 0,2,2 +21855: c 2 0 2 2,2,2 +21855: b 2 0 2 1,2,2 +21855: a 3 0 3 1,2 +% SZS status Timeout for LAT020-1.p +NO CLASH, using fixed ground order +21955: Facts: +21955: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +21955: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +21955: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +21955: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +21955: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +21955: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +21955: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +21955: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +21955: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +21955: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +21955: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +21955: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +21955: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +21955: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +21955: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +21955: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +21955: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +21955: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +21955: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +21955: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +21955: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +21955: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +21955: Goal: +21955: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +21955: Order: +21955: nrkbo +21955: Leaf order: +21955: commutator 1 2 0 +21955: additive_inverse 22 1 0 +21955: multiply 40 2 0 +21955: additive_identity 9 0 1 3 +21955: add 25 2 1 0,2 +21955: associator 3 3 2 0,1,2 +21955: z 2 0 2 3,1,2 +21955: y 2 0 2 2,1,2 +21955: x 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21956: Facts: +21956: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +21956: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +21956: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +21956: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +21956: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +21956: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +21956: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +21956: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +21956: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +21956: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +21956: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +21956: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +21956: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +21956: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +21956: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +21956: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +21956: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +21956: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +21956: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +21956: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +21956: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +21956: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +21956: Goal: +21956: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +21956: Order: +21956: kbo +21956: Leaf order: +21956: commutator 1 2 0 +21956: additive_inverse 22 1 0 +21956: multiply 40 2 0 +21956: additive_identity 9 0 1 3 +21956: add 25 2 1 0,2 +21956: associator 3 3 2 0,1,2 +21956: z 2 0 2 3,1,2 +21956: y 2 0 2 2,1,2 +21956: x 2 0 2 1,1,2 +NO CLASH, using fixed ground order +21957: Facts: +21957: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +21957: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +21957: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +21957: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +21957: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +21957: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +21957: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +21957: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +21957: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +21957: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +21957: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +21957: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +21957: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +21957: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +21957: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +21957: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +21957: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +21957: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +21957: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +21957: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +21957: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +21957: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +21957: Goal: +21957: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +21957: Order: +21957: lpo +21957: Leaf order: +21957: commutator 1 2 0 +21957: additive_inverse 22 1 0 +21957: multiply 40 2 0 +21957: additive_identity 9 0 1 3 +21957: add 25 2 1 0,2 +21957: associator 3 3 2 0,1,2 +21957: z 2 0 2 3,1,2 +21957: y 2 0 2 2,1,2 +21957: x 2 0 2 1,1,2 +% SZS status Timeout for RNG025-5.p +NO CLASH, using fixed ground order +21975: Facts: +21975: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +21975: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +21975: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +21975: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +21975: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +21975: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +21975: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +21975: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +21975: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +21975: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +21975: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +21975: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +21975: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +21975: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +21975: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +21975: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +21975: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +21975: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +21975: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +21975: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +21975: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +21975: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +21975: Goal: +21975: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +21975: Order: +21975: nrkbo +21975: Leaf order: +21975: commutator 1 2 0 +21975: additive_inverse 22 1 0 +21975: multiply 40 2 0 +21975: add 24 2 0 +21975: additive_identity 9 0 1 3 +21975: associator 2 3 1 0,2 +21975: y 1 0 1 2,2 +21975: x 2 0 2 1,2 +NO CLASH, using fixed ground order +21976: Facts: +21976: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +21976: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +21976: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +21976: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +21976: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +21976: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +21976: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +21976: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +21976: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +21976: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +21976: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +21976: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +21976: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +21976: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +21976: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +21976: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +21976: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +21976: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +21976: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +21976: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +21976: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +21976: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +21976: Goal: +21976: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +21976: Order: +21976: kbo +21976: Leaf order: +21976: commutator 1 2 0 +21976: additive_inverse 22 1 0 +21976: multiply 40 2 0 +21976: add 24 2 0 +21976: additive_identity 9 0 1 3 +21976: associator 2 3 1 0,2 +21976: y 1 0 1 2,2 +21976: x 2 0 2 1,2 +NO CLASH, using fixed ground order +21977: Facts: +21977: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +21977: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +21977: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +21977: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +21977: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +21977: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +21977: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +21977: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +21977: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +21977: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +21977: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +21977: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +21977: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +21977: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +21977: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +21977: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +21977: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +21977: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +21977: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +21977: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +21977: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +21977: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +21977: Goal: +21977: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +21977: Order: +21977: lpo +21977: Leaf order: +21977: commutator 1 2 0 +21977: additive_inverse 22 1 0 +21977: multiply 40 2 0 +21977: add 24 2 0 +21977: additive_identity 9 0 1 3 +21977: associator 2 3 1 0,2 +21977: y 1 0 1 2,2 +21977: x 2 0 2 1,2 +% SZS status Timeout for RNG025-7.p +CLASH, statistics insufficient +22004: Facts: +22004: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +CLASH, statistics insufficient +22005: Facts: +22005: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22005: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +22005: Goal: +22005: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22005: Order: +22005: kbo +22005: Leaf order: +22005: k 1 0 0 +22005: s 1 0 0 +22005: apply 11 2 3 0,2 +22005: f 3 1 3 0,2,2 +22004: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +22004: Goal: +22004: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22004: Order: +22004: nrkbo +22004: Leaf order: +22004: k 1 0 0 +22004: s 1 0 0 +22004: apply 11 2 3 0,2 +22004: f 3 1 3 0,2,2 +CLASH, statistics insufficient +22006: Facts: +22006: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22006: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +22006: Goal: +22006: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22006: Order: +22006: lpo +22006: Leaf order: +22006: k 1 0 0 +22006: s 1 0 0 +22006: apply 11 2 3 0,2 +22006: f 3 1 3 0,2,2 +% SZS status Timeout for COL006-1.p +NO CLASH, using fixed ground order +22027: Facts: +22027: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +22027: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +NO CLASH, using fixed ground order +22028: Facts: +22028: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +22028: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +22028: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply k (apply (apply s s) (apply s k)))) + (apply (apply s (apply k s)) k)) + [] by strong_fixed_point +22028: Goal: +22028: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22028: Order: +22028: kbo +22028: Leaf order: +22028: k 10 0 0 +22028: s 11 0 0 +22028: apply 29 2 3 0,2 +22028: fixed_pt 3 0 3 2,2 +22028: strong_fixed_point 3 0 2 1,2 +22027: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply k (apply (apply s s) (apply s k)))) + (apply (apply s (apply k s)) k)) + [] by strong_fixed_point +22027: Goal: +22027: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22027: Order: +22027: nrkbo +22027: Leaf order: +22027: k 10 0 0 +22027: s 11 0 0 +22027: apply 29 2 3 0,2 +22027: fixed_pt 3 0 3 2,2 +22027: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22029: Facts: +22029: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +22029: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +22029: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply k (apply (apply s s) (apply s k)))) + (apply (apply s (apply k s)) k)) + [] by strong_fixed_point +22029: Goal: +22029: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22029: Order: +22029: lpo +22029: Leaf order: +22029: k 10 0 0 +22029: s 11 0 0 +22029: apply 29 2 3 0,2 +22029: fixed_pt 3 0 3 2,2 +22029: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL006-5.p +NO CLASH, using fixed ground order +22056: Facts: +22056: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +22056: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +22056: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply (apply s s) (apply (apply s k) k)) + (apply (apply s s) (apply s k))))) + (apply (apply s (apply k s)) k) + [] by strong_fixed_point +22056: Goal: +22056: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22056: Order: +22056: nrkbo +22056: Leaf order: +22056: k 7 0 0 +22056: s 10 0 0 +22056: apply 25 2 3 0,2 +22056: fixed_pt 3 0 3 2,2 +22056: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22057: Facts: +22057: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +22057: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +22057: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply (apply s s) (apply (apply s k) k)) + (apply (apply s s) (apply s k))))) + (apply (apply s (apply k s)) k) + [] by strong_fixed_point +22057: Goal: +22057: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22057: Order: +22057: kbo +22057: Leaf order: +22057: k 7 0 0 +22057: s 10 0 0 +22057: apply 25 2 3 0,2 +22057: fixed_pt 3 0 3 2,2 +22057: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22058: Facts: +22058: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +22058: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +22058: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply (apply s s) (apply (apply s k) k)) + (apply (apply s s) (apply s k))))) + (apply (apply s (apply k s)) k) + [] by strong_fixed_point +22058: Goal: +22058: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22058: Order: +22058: lpo +22058: Leaf order: +22058: k 7 0 0 +22058: s 10 0 0 +22058: apply 25 2 3 0,2 +22058: fixed_pt 3 0 3 2,2 +22058: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL006-7.p +NO CLASH, using fixed ground order +22074: Facts: +22074: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22074: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +22074: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply (apply b b) n)) n))) n)) b)) b + [] by strong_fixed_point +22074: Goal: +22074: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22074: Order: +22074: nrkbo +22074: Leaf order: +22074: n 6 0 0 +22074: b 9 0 0 +22074: apply 26 2 3 0,2 +22074: fixed_pt 3 0 3 2,2 +22074: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22075: Facts: +22075: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22075: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +22075: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply (apply b b) n)) n))) n)) b)) b + [] by strong_fixed_point +22075: Goal: +22075: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22075: Order: +22075: kbo +22075: Leaf order: +22075: n 6 0 0 +22075: b 9 0 0 +22075: apply 26 2 3 0,2 +22075: fixed_pt 3 0 3 2,2 +22075: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22076: Facts: +22076: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22076: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +22076: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply (apply b b) n)) n))) n)) b)) b + [] by strong_fixed_point +22076: Goal: +22076: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22076: Order: +22076: lpo +22076: Leaf order: +22076: n 6 0 0 +22076: b 9 0 0 +22076: apply 26 2 3 0,2 +22076: fixed_pt 3 0 3 2,2 +22076: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL044-6.p +NO CLASH, using fixed ground order +22116: Facts: +22116: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22116: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +22116: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply n (apply b b))) n))) n)) b)) b + [] by strong_fixed_point +22116: Goal: +22116: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22116: Order: +22116: nrkbo +22116: Leaf order: +22116: n 6 0 0 +22116: b 9 0 0 +22116: apply 26 2 3 0,2 +22116: fixed_pt 3 0 3 2,2 +22116: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22117: Facts: +22117: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22117: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +22117: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply n (apply b b))) n))) n)) b)) b + [] by strong_fixed_point +22117: Goal: +22117: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22117: Order: +22117: kbo +22117: Leaf order: +22117: n 6 0 0 +22117: b 9 0 0 +22117: apply 26 2 3 0,2 +22117: fixed_pt 3 0 3 2,2 +22117: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +22118: Facts: +22118: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22118: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +22118: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply n (apply b b))) n))) n)) b)) b + [] by strong_fixed_point +22118: Goal: +22118: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22118: Order: +22118: lpo +22118: Leaf order: +22118: n 6 0 0 +22118: b 9 0 0 +22118: apply 26 2 3 0,2 +22118: fixed_pt 3 0 3 2,2 +22118: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL044-7.p +CLASH, statistics insufficient +22135: Facts: +22135: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22135: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +22135: Goal: +22135: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (f ?1)) (g ?1) + [1] by prove_v_combinator ?1 +22135: Order: +22135: nrkbo +22135: Leaf order: +22135: t 1 0 0 +22135: b 1 0 0 +22135: h 2 1 2 0,2,2 +22135: g 2 1 2 0,2,1,2 +22135: apply 13 2 5 0,2 +22135: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +22136: Facts: +22136: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22136: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +22136: Goal: +22136: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (f ?1)) (g ?1) + [1] by prove_v_combinator ?1 +22136: Order: +22136: kbo +22136: Leaf order: +22136: t 1 0 0 +22136: b 1 0 0 +22136: h 2 1 2 0,2,2 +22136: g 2 1 2 0,2,1,2 +22136: apply 13 2 5 0,2 +22136: f 2 1 2 0,2,1,1,2 +CLASH, statistics insufficient +22137: Facts: +22137: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22137: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +22137: Goal: +22137: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (f ?1)) (g ?1) + [1] by prove_v_combinator ?1 +22137: Order: +22137: lpo +22137: Leaf order: +22137: t 1 0 0 +22137: b 1 0 0 +22137: h 2 1 2 0,2,2 +22137: g 2 1 2 0,2,1,2 +22137: apply 13 2 5 0,2 +22137: f 2 1 2 0,2,1,1,2 +Goal subsumed +Statistics : +Max weight : 124 +Found proof, 35.273110s +% SZS status Unsatisfiable for COL064-1.p +% SZS output start CNFRefutation for COL064-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2 +Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2 +Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2 +Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2 +Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2 +Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1 +% SZS output end CNFRefutation for COL064-1.p +22135: solved COL064-1.p in 35.146196 using nrkbo +22135: status Unsatisfiable for COL064-1.p +CLASH, statistics insufficient +22153: Facts: +22153: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22153: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +22153: Goal: +22153: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) + =>= + apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) + [1] by prove_g_combinator ?1 +22153: Order: +22153: nrkbo +22153: Leaf order: +22153: t 1 0 0 +22153: b 1 0 0 +22153: i 2 1 2 0,2,2 +22153: h 2 1 2 0,2,1,2 +22153: g 2 1 2 0,2,1,1,2 +22153: apply 15 2 7 0,2 +22153: f 2 1 2 0,2,1,1,1,2 +CLASH, statistics insufficient +22154: Facts: +22154: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22154: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +22154: Goal: +22154: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) + =>= + apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) + [1] by prove_g_combinator ?1 +22154: Order: +22154: kbo +22154: Leaf order: +22154: t 1 0 0 +22154: b 1 0 0 +22154: i 2 1 2 0,2,2 +22154: h 2 1 2 0,2,1,2 +22154: g 2 1 2 0,2,1,1,2 +22154: apply 15 2 7 0,2 +22154: f 2 1 2 0,2,1,1,1,2 +CLASH, statistics insufficient +22155: Facts: +22155: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22155: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +22155: Goal: +22155: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) + =>= + apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) + [1] by prove_g_combinator ?1 +22155: Order: +22155: lpo +22155: Leaf order: +22155: t 1 0 0 +22155: b 1 0 0 +22155: i 2 1 2 0,2,2 +22155: h 2 1 2 0,2,1,2 +22155: g 2 1 2 0,2,1,1,2 +22155: apply 15 2 7 0,2 +22155: f 2 1 2 0,2,1,1,1,2 +% SZS status Timeout for COL065-1.p +CLASH, statistics insufficient +22171: Facts: +22171: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22171: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22171: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22171: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22171: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22171: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22171: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22171: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22171: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22171: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22171: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22171: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22171: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22171: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22171: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22171: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_1 +22171: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2 +22171: Goal: +22171: Id : 1, {_}: a =>= b [] by prove_p12 +22171: Order: +22171: nrkbo +22171: Leaf order: +22171: c 4 0 0 +22171: least_upper_bound 15 2 0 +22171: greatest_lower_bound 15 2 0 +22171: inverse 1 1 0 +22171: multiply 18 2 0 +22171: identity 2 0 0 +22171: b 3 0 1 3 +22171: a 3 0 1 2 +CLASH, statistics insufficient +22172: Facts: +22172: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22172: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22172: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22172: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22172: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22172: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22172: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22172: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22172: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22172: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22172: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22172: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22172: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22172: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22172: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22172: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_1 +22172: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2 +22172: Goal: +22172: Id : 1, {_}: a =>= b [] by prove_p12 +22172: Order: +22172: kbo +22172: Leaf order: +22172: c 4 0 0 +22172: least_upper_bound 15 2 0 +22172: greatest_lower_bound 15 2 0 +22172: inverse 1 1 0 +22172: multiply 18 2 0 +22172: identity 2 0 0 +22172: b 3 0 1 3 +22172: a 3 0 1 2 +CLASH, statistics insufficient +22173: Facts: +22173: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22173: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22173: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22173: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22173: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22173: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22173: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22173: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22173: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22173: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22173: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22173: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22173: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22173: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22173: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22173: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_1 +22173: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2 +22173: Goal: +22173: Id : 1, {_}: a =>= b [] by prove_p12 +22173: Order: +22173: lpo +22173: Leaf order: +22173: c 4 0 0 +22173: least_upper_bound 15 2 0 +22173: greatest_lower_bound 15 2 0 +22173: inverse 1 1 0 +22173: multiply 18 2 0 +22173: identity 2 0 0 +22173: b 3 0 1 3 +22173: a 3 0 1 2 +% SZS status Timeout for GRP181-1.p +CLASH, statistics insufficient +22201: Facts: +22201: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22201: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22201: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22201: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22201: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22201: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22201: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22201: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22201: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22201: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22201: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22201: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22201: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22201: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22201: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22201: Id : 17, {_}: inverse identity =>= identity [] by p12_1 +22201: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51 +22201: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12_3 ?53 ?54 +22201: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_4 +22201: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5 +22201: Goal: +22201: Id : 1, {_}: a =>= b [] by prove_p12 +22201: Order: +22201: kbo +22201: Leaf order: +22201: c 4 0 0 +22201: least_upper_bound 15 2 0 +22201: greatest_lower_bound 15 2 0 +22201: inverse 7 1 0 +22201: multiply 20 2 0 +22201: identity 4 0 0 +22201: b 3 0 1 3 +22201: a 3 0 1 2 +CLASH, statistics insufficient +22202: Facts: +22202: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22202: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22202: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22202: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22202: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22202: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22202: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22202: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22202: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22202: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22202: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22202: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22202: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22202: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22202: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22202: Id : 17, {_}: inverse identity =>= identity [] by p12_1 +22202: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51 +22202: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12_3 ?53 ?54 +22202: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_4 +22202: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5 +22202: Goal: +22202: Id : 1, {_}: a =>= b [] by prove_p12 +22202: Order: +22202: lpo +22202: Leaf order: +22202: c 4 0 0 +22202: least_upper_bound 15 2 0 +22202: greatest_lower_bound 15 2 0 +22202: inverse 7 1 0 +22202: multiply 20 2 0 +22202: identity 4 0 0 +22202: b 3 0 1 3 +22202: a 3 0 1 2 +CLASH, statistics insufficient +22200: Facts: +22200: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22200: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22200: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22200: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22200: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22200: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22200: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22200: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22200: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22200: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22200: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22200: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22200: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22200: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22200: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22200: Id : 17, {_}: inverse identity =>= identity [] by p12_1 +22200: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51 +22200: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12_3 ?53 ?54 +22200: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_4 +22200: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5 +22200: Goal: +22200: Id : 1, {_}: a =>= b [] by prove_p12 +22200: Order: +22200: nrkbo +22200: Leaf order: +22200: c 4 0 0 +22200: least_upper_bound 15 2 0 +22200: greatest_lower_bound 15 2 0 +22200: inverse 7 1 0 +22200: multiply 20 2 0 +22200: identity 4 0 0 +22200: b 3 0 1 3 +22200: a 3 0 1 2 +% SZS status Timeout for GRP181-2.p +NO CLASH, using fixed ground order +22218: Facts: +22218: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22218: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22218: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22218: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22218: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22218: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22218: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22218: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22218: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22218: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22218: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22218: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22218: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22218: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22218: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22218: Id : 17, {_}: + greatest_lower_bound (least_upper_bound a (inverse a)) + (least_upper_bound b (inverse b)) + =>= + identity + [] by p33_1 +22218: Goal: +22218: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33 +22218: Order: +22218: nrkbo +22218: Leaf order: +22218: least_upper_bound 15 2 0 +22218: greatest_lower_bound 14 2 0 +22218: inverse 3 1 0 +22218: identity 3 0 0 +22218: multiply 20 2 2 0,2 +22218: b 4 0 2 2,2 +22218: a 4 0 2 1,2 +NO CLASH, using fixed ground order +22219: Facts: +22219: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22219: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22219: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22219: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22219: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22219: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22219: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22219: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22219: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22219: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22219: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22219: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22219: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22219: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22219: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22219: Id : 17, {_}: + greatest_lower_bound (least_upper_bound a (inverse a)) + (least_upper_bound b (inverse b)) + =>= + identity + [] by p33_1 +22219: Goal: +22219: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33 +22219: Order: +22219: kbo +22219: Leaf order: +22219: least_upper_bound 15 2 0 +22219: greatest_lower_bound 14 2 0 +22219: inverse 3 1 0 +22219: identity 3 0 0 +22219: multiply 20 2 2 0,2 +22219: b 4 0 2 2,2 +22219: a 4 0 2 1,2 +NO CLASH, using fixed ground order +22220: Facts: +22220: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22220: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22220: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22220: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22220: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22220: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22220: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22220: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22220: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22220: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22220: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22220: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22220: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22220: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22220: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22220: Id : 17, {_}: + greatest_lower_bound (least_upper_bound a (inverse a)) + (least_upper_bound b (inverse b)) + =>= + identity + [] by p33_1 +22220: Goal: +22220: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_p33 +22220: Order: +22220: lpo +22220: Leaf order: +22220: least_upper_bound 15 2 0 +22220: greatest_lower_bound 14 2 0 +22220: inverse 3 1 0 +22220: identity 3 0 0 +22220: multiply 20 2 2 0,2 +22220: b 4 0 2 2,2 +22220: a 4 0 2 1,2 +% SZS status Timeout for GRP187-1.p +NO CLASH, using fixed ground order +22280: Facts: +22280: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22280: Goal: +22280: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +22280: Order: +22280: nrkbo +22280: Leaf order: +22280: b1 2 0 2 1,1,3 +22280: multiply 12 2 2 0,2 +22280: inverse 9 1 2 0,1,2 +22280: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +22281: Facts: +22281: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22281: Goal: +22281: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +22281: Order: +22281: kbo +22281: Leaf order: +22281: b1 2 0 2 1,1,3 +22281: multiply 12 2 2 0,2 +22281: inverse 9 1 2 0,1,2 +22281: a1 2 0 2 1,1,2 +NO CLASH, using fixed ground order +22282: Facts: +22282: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22282: Goal: +22282: Id : 1, {_}: + multiply (inverse a1) a1 =>= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +22282: Order: +22282: lpo +22282: Leaf order: +22282: b1 2 0 2 1,1,3 +22282: multiply 12 2 2 0,2 +22282: inverse 9 1 2 0,1,2 +22282: a1 2 0 2 1,1,2 +% SZS status Timeout for GRP505-1.p +NO CLASH, using fixed ground order +22298: Facts: +22298: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22298: Goal: +22298: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +22298: Order: +22298: nrkbo +22298: Leaf order: +22298: inverse 7 1 0 +22298: c3 2 0 2 2,2 +22298: multiply 14 2 4 0,2 +22298: b3 2 0 2 2,1,2 +22298: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +22299: Facts: +22299: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22299: Goal: +22299: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +22299: Order: +22299: kbo +22299: Leaf order: +22299: inverse 7 1 0 +22299: c3 2 0 2 2,2 +22299: multiply 14 2 4 0,2 +22299: b3 2 0 2 2,1,2 +22299: a3 2 0 2 1,1,2 +NO CLASH, using fixed ground order +22300: Facts: +22300: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22300: Goal: +22300: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +22300: Order: +22300: lpo +22300: Leaf order: +22300: inverse 7 1 0 +22300: c3 2 0 2 2,2 +22300: multiply 14 2 4 0,2 +22300: b3 2 0 2 2,1,2 +22300: a3 2 0 2 1,1,2 +% SZS status Timeout for GRP507-1.p +NO CLASH, using fixed ground order +22343: Facts: +22343: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22343: Goal: +22343: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4 +22343: Order: +22343: nrkbo +22343: Leaf order: +22343: inverse 7 1 0 +22343: multiply 12 2 2 0,2 +22343: b 2 0 2 2,2 +22343: a 2 0 2 1,2 +NO CLASH, using fixed ground order +22344: Facts: +22344: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22344: Goal: +22344: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4 +22344: Order: +22344: kbo +22344: Leaf order: +22344: inverse 7 1 0 +22344: multiply 12 2 2 0,2 +22344: b 2 0 2 2,2 +22344: a 2 0 2 1,2 +NO CLASH, using fixed ground order +22345: Facts: +22345: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22345: Goal: +22345: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_these_axioms_4 +22345: Order: +22345: lpo +22345: Leaf order: +22345: inverse 7 1 0 +22345: multiply 12 2 2 0,2 +22345: b 2 0 2 2,2 +22345: a 2 0 2 1,2 +% SZS status Timeout for GRP508-1.p +NO CLASH, using fixed ground order +22381: Facts: +22381: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +22381: Goal: +22381: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1 +22381: Order: +22381: nrkbo +22381: Leaf order: +22381: join 20 2 0 +22381: meet 19 2 1 0,2 +22381: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22382: Facts: +22382: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +22382: Goal: +22382: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1 +22382: Order: +22382: kbo +22382: Leaf order: +22382: join 20 2 0 +22382: meet 19 2 1 0,2 +22382: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22383: Facts: +22383: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +22383: Goal: +22383: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1 +22383: Order: +22383: lpo +22383: Leaf order: +22383: join 20 2 0 +22383: meet 19 2 1 0,2 +22383: a 3 0 3 1,2 +% SZS status Timeout for LAT080-1.p +NO CLASH, using fixed ground order +22413: Facts: +22413: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +22413: Goal: +22413: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4 +22413: Order: +22413: nrkbo +22413: Leaf order: +22413: meet 18 2 0 +22413: join 21 2 1 0,2 +22413: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22414: Facts: +22414: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +22414: Goal: +22414: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4 +22414: Order: +22414: kbo +22414: Leaf order: +22414: meet 18 2 0 +22414: join 21 2 1 0,2 +22414: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22415: Facts: +22415: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +22415: Goal: +22415: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4 +22415: Order: +22415: lpo +22415: Leaf order: +22415: meet 18 2 0 +22415: join 21 2 1 0,2 +22415: a 3 0 3 1,2 +% SZS status Timeout for LAT083-1.p +NO CLASH, using fixed ground order +22432: Facts: +22432: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22432: Goal: +22432: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1 +22432: Order: +22432: nrkbo +22432: Leaf order: +22432: join 18 2 0 +22432: meet 19 2 1 0,2 +22432: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22434: Facts: +22434: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22434: Goal: +22434: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1 +22434: Order: +22434: lpo +22434: Leaf order: +22434: join 18 2 0 +22434: meet 19 2 1 0,2 +22434: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22433: Facts: +22433: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22433: Goal: +22433: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1 +22433: Order: +22433: kbo +22433: Leaf order: +22433: join 18 2 0 +22433: meet 19 2 1 0,2 +22433: a 3 0 3 1,2 +% SZS status Timeout for LAT092-1.p +NO CLASH, using fixed ground order +22466: Facts: +22466: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22466: Goal: +22466: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2 +22466: Order: +22466: nrkbo +22466: Leaf order: +22466: join 18 2 0 +22466: meet 20 2 2 0,2 +22466: a 2 0 2 2,2 +22466: b 2 0 2 1,2 +NO CLASH, using fixed ground order +22467: Facts: +22467: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22467: Goal: +22467: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2 +22467: Order: +22467: kbo +22467: Leaf order: +22467: join 18 2 0 +22467: meet 20 2 2 0,2 +22467: a 2 0 2 2,2 +22467: b 2 0 2 1,2 +NO CLASH, using fixed ground order +22468: Facts: +22468: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22468: Goal: +22468: Id : 1, {_}: meet b a =>= meet a b [] by prove_wal_axioms_2 +22468: Order: +22468: lpo +22468: Leaf order: +22468: join 18 2 0 +22468: meet 20 2 2 0,2 +22468: a 2 0 2 2,2 +22468: b 2 0 2 1,2 +% SZS status Timeout for LAT093-1.p +NO CLASH, using fixed ground order +22493: Facts: +22493: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22493: Goal: +22493: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3 +22493: Order: +22493: nrkbo +22493: Leaf order: +22493: meet 18 2 0 +22493: join 19 2 1 0,2 +22493: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22494: Facts: +22494: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22494: Goal: +22494: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3 +22494: Order: +22494: kbo +22494: Leaf order: +22494: meet 18 2 0 +22494: join 19 2 1 0,2 +22494: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22495: Facts: +22495: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22495: Goal: +22495: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3 +22495: Order: +22495: lpo +22495: Leaf order: +22495: meet 18 2 0 +22495: join 19 2 1 0,2 +22495: a 3 0 3 1,2 +% SZS status Timeout for LAT094-1.p +NO CLASH, using fixed ground order +22522: Facts: +22522: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22522: Goal: +22522: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4 +22522: Order: +22522: nrkbo +22522: Leaf order: +22522: meet 18 2 0 +22522: join 20 2 2 0,2 +22522: a 2 0 2 2,2 +22522: b 2 0 2 1,2 +NO CLASH, using fixed ground order +22523: Facts: +22523: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22523: Goal: +22523: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4 +22523: Order: +22523: kbo +22523: Leaf order: +22523: meet 18 2 0 +22523: join 20 2 2 0,2 +22523: a 2 0 2 2,2 +22523: b 2 0 2 1,2 +NO CLASH, using fixed ground order +22524: Facts: +22524: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22524: Goal: +22524: Id : 1, {_}: join b a =>= join a b [] by prove_wal_axioms_4 +22524: Order: +22524: lpo +22524: Leaf order: +22524: meet 18 2 0 +22524: join 20 2 2 0,2 +22524: a 2 0 2 2,2 +22524: b 2 0 2 1,2 +% SZS status Timeout for LAT095-1.p +NO CLASH, using fixed ground order +22540: Facts: +22540: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22540: Goal: +22540: Id : 1, {_}: + meet (meet (join a b) (join c b)) b =>= b + [] by prove_wal_axioms_5 +22540: Order: +22540: nrkbo +22540: Leaf order: +22540: meet 20 2 2 0,2 +22540: c 1 0 1 1,2,1,2 +22540: join 20 2 2 0,1,1,2 +22540: b 4 0 4 2,1,1,2 +22540: a 1 0 1 1,1,1,2 +NO CLASH, using fixed ground order +22541: Facts: +22541: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22541: Goal: +22541: Id : 1, {_}: + meet (meet (join a b) (join c b)) b =>= b + [] by prove_wal_axioms_5 +22541: Order: +22541: kbo +22541: Leaf order: +22541: meet 20 2 2 0,2 +22541: c 1 0 1 1,2,1,2 +22541: join 20 2 2 0,1,1,2 +22541: b 4 0 4 2,1,1,2 +22541: a 1 0 1 1,1,1,2 +NO CLASH, using fixed ground order +22542: Facts: +22542: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22542: Goal: +22542: Id : 1, {_}: + meet (meet (join a b) (join c b)) b =>= b + [] by prove_wal_axioms_5 +22542: Order: +22542: lpo +22542: Leaf order: +22542: meet 20 2 2 0,2 +22542: c 1 0 1 1,2,1,2 +22542: join 20 2 2 0,1,1,2 +22542: b 4 0 4 2,1,1,2 +22542: a 1 0 1 1,1,1,2 +% SZS status Timeout for LAT096-1.p +NO CLASH, using fixed ground order +22569: Facts: +22569: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22569: Goal: +22569: Id : 1, {_}: + join (join (meet a b) (meet c b)) b =>= b + [] by prove_wal_axioms_6 +22569: Order: +22569: nrkbo +22569: Leaf order: +22569: join 20 2 2 0,2 +22569: c 1 0 1 1,2,1,2 +22569: meet 20 2 2 0,1,1,2 +22569: b 4 0 4 2,1,1,2 +22569: a 1 0 1 1,1,1,2 +NO CLASH, using fixed ground order +22570: Facts: +22570: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22570: Goal: +22570: Id : 1, {_}: + join (join (meet a b) (meet c b)) b =>= b + [] by prove_wal_axioms_6 +22570: Order: +22570: kbo +22570: Leaf order: +22570: join 20 2 2 0,2 +22570: c 1 0 1 1,2,1,2 +22570: meet 20 2 2 0,1,1,2 +22570: b 4 0 4 2,1,1,2 +22570: a 1 0 1 1,1,1,2 +NO CLASH, using fixed ground order +22571: Facts: +22571: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +22571: Goal: +22571: Id : 1, {_}: + join (join (meet a b) (meet c b)) b =>= b + [] by prove_wal_axioms_6 +22571: Order: +22571: lpo +22571: Leaf order: +22571: join 20 2 2 0,2 +22571: c 1 0 1 1,2,1,2 +22571: meet 20 2 2 0,1,1,2 +22571: b 4 0 4 2,1,1,2 +22571: a 1 0 1 1,1,1,2 +% SZS status Timeout for LAT097-1.p +NO CLASH, using fixed ground order +22740: Facts: +22740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22740: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22740: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22740: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22740: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22740: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +22740: Goal: +22740: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (meet d (join a (meet b d))))) + [] by prove_H28 +22740: Order: +22740: nrkbo +22740: Leaf order: +22740: join 16 2 3 0,2,2 +22740: meet 21 2 7 0,2 +22740: d 3 0 3 2,2,2,2,2 +22740: c 2 0 2 1,2,2,2,2 +22740: b 3 0 3 1,2,2 +22740: a 4 0 4 1,2 +NO CLASH, using fixed ground order +22742: Facts: +22742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22742: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22742: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22742: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22742: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22742: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +22742: Goal: +22742: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (meet d (join a (meet b d))))) + [] by prove_H28 +22742: Order: +22742: lpo +22742: Leaf order: +22742: join 16 2 3 0,2,2 +22742: meet 21 2 7 0,2 +22742: d 3 0 3 2,2,2,2,2 +22742: c 2 0 2 1,2,2,2,2 +22742: b 3 0 3 1,2,2 +22742: a 4 0 4 1,2 +NO CLASH, using fixed ground order +22741: Facts: +22741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22741: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22741: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22741: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22741: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22741: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +22741: Goal: +22741: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (meet d (join a (meet b d))))) + [] by prove_H28 +22741: Order: +22741: kbo +22741: Leaf order: +22741: join 16 2 3 0,2,2 +22741: meet 21 2 7 0,2 +22741: d 3 0 3 2,2,2,2,2 +22741: c 2 0 2 1,2,2,2,2 +22741: b 3 0 3 1,2,2 +22741: a 4 0 4 1,2 +% SZS status Timeout for LAT146-1.p +NO CLASH, using fixed ground order +22773: Facts: +22773: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22773: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22773: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22773: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22773: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22773: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22773: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22773: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22773: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +22773: Goal: +22773: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +22773: Order: +22773: nrkbo +22773: Leaf order: +22773: join 17 2 4 0,2,2 +22773: meet 20 2 6 0,2 +22773: c 2 0 2 2,2,2,2 +22773: b 4 0 4 1,2,2 +22773: a 6 0 6 1,2 +NO CLASH, using fixed ground order +22774: Facts: +22774: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22774: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22774: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22774: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22774: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22774: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22774: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22774: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22774: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +22774: Goal: +22774: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +22774: Order: +22774: kbo +22774: Leaf order: +22774: join 17 2 4 0,2,2 +22774: meet 20 2 6 0,2 +22774: c 2 0 2 2,2,2,2 +22774: b 4 0 4 1,2,2 +22774: a 6 0 6 1,2 +NO CLASH, using fixed ground order +22775: Facts: +22775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22775: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22775: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22775: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22775: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22775: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +22775: Goal: +22775: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +22775: Order: +22775: lpo +22775: Leaf order: +22775: join 17 2 4 0,2,2 +22775: meet 20 2 6 0,2 +22775: c 2 0 2 2,2,2,2 +22775: b 4 0 4 1,2,2 +22775: a 6 0 6 1,2 +% SZS status Timeout for LAT148-1.p +NO CLASH, using fixed ground order +22791: Facts: +22791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22791: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22791: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22791: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22791: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22791: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +22791: Goal: +22791: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +22791: Order: +22791: nrkbo +22791: Leaf order: +22791: join 18 2 4 0,2,2 +22791: meet 20 2 6 0,2 +22791: c 3 0 3 2,2,2,2 +22791: b 3 0 3 1,2,2 +22791: a 6 0 6 1,2 +NO CLASH, using fixed ground order +22792: Facts: +22792: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22792: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22792: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22792: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22792: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22792: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22792: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22792: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22792: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +22792: Goal: +22792: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +22792: Order: +22792: kbo +22792: Leaf order: +22792: join 18 2 4 0,2,2 +22792: meet 20 2 6 0,2 +22792: c 3 0 3 2,2,2,2 +22792: b 3 0 3 1,2,2 +22792: a 6 0 6 1,2 +NO CLASH, using fixed ground order +22793: Facts: +22793: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22793: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22793: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22793: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22793: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22793: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22793: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22793: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22793: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +22793: Goal: +22793: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +22793: Order: +22793: lpo +22793: Leaf order: +22793: join 18 2 4 0,2,2 +22793: meet 20 2 6 0,2 +22793: c 3 0 3 2,2,2,2 +22793: b 3 0 3 1,2,2 +22793: a 6 0 6 1,2 +% SZS status Timeout for LAT156-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +22830: Facts: +22830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22830: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22830: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22830: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22830: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22830: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29 +22830: Goal: +22830: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c d))) + [] by prove_H51 +22830: Order: +22830: kbo +22830: Leaf order: +22830: meet 19 2 5 0,2 +22830: join 18 2 4 0,2,2 +22830: d 2 0 2 2,2,2,2,2 +22830: c 3 0 3 1,2,2,2 +22830: b 2 0 2 1,2,2 +22830: a 4 0 4 1,2 +NO CLASH, using fixed ground order +22831: Facts: +22831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22831: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22831: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22831: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22831: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22831: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29 +22831: Goal: +22831: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c d))) + [] by prove_H51 +22831: Order: +22831: lpo +22831: Leaf order: +22831: meet 19 2 5 0,2 +22831: join 18 2 4 0,2,2 +22831: d 2 0 2 2,2,2,2,2 +22831: c 3 0 3 1,2,2,2 +22831: b 2 0 2 1,2,2 +22831: a 4 0 4 1,2 +22829: Facts: +22829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +22829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +22829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +22829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +22829: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +22829: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +22829: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +22829: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +22829: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29 +22829: Goal: +22829: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c d))) + [] by prove_H51 +22829: Order: +22829: nrkbo +22829: Leaf order: +22829: meet 19 2 5 0,2 +22829: join 18 2 4 0,2,2 +22829: d 2 0 2 2,2,2,2,2 +22829: c 3 0 3 1,2,2,2 +22829: b 2 0 2 1,2,2 +22829: a 4 0 4 1,2 +% SZS status Timeout for LAT160-1.p +NO CLASH, using fixed ground order +22849: Facts: +22849: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +22849: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +22849: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +22849: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +22849: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +22849: Id : 7, {_}: + or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +22849: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +22849: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +22849: Id : 10, {_}: + and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +22849: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +22849: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +22849: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +22849: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +22849: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +22849: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +22849: Id : 17, {_}: not truth =>= falsehood [] by false_definition +22849: Goal: +22849: Id : 1, {_}: + and_star (xor (and_star (xor truth x) y) truth) y + =>= + and_star (xor (and_star (xor truth y) x) truth) x + [] by prove_alternative_wajsberg_axiom +22849: Order: +22849: nrkbo +22849: Leaf order: +22849: falsehood 1 0 0 +22849: and 9 2 0 +22849: or 10 2 0 +22849: not 12 1 0 +22849: implies 14 2 0 +22849: and_star 11 2 4 0,2 +22849: y 3 0 3 2,1,1,2 +22849: xor 7 2 4 0,1,2 +22849: x 3 0 3 2,1,1,1,2 +22849: truth 8 0 4 1,1,1,1,2 +NO CLASH, using fixed ground order +22850: Facts: +22850: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +22850: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +22850: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +22850: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +22850: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +22850: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +22850: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +22850: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +22850: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +22850: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +22850: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +22850: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +22850: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +22850: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +22850: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +22850: Id : 17, {_}: not truth =>= falsehood [] by false_definition +22850: Goal: +22850: Id : 1, {_}: + and_star (xor (and_star (xor truth x) y) truth) y + =?= + and_star (xor (and_star (xor truth y) x) truth) x + [] by prove_alternative_wajsberg_axiom +22850: Order: +22850: kbo +22850: Leaf order: +22850: falsehood 1 0 0 +22850: and 9 2 0 +22850: or 10 2 0 +22850: not 12 1 0 +22850: implies 14 2 0 +22850: and_star 11 2 4 0,2 +22850: y 3 0 3 2,1,1,2 +22850: xor 7 2 4 0,1,2 +22850: x 3 0 3 2,1,1,1,2 +22850: truth 8 0 4 1,1,1,1,2 +NO CLASH, using fixed ground order +22851: Facts: +22851: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +22851: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +22851: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +22851: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +22851: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +22851: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +22851: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +22851: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +22851: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +22851: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +22851: Id : 12, {_}: + xor ?34 ?35 =>= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +22851: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +22851: Id : 14, {_}: + and_star ?40 ?41 =>= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +22851: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +22851: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +22851: Id : 17, {_}: not truth =>= falsehood [] by false_definition +22851: Goal: +22851: Id : 1, {_}: + and_star (xor (and_star (xor truth x) y) truth) y + =>= + and_star (xor (and_star (xor truth y) x) truth) x + [] by prove_alternative_wajsberg_axiom +22851: Order: +22851: lpo +22851: Leaf order: +22851: falsehood 1 0 0 +22851: and 9 2 0 +22851: or 10 2 0 +22851: not 12 1 0 +22851: implies 14 2 0 +22851: and_star 11 2 4 0,2 +22851: y 3 0 3 2,1,1,2 +22851: xor 7 2 4 0,1,2 +22851: x 3 0 3 2,1,1,1,2 +22851: truth 8 0 4 1,1,1,1,2 +% SZS status Timeout for LCL160-1.p +NO CLASH, using fixed ground order +22879: Facts: +22879: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2 +22879: Id : 3, {_}: + add ?4 (additive_inverse ?4) =>= additive_identity + [4] by right_additive_inverse ?4 +22879: Id : 4, {_}: + multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8) + [8, 7, 6] by distribute1 ?6 ?7 ?8 +22879: Id : 5, {_}: + multiply (add ?10 ?11) ?12 + =<= + add (multiply ?10 ?12) (multiply ?11 ?12) + [12, 11, 10] by distribute2 ?10 ?11 ?12 +22879: Id : 6, {_}: + add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16) + [16, 15, 14] by associative_addition ?14 ?15 ?16 +22879: Id : 7, {_}: + add ?18 ?19 =?= add ?19 ?18 + [19, 18] by commutative_addition ?18 ?19 +22879: Id : 8, {_}: + multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23) + [23, 22, 21] by associative_multiplication ?21 ?22 ?23 +22879: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25 +22879: Goal: +22879: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity +22879: Order: +22879: nrkbo +22879: Leaf order: +22879: additive_inverse 1 1 0 +22879: add 12 2 0 +22879: additive_identity 2 0 0 +22879: multiply 14 2 2 0,2 +22879: b 2 0 2 2,2 +22879: a 2 0 2 1,2 +NO CLASH, using fixed ground order +22880: Facts: +22880: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2 +22880: Id : 3, {_}: + add ?4 (additive_inverse ?4) =>= additive_identity + [4] by right_additive_inverse ?4 +22880: Id : 4, {_}: + multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8) + [8, 7, 6] by distribute1 ?6 ?7 ?8 +22880: Id : 5, {_}: + multiply (add ?10 ?11) ?12 + =<= + add (multiply ?10 ?12) (multiply ?11 ?12) + [12, 11, 10] by distribute2 ?10 ?11 ?12 +22880: Id : 6, {_}: + add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16) + [16, 15, 14] by associative_addition ?14 ?15 ?16 +22880: Id : 7, {_}: + add ?18 ?19 =?= add ?19 ?18 + [19, 18] by commutative_addition ?18 ?19 +22880: Id : 8, {_}: + multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23) + [23, 22, 21] by associative_multiplication ?21 ?22 ?23 +22880: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25 +22880: Goal: +22880: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity +22880: Order: +22880: kbo +22880: Leaf order: +22880: additive_inverse 1 1 0 +22880: add 12 2 0 +22880: additive_identity 2 0 0 +22880: multiply 14 2 2 0,2 +22880: b 2 0 2 2,2 +22880: a 2 0 2 1,2 +NO CLASH, using fixed ground order +22881: Facts: +22881: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2 +22881: Id : 3, {_}: + add ?4 (additive_inverse ?4) =>= additive_identity + [4] by right_additive_inverse ?4 +22881: Id : 4, {_}: + multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8) + [8, 7, 6] by distribute1 ?6 ?7 ?8 +22881: Id : 5, {_}: + multiply (add ?10 ?11) ?12 + =>= + add (multiply ?10 ?12) (multiply ?11 ?12) + [12, 11, 10] by distribute2 ?10 ?11 ?12 +22881: Id : 6, {_}: + add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16) + [16, 15, 14] by associative_addition ?14 ?15 ?16 +22881: Id : 7, {_}: + add ?18 ?19 =?= add ?19 ?18 + [19, 18] by commutative_addition ?18 ?19 +22881: Id : 8, {_}: + multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23) + [23, 22, 21] by associative_multiplication ?21 ?22 ?23 +22881: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25 +22881: Goal: +22881: Id : 1, {_}: multiply a b =>= multiply b a [] by prove_commutativity +22881: Order: +22881: lpo +22881: Leaf order: +22881: additive_inverse 1 1 0 +22881: add 12 2 0 +22881: additive_identity 2 0 0 +22881: multiply 14 2 2 0,2 +22881: b 2 0 2 2,2 +22881: a 2 0 2 1,2 +% SZS status Timeout for RNG009-5.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +22919: Facts: +22919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22919: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22919: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +22919: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +22919: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +22919: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +22919: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +22919: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +22919: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +22919: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29 +22919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +22919: Goal: +22919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +22919: Order: +22919: kbo +22919: Leaf order: +22919: additive_inverse 2 1 0 +22919: add 14 2 0 +22919: additive_identity 4 0 0 +22919: c 2 0 1 3 +22919: multiply 14 2 1 0,2 +22919: a 2 0 1 2,2 +22919: b 2 0 1 1,2 +22918: Facts: +22918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22918: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22918: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +22918: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +22918: Id : 6, {_}: + add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +22918: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +22918: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +22918: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +22918: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +22918: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29 +22918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +22918: Goal: +22918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +22918: Order: +22918: nrkbo +22918: Leaf order: +22918: additive_inverse 2 1 0 +22918: add 14 2 0 +22918: additive_identity 4 0 0 +22918: c 2 0 1 3 +22918: multiply 14 2 1 0,2 +22918: a 2 0 1 2,2 +22918: b 2 0 1 1,2 +NO CLASH, using fixed ground order +22920: Facts: +22920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22920: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22920: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +22920: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +22920: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +22920: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +22920: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +22920: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +22920: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +22920: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29 +22920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +22920: Goal: +22920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +22920: Order: +22920: lpo +22920: Leaf order: +22920: additive_inverse 2 1 0 +22920: add 14 2 0 +22920: additive_identity 4 0 0 +22920: c 2 0 1 3 +22920: multiply 14 2 1 0,2 +22920: a 2 0 1 2,2 +22920: b 2 0 1 1,2 +% SZS status Timeout for RNG009-7.p +NO CLASH, using fixed ground order +22947: Facts: +22947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22947: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22947: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22947: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22947: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22947: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22947: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22947: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22947: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22947: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22947: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22947: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22947: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22947: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22947: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22947: Goal: +22947: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +22947: Order: +22947: nrkbo +22947: Leaf order: +22947: commutator 1 2 0 +22947: additive_identity 9 0 1 3 +22947: additive_inverse 7 1 1 0,2,2 +22947: add 20 2 4 0,2 +22947: associator 6 3 5 0,1,1,2 +22947: d 5 0 5 3,1,1,2 +22947: c 5 0 5 2,1,1,2 +22947: multiply 27 2 5 0,1,1,1,2 +22947: b 5 0 5 2,1,1,1,2 +22947: a 5 0 5 1,1,1,1,2 +NO CLASH, using fixed ground order +22948: Facts: +22948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22948: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22948: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22948: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22948: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22948: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22948: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22948: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22948: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22948: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22948: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22948: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22948: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22948: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22948: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22948: Goal: +22948: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +22948: Order: +22948: kbo +22948: Leaf order: +22948: commutator 1 2 0 +22948: additive_identity 9 0 1 3 +22948: additive_inverse 7 1 1 0,2,2 +22948: add 20 2 4 0,2 +22948: associator 6 3 5 0,1,1,2 +22948: d 5 0 5 3,1,1,2 +22948: c 5 0 5 2,1,1,2 +22948: multiply 27 2 5 0,1,1,1,2 +22948: b 5 0 5 2,1,1,1,2 +22948: a 5 0 5 1,1,1,1,2 +NO CLASH, using fixed ground order +22949: Facts: +22949: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22949: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22949: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22949: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22949: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22949: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22949: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22949: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22949: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22949: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22949: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22949: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22949: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22949: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22949: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22949: Goal: +22949: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +22949: Order: +22949: lpo +22949: Leaf order: +22949: commutator 1 2 0 +22949: additive_identity 9 0 1 3 +22949: additive_inverse 7 1 1 0,2,2 +22949: add 20 2 4 0,2 +22949: associator 6 3 5 0,1,1,2 +22949: d 5 0 5 3,1,1,2 +22949: c 5 0 5 2,1,1,2 +22949: multiply 27 2 5 0,1,1,1,2 +22949: b 5 0 5 2,1,1,1,2 +22949: a 5 0 5 1,1,1,1,2 +% SZS status Timeout for RNG026-6.p +NO CLASH, using fixed ground order +22966: Facts: +NO CLASH, using fixed ground order +22967: Facts: +22967: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22967: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22967: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +NO CLASH, using fixed ground order +22966: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22966: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22966: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22966: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22966: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22966: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22966: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22965: Facts: +22966: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22966: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22966: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22965: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22965: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22965: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22965: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22965: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22965: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22965: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22965: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22965: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22965: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22965: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22965: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22965: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22965: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22965: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22965: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +22965: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +22965: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +22965: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +22965: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +22965: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +22965: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +22965: Goal: +22965: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +22965: Order: +22965: nrkbo +22965: Leaf order: +22965: commutator 1 2 0 +22965: additive_identity 9 0 1 3 +22965: additive_inverse 23 1 1 0,2,2 +22965: add 28 2 4 0,2 +22965: associator 6 3 5 0,1,1,2 +22965: d 5 0 5 3,1,1,2 +22965: c 5 0 5 2,1,1,2 +22965: multiply 45 2 5 0,1,1,1,2 +22965: b 5 0 5 2,1,1,1,2 +22965: a 5 0 5 1,1,1,1,2 +22967: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22966: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22966: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22966: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22966: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22966: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22966: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +22966: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +22966: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +22966: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +22966: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +22966: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +22966: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +22966: Goal: +22966: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +22966: Order: +22966: kbo +22966: Leaf order: +22966: commutator 1 2 0 +22966: additive_identity 9 0 1 3 +22966: additive_inverse 23 1 1 0,2,2 +22966: add 28 2 4 0,2 +22966: associator 6 3 5 0,1,1,2 +22966: d 5 0 5 3,1,1,2 +22966: c 5 0 5 2,1,1,2 +22966: multiply 45 2 5 0,1,1,1,2 +22966: b 5 0 5 2,1,1,1,2 +22966: a 5 0 5 1,1,1,1,2 +22967: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22967: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22967: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22967: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22967: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22967: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22967: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22967: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22967: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22967: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22967: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22967: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +22967: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +22967: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +22967: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +22967: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +22967: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +22967: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +22967: Goal: +22967: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +22967: Order: +22967: lpo +22967: Leaf order: +22967: commutator 1 2 0 +22967: additive_identity 9 0 1 3 +22967: additive_inverse 23 1 1 0,2,2 +22967: add 28 2 4 0,2 +22967: associator 6 3 5 0,1,1,2 +22967: d 5 0 5 3,1,1,2 +22967: c 5 0 5 2,1,1,2 +22967: multiply 45 2 5 0,1,1,1,2 +22967: b 5 0 5 2,1,1,1,2 +22967: a 5 0 5 1,1,1,1,2 +% SZS status Timeout for RNG026-7.p +NO CLASH, using fixed ground order +22994: Facts: +22994: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by sh_1 ?2 ?3 ?4 +22994: Goal: +22994: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +22994: Order: +22994: nrkbo +22994: Leaf order: +22994: nand 12 2 6 0,2 +22994: c 2 0 2 2,2,2,2 +22994: b 3 0 3 1,2,2 +22994: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22995: Facts: +22995: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by sh_1 ?2 ?3 ?4 +22995: Goal: +22995: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +22995: Order: +22995: kbo +22995: Leaf order: +22995: nand 12 2 6 0,2 +22995: c 2 0 2 2,2,2,2 +22995: b 3 0 3 1,2,2 +22995: a 3 0 3 1,2 +NO CLASH, using fixed ground order +22996: Facts: +22996: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by sh_1 ?2 ?3 ?4 +22996: Goal: +22996: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +22996: Order: +22996: lpo +22996: Leaf order: +22996: nand 12 2 6 0,2 +22996: c 2 0 2 2,2,2,2 +22996: b 3 0 3 1,2,2 +22996: a 3 0 3 1,2 +% SZS status Timeout for BOO076-1.p +CLASH, statistics insufficient +23012: Facts: +23012: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +23012: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +23012: Goal: +23012: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +23012: Order: +23012: nrkbo +23012: Leaf order: +23012: w 1 0 0 +23012: b 1 0 0 +23012: apply 12 2 3 0,2 +23012: f 3 1 3 0,2,2 +CLASH, statistics insufficient +23013: Facts: +23013: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +23013: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +23013: Goal: +23013: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +23013: Order: +23013: kbo +23013: Leaf order: +23013: w 1 0 0 +23013: b 1 0 0 +23013: apply 12 2 3 0,2 +23013: f 3 1 3 0,2,2 +CLASH, statistics insufficient +23014: Facts: +23014: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +23014: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +23014: Goal: +23014: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +23014: Order: +23014: lpo +23014: Leaf order: +23014: w 1 0 0 +23014: b 1 0 0 +23014: apply 12 2 3 0,2 +23014: f 3 1 3 0,2,2 +% SZS status Timeout for COL003-1.p +CLASH, statistics insufficient +23460: Facts: +23460: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +23460: Id : 3, {_}: + apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7 + [8, 7] by w1_definition ?7 ?8 +23460: Goal: +23460: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +23460: Order: +23460: nrkbo +23460: Leaf order: +23460: w1 1 0 0 +23460: b 1 0 0 +23460: apply 12 2 3 0,2 +23460: f 3 1 3 0,2,2 +CLASH, statistics insufficient +23462: Facts: +23462: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +23462: Id : 3, {_}: + apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7 + [8, 7] by w1_definition ?7 ?8 +23462: Goal: +23462: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +23462: Order: +23462: lpo +23462: Leaf order: +23462: w1 1 0 0 +23462: b 1 0 0 +23462: apply 12 2 3 0,2 +23462: f 3 1 3 0,2,2 +CLASH, statistics insufficient +23461: Facts: +23461: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +23461: Id : 3, {_}: + apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7 + [8, 7] by w1_definition ?7 ?8 +23461: Goal: +23461: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +23461: Order: +23461: kbo +23461: Leaf order: +23461: w1 1 0 0 +23461: b 1 0 0 +23461: apply 12 2 3 0,2 +23461: f 3 1 3 0,2,2 +% SZS status Timeout for COL042-1.p +NO CLASH, using fixed ground order +23502: Facts: +23502: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23502: Id : 3, {_}: + apply (apply (apply h ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?7) ?8) ?7 + [8, 7, 6] by h_definition ?6 ?7 ?8 +23502: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply h + (apply (apply b (apply (apply b h) (apply b b))) + (apply h (apply (apply b h) (apply b b))))) h)) b)) b + [] by strong_fixed_point +23502: Goal: +23502: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23502: Order: +23502: nrkbo +23502: Leaf order: +23502: h 6 0 0 +23502: b 12 0 0 +23502: apply 29 2 3 0,2 +23502: fixed_pt 3 0 3 2,2 +23502: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +23503: Facts: +23503: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23503: Id : 3, {_}: + apply (apply (apply h ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?7) ?8) ?7 + [8, 7, 6] by h_definition ?6 ?7 ?8 +23503: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply h + (apply (apply b (apply (apply b h) (apply b b))) + (apply h (apply (apply b h) (apply b b))))) h)) b)) b + [] by strong_fixed_point +23503: Goal: +23503: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23503: Order: +23503: kbo +23503: Leaf order: +23503: h 6 0 0 +23503: b 12 0 0 +23503: apply 29 2 3 0,2 +23503: fixed_pt 3 0 3 2,2 +23503: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +23504: Facts: +23504: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23504: Id : 3, {_}: + apply (apply (apply h ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?7) ?8) ?7 + [8, 7, 6] by h_definition ?6 ?7 ?8 +23504: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply h + (apply (apply b (apply (apply b h) (apply b b))) + (apply h (apply (apply b h) (apply b b))))) h)) b)) b + [] by strong_fixed_point +23504: Goal: +23504: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23504: Order: +23504: lpo +23504: Leaf order: +23504: h 6 0 0 +23504: b 12 0 0 +23504: apply 29 2 3 0,2 +23504: fixed_pt 3 0 3 2,2 +23504: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL043-3.p +NO CLASH, using fixed ground order +23537: Facts: +23537: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23537: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +23537: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply (apply b b) n))))) n)) b)) b + [] by strong_fixed_point +23537: Goal: +23537: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23537: Order: +23537: nrkbo +23537: Leaf order: +23537: n 6 0 0 +23537: b 10 0 0 +23537: apply 27 2 3 0,2 +23537: fixed_pt 3 0 3 2,2 +23537: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +23538: Facts: +23538: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23538: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +23538: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply (apply b b) n))))) n)) b)) b + [] by strong_fixed_point +23538: Goal: +23538: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23538: Order: +23538: kbo +23538: Leaf order: +23538: n 6 0 0 +23538: b 10 0 0 +23538: apply 27 2 3 0,2 +23538: fixed_pt 3 0 3 2,2 +23538: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +23539: Facts: +23539: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23539: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +23539: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply (apply b b) n))))) n)) b)) b + [] by strong_fixed_point +23539: Goal: +23539: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23539: Order: +23539: lpo +23539: Leaf order: +23539: n 6 0 0 +23539: b 10 0 0 +23539: apply 27 2 3 0,2 +23539: fixed_pt 3 0 3 2,2 +23539: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL044-8.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +23557: Facts: +23557: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23557: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +23557: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply n (apply b b)))))) n)) b)) b + [] by strong_fixed_point +23557: Goal: +23557: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23557: Order: +23557: kbo +23557: Leaf order: +23557: n 6 0 0 +23557: b 10 0 0 +23557: apply 27 2 3 0,2 +23557: fixed_pt 3 0 3 2,2 +23557: strong_fixed_point 3 0 2 1,2 +NO CLASH, using fixed ground order +23558: Facts: +23558: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23558: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +23558: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply n (apply b b)))))) n)) b)) b + [] by strong_fixed_point +23558: Goal: +23558: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23558: Order: +23558: lpo +23558: Leaf order: +23558: n 6 0 0 +23558: b 10 0 0 +23558: apply 27 2 3 0,2 +23558: fixed_pt 3 0 3 2,2 +23558: strong_fixed_point 3 0 2 1,2 +23556: Facts: +23556: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +23556: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +23556: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply n (apply b b)))))) n)) b)) b + [] by strong_fixed_point +23556: Goal: +23556: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +23556: Order: +23556: nrkbo +23556: Leaf order: +23556: n 6 0 0 +23556: b 10 0 0 +23556: apply 27 2 3 0,2 +23556: fixed_pt 3 0 3 2,2 +23556: strong_fixed_point 3 0 2 1,2 +% SZS status Timeout for COL044-9.p +NO CLASH, using fixed ground order +23710: Facts: +23710: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +23710: Goal: +23710: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23710: Order: +23710: nrkbo +23710: Leaf order: +23710: a2 2 0 2 2,2 +23710: multiply 12 2 2 0,2 +23710: inverse 8 1 1 0,1,1,2 +23710: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +23711: Facts: +23711: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +23711: Goal: +23711: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23711: Order: +23711: kbo +23711: Leaf order: +23711: a2 2 0 2 2,2 +23711: multiply 12 2 2 0,2 +23711: inverse 8 1 1 0,1,1,2 +23711: b2 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +23712: Facts: +23712: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +23712: Goal: +23712: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23712: Order: +23712: lpo +23712: Leaf order: +23712: a2 2 0 2 2,2 +23712: multiply 12 2 2 0,2 +23712: inverse 8 1 1 0,1,1,2 +23712: b2 2 0 2 1,1,1,2 +% SZS status Timeout for GRP506-1.p +NO CLASH, using fixed ground order +23731: Facts: +23731: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +23731: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +23731: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +23731: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +23731: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +23731: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +23731: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +23731: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +23731: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +23731: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +23731: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +23731: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +23731: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +23731: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by megill ?38 ?39 +23731: Goal: +23731: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_this +23731: Order: +23731: nrkbo +23731: Leaf order: +23731: n0 1 0 0 +23731: n1 2 0 0 +23731: join 18 2 3 0,2,2 +23731: meet 19 2 5 0,2 +23731: complement 14 1 2 0,1,2,2,2,2 +23731: b 3 0 3 1,2,2 +23731: a 7 0 7 1,2 +NO CLASH, using fixed ground order +23732: Facts: +23732: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +23732: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +23732: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +23732: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +23732: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +23732: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +23732: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +23732: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +23732: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +23732: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +23732: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +23732: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +23732: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +23732: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by megill ?38 ?39 +23732: Goal: +23732: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_this +23732: Order: +23732: kbo +23732: Leaf order: +23732: n0 1 0 0 +23732: n1 2 0 0 +23732: join 18 2 3 0,2,2 +23732: meet 19 2 5 0,2 +23732: complement 14 1 2 0,1,2,2,2,2 +23732: b 3 0 3 1,2,2 +23732: a 7 0 7 1,2 +NO CLASH, using fixed ground order +23733: Facts: +23733: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +23733: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +23733: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +23733: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +23733: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +23733: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +23733: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +23733: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +23733: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +23733: Id : 11, {_}: + complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +23733: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +23733: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +23733: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +23733: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by megill ?38 ?39 +23733: Goal: +23733: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_this +23733: Order: +23733: lpo +23733: Leaf order: +23733: n0 1 0 0 +23733: n1 2 0 0 +23733: join 18 2 3 0,2,2 +23733: meet 19 2 5 0,2 +23733: complement 14 1 2 0,1,2,2,2,2 +23733: b 3 0 3 1,2,2 +23733: a 7 0 7 1,2 +% SZS status Timeout for LAT053-1.p +NO CLASH, using fixed ground order +23764: Facts: +NO CLASH, using fixed ground order +23765: Facts: +23764: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23764: Goal: +23764: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2 +23764: Order: +23764: nrkbo +23764: Leaf order: +23764: join 20 2 0 +23764: meet 20 2 2 0,2 +23764: b 2 0 2 2,2 +23764: a 2 0 2 1,2 +23765: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23765: Goal: +23765: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2 +23765: Order: +23765: kbo +23765: Leaf order: +23765: join 20 2 0 +23765: meet 20 2 2 0,2 +23765: b 2 0 2 2,2 +23765: a 2 0 2 1,2 +NO CLASH, using fixed ground order +23766: Facts: +23766: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23766: Goal: +23766: Id : 1, {_}: meet a b =>= meet b a [] by prove_normal_axioms_2 +23766: Order: +23766: lpo +23766: Leaf order: +23766: join 20 2 0 +23766: meet 20 2 2 0,2 +23766: b 2 0 2 2,2 +23766: a 2 0 2 1,2 +% SZS status Timeout for LAT081-1.p +NO CLASH, using fixed ground order +23787: Facts: +23787: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23787: Goal: +23787: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5 +23787: Order: +23787: nrkbo +23787: Leaf order: +23787: meet 18 2 0 +23787: join 22 2 2 0,2 +23787: b 2 0 2 2,2 +23787: a 2 0 2 1,2 +NO CLASH, using fixed ground order +23788: Facts: +23788: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23788: Goal: +23788: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5 +23788: Order: +23788: kbo +23788: Leaf order: +23788: meet 18 2 0 +23788: join 22 2 2 0,2 +23788: b 2 0 2 2,2 +23788: a 2 0 2 1,2 +NO CLASH, using fixed ground order +23789: Facts: +23789: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23789: Goal: +23789: Id : 1, {_}: join a b =>= join b a [] by prove_normal_axioms_5 +23789: Order: +23789: lpo +23789: Leaf order: +23789: meet 18 2 0 +23789: join 22 2 2 0,2 +23789: b 2 0 2 2,2 +23789: a 2 0 2 1,2 +% SZS status Timeout for LAT084-1.p +NO CLASH, using fixed ground order +23816: Facts: +23816: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23816: Goal: +23816: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7 +23816: Order: +23816: nrkbo +23816: Leaf order: +23816: meet 19 2 1 0,2 +23816: join 21 2 1 0,2,2 +23816: b 1 0 1 2,2,2 +23816: a 3 0 3 1,2 +NO CLASH, using fixed ground order +23817: Facts: +23817: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23817: Goal: +23817: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7 +23817: Order: +23817: kbo +23817: Leaf order: +23817: meet 19 2 1 0,2 +23817: join 21 2 1 0,2,2 +23817: b 1 0 1 2,2,2 +23817: a 3 0 3 1,2 +NO CLASH, using fixed ground order +23818: Facts: +23818: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23818: Goal: +23818: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7 +23818: Order: +23818: lpo +23818: Leaf order: +23818: meet 19 2 1 0,2 +23818: join 21 2 1 0,2,2 +23818: b 1 0 1 2,2,2 +23818: a 3 0 3 1,2 +% SZS status Timeout for LAT086-1.p +NO CLASH, using fixed ground order +23840: Facts: +23840: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23840: Goal: +23840: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8 +23840: Order: +23840: nrkbo +23840: Leaf order: +23840: join 21 2 1 0,2 +23840: meet 19 2 1 0,2,2 +23840: b 1 0 1 2,2,2 +23840: a 3 0 3 1,2 +NO CLASH, using fixed ground order +23842: Facts: +23842: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23842: Goal: +23842: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8 +23842: Order: +23842: lpo +23842: Leaf order: +23842: join 21 2 1 0,2 +23842: meet 19 2 1 0,2,2 +23842: b 1 0 1 2,2,2 +23842: a 3 0 3 1,2 +NO CLASH, using fixed ground order +23841: Facts: +23841: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +23841: Goal: +23841: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8 +23841: Order: +23841: kbo +23841: Leaf order: +23841: join 21 2 1 0,2 +23841: meet 19 2 1 0,2,2 +23841: b 1 0 1 2,2,2 +23841: a 3 0 3 1,2 +% SZS status Timeout for LAT087-1.p +NO CLASH, using fixed ground order +23873: Facts: +23873: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +23873: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +23873: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +23873: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +23873: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +23873: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +23873: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +23873: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +23873: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H3 ?26 ?27 ?28 +23873: Goal: +23873: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +23873: Order: +23873: nrkbo +23873: Leaf order: +23873: join 17 2 4 0,2,2 +23873: meet 21 2 6 0,2 +23873: c 4 0 4 2,2,2,2 +23873: b 4 0 4 1,2,2 +23873: a 4 0 4 1,2 +NO CLASH, using fixed ground order +23874: Facts: +23874: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +23874: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +23874: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +23874: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +23874: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +23874: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +23874: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +23874: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +23874: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H3 ?26 ?27 ?28 +23874: Goal: +23874: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +23874: Order: +23874: kbo +23874: Leaf order: +23874: join 17 2 4 0,2,2 +23874: meet 21 2 6 0,2 +23874: c 4 0 4 2,2,2,2 +23874: b 4 0 4 1,2,2 +23874: a 4 0 4 1,2 +NO CLASH, using fixed ground order +23875: Facts: +23875: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +23875: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +23875: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +23875: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +23875: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +23875: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +23875: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +23875: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +23875: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H3 ?26 ?27 ?28 +23875: Goal: +23875: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +23875: Order: +23875: lpo +23875: Leaf order: +23875: join 17 2 4 0,2,2 +23875: meet 21 2 6 0,2 +23875: c 4 0 4 2,2,2,2 +23875: b 4 0 4 1,2,2 +23875: a 4 0 4 1,2 +% SZS status Timeout for LAT099-1.p +NO CLASH, using fixed ground order +24259: Facts: +24259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24259: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24259: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24259: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24259: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24259: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +24259: Goal: +24259: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +24259: Order: +24259: nrkbo +24259: Leaf order: +24259: meet 19 2 5 0,2 +24259: join 19 2 5 0,2,2 +24259: d 2 0 2 2,2,2,2,2 +24259: c 3 0 3 1,2,2,2 +24259: b 3 0 3 1,2,2 +24259: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24260: Facts: +24260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24260: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24260: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24260: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24260: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24260: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +24260: Goal: +24260: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +24260: Order: +24260: kbo +24260: Leaf order: +24260: meet 19 2 5 0,2 +24260: join 19 2 5 0,2,2 +24260: d 2 0 2 2,2,2,2,2 +24260: c 3 0 3 1,2,2,2 +24260: b 3 0 3 1,2,2 +24260: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24261: Facts: +24261: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24261: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24261: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24261: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24261: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24261: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24261: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24261: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24261: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +24261: Goal: +24261: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +24261: Order: +24261: lpo +24261: Leaf order: +24261: meet 19 2 5 0,2 +24261: join 19 2 5 0,2,2 +24261: d 2 0 2 2,2,2,2,2 +24261: c 3 0 3 1,2,2,2 +24261: b 3 0 3 1,2,2 +24261: a 4 0 4 1,2 +% SZS status Timeout for LAT110-1.p +NO CLASH, using fixed ground order +24393: Facts: +24393: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24393: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24393: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24393: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24393: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24393: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24393: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24393: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24393: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29)) + [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29 +24393: Goal: +24393: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +24393: Order: +24393: nrkbo +24393: Leaf order: +24393: meet 20 2 5 0,2 +24393: join 17 2 4 0,2,2 +24393: c 3 0 3 2,2,2 +24393: b 3 0 3 1,2,2 +24393: a 5 0 5 1,2 +NO CLASH, using fixed ground order +24394: Facts: +24394: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24394: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24394: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24394: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24394: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24394: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24394: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24394: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24394: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29)) + [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29 +24394: Goal: +24394: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +24394: Order: +24394: kbo +24394: Leaf order: +24394: meet 20 2 5 0,2 +24394: join 17 2 4 0,2,2 +24394: c 3 0 3 2,2,2 +24394: b 3 0 3 1,2,2 +24394: a 5 0 5 1,2 +NO CLASH, using fixed ground order +24395: Facts: +24395: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24395: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24395: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24395: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24395: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24395: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24395: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24395: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24395: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29)) + [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29 +24395: Goal: +24395: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +24395: Order: +24395: lpo +24395: Leaf order: +24395: meet 20 2 5 0,2 +24395: join 17 2 4 0,2,2 +24395: c 3 0 3 2,2,2 +24395: b 3 0 3 1,2,2 +24395: a 5 0 5 1,2 +% SZS status Timeout for LAT118-1.p +NO CLASH, using fixed ground order +24412: Facts: +24412: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24412: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24412: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24412: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24412: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24412: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24412: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24412: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24412: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +24412: Goal: +24412: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24412: Order: +24412: nrkbo +24412: Leaf order: +24412: join 17 2 4 0,2,2 +24412: meet 21 2 6 0,2 +24412: c 3 0 3 2,2,2,2 +24412: b 3 0 3 1,2,2 +24412: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24413: Facts: +24413: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24413: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24413: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24413: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24413: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24413: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24413: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24413: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24413: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +24413: Goal: +24413: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24413: Order: +24413: kbo +24413: Leaf order: +24413: join 17 2 4 0,2,2 +24413: meet 21 2 6 0,2 +24413: c 3 0 3 2,2,2,2 +24413: b 3 0 3 1,2,2 +24413: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24414: Facts: +24414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24414: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24414: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24414: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24414: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24414: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +24414: Goal: +24414: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24414: Order: +24414: lpo +24414: Leaf order: +24414: join 17 2 4 0,2,2 +24414: meet 21 2 6 0,2 +24414: c 3 0 3 2,2,2,2 +24414: b 3 0 3 1,2,2 +24414: a 6 0 6 1,2 +% SZS status Timeout for LAT142-1.p +NO CLASH, using fixed ground order +24444: Facts: +24444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24444: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24444: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24444: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24444: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24444: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +24444: Goal: +24444: Id : 1, {_}: + meet a (meet b (join c (meet a d))) + =<= + meet a (meet b (join c (meet d (join a (meet b c))))) + [] by prove_H45 +24444: Order: +24444: nrkbo +24444: Leaf order: +24444: join 16 2 3 0,2,2,2 +24444: meet 21 2 7 0,2 +24444: d 2 0 2 2,2,2,2,2 +24444: c 3 0 3 1,2,2,2 +24444: b 3 0 3 1,2,2 +24444: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24445: Facts: +24445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24445: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24445: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24445: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24445: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24445: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +24445: Goal: +24445: Id : 1, {_}: + meet a (meet b (join c (meet a d))) + =<= + meet a (meet b (join c (meet d (join a (meet b c))))) + [] by prove_H45 +24445: Order: +24445: kbo +24445: Leaf order: +24445: join 16 2 3 0,2,2,2 +24445: meet 21 2 7 0,2 +24445: d 2 0 2 2,2,2,2,2 +24445: c 3 0 3 1,2,2,2 +24445: b 3 0 3 1,2,2 +24445: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24446: Facts: +24446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24446: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24446: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24446: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24446: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24446: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +24446: Goal: +24446: Id : 1, {_}: + meet a (meet b (join c (meet a d))) + =>= + meet a (meet b (join c (meet d (join a (meet b c))))) + [] by prove_H45 +24446: Order: +24446: lpo +24446: Leaf order: +24446: join 16 2 3 0,2,2,2 +24446: meet 21 2 7 0,2 +24446: d 2 0 2 2,2,2,2,2 +24446: c 3 0 3 1,2,2,2 +24446: b 3 0 3 1,2,2 +24446: a 4 0 4 1,2 +% SZS status Timeout for LAT147-1.p +NO CLASH, using fixed ground order +24463: Facts: +24463: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24463: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24463: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24463: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24463: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24463: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24463: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24463: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24463: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29 +24463: Goal: +24463: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24463: Order: +24463: kbo +24463: Leaf order: +24463: join 18 2 4 0,2,2 +24463: meet 20 2 6 0,2 +24463: c 3 0 3 2,2,2,2 +24463: b 3 0 3 1,2,2 +24463: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24464: Facts: +24464: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24464: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24464: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24464: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24464: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24464: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24464: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24464: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24464: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29 +24464: Goal: +24464: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24464: Order: +24464: lpo +24464: Leaf order: +24464: join 18 2 4 0,2,2 +24464: meet 20 2 6 0,2 +24464: c 3 0 3 2,2,2,2 +24464: b 3 0 3 1,2,2 +24464: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24462: Facts: +24462: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24462: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24462: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24462: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24462: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24462: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24462: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24462: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24462: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29 +24462: Goal: +24462: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24462: Order: +24462: nrkbo +24462: Leaf order: +24462: join 18 2 4 0,2,2 +24462: meet 20 2 6 0,2 +24462: c 3 0 3 2,2,2,2 +24462: b 3 0 3 1,2,2 +24462: a 6 0 6 1,2 +% SZS status Timeout for LAT154-1.p +NO CLASH, using fixed ground order +24500: Facts: +24500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24500: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24500: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24500: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24500: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24500: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +24500: Goal: +24500: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +24500: Order: +24500: nrkbo +24500: Leaf order: +24500: join 18 2 4 0,2,2 +24500: meet 20 2 6 0,2 +24500: c 4 0 4 2,2,2,2 +24500: b 4 0 4 1,2,2 +24500: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24501: Facts: +24501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24501: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24501: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24501: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24501: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24501: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +24501: Goal: +24501: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +24501: Order: +24501: kbo +24501: Leaf order: +24501: join 18 2 4 0,2,2 +24501: meet 20 2 6 0,2 +24501: c 4 0 4 2,2,2,2 +24501: b 4 0 4 1,2,2 +24501: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24502: Facts: +24502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24502: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24502: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24502: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24502: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24502: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +24502: Goal: +24502: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +24502: Order: +24502: lpo +24502: Leaf order: +24502: join 18 2 4 0,2,2 +24502: meet 20 2 6 0,2 +24502: c 4 0 4 2,2,2,2 +24502: b 4 0 4 1,2,2 +24502: a 4 0 4 1,2 +% SZS status Timeout for LAT155-1.p +NO CLASH, using fixed ground order +24518: Facts: +24518: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24518: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24518: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24518: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24518: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24518: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24518: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24518: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24518: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29 +24518: Goal: +24518: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +24518: Order: +24518: nrkbo +24518: Leaf order: +24518: meet 18 2 4 0,2 +24518: join 18 2 4 0,2,2 +24518: c 2 0 2 2,2,2 +24518: b 4 0 4 1,2,2 +24518: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24519: Facts: +24519: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24519: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24519: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24519: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24519: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24519: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24519: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24519: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24519: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29 +24519: Goal: +24519: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +24519: Order: +24519: kbo +24519: Leaf order: +24519: meet 18 2 4 0,2 +24519: join 18 2 4 0,2,2 +24519: c 2 0 2 2,2,2 +24519: b 4 0 4 1,2,2 +24519: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24520: Facts: +24520: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24520: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24520: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24520: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24520: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24520: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24520: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24520: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24520: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29 +24520: Goal: +24520: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +24520: Order: +24520: lpo +24520: Leaf order: +24520: meet 18 2 4 0,2 +24520: join 18 2 4 0,2,2 +24520: c 2 0 2 2,2,2 +24520: b 4 0 4 1,2,2 +24520: a 4 0 4 1,2 +% SZS status Timeout for LAT170-1.p +NO CLASH, using fixed ground order +24547: Facts: +24547: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +24547: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +24547: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +24547: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +24547: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +24547: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +24547: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +24547: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +24547: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +24547: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +24547: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +24547: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24547: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +24547: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +24547: Goal: +24547: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +24547: Order: +24547: nrkbo +24547: Leaf order: +24547: commutator 1 2 0 +24547: additive_inverse 6 1 0 +24547: add 16 2 0 +24547: additive_identity 9 0 1 3 +24547: multiply 22 2 4 0,2 +24547: associator 5 3 4 0,1,1,1,2 +24547: y 4 0 4 3,1,1,1,2 +24547: x 9 0 9 1,1,1,1,2 +NO CLASH, using fixed ground order +24548: Facts: +24548: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +24548: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +24548: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +24548: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +24548: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +24548: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +24548: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +24548: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +24548: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +24548: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +24548: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +24548: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24548: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +24548: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +24548: Goal: +24548: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +24548: Order: +24548: kbo +24548: Leaf order: +24548: commutator 1 2 0 +24548: additive_inverse 6 1 0 +24548: add 16 2 0 +24548: additive_identity 9 0 1 3 +24548: multiply 22 2 4 0,2 +24548: associator 5 3 4 0,1,1,1,2 +24548: y 4 0 4 3,1,1,1,2 +24548: x 9 0 9 1,1,1,1,2 +NO CLASH, using fixed ground order +24549: Facts: +24549: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +24549: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +24549: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +24549: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +24549: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +24549: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +24549: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +24549: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +24549: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +24549: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +24549: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +24549: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24549: Id : 14, {_}: + associator ?34 ?35 ?36 + =>= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +24549: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +24549: Goal: +24549: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +24549: Order: +24549: lpo +24549: Leaf order: +24549: commutator 1 2 0 +24549: additive_inverse 6 1 0 +24549: add 16 2 0 +24549: additive_identity 9 0 1 3 +24549: multiply 22 2 4 0,2 +24549: associator 5 3 4 0,1,1,1,2 +24549: y 4 0 4 3,1,1,1,2 +24549: x 9 0 9 1,1,1,1,2 +% SZS status Timeout for RNG031-6.p +NO CLASH, using fixed ground order +24576: Facts: +24576: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +24576: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +24576: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +24576: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +24576: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +24576: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +24576: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +24576: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +24576: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +24576: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +24576: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +24576: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +24576: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +24576: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +24576: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +24576: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +24576: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +24576: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +24576: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +24576: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +24576: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +24576: Goal: +24576: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +24576: Order: +24576: nrkbo +24576: Leaf order: +24576: commutator 1 2 0 +24576: add 24 2 0 +24576: additive_inverse 22 1 0 +24576: additive_identity 9 0 1 3 +24576: multiply 40 2 4 0,2add +24576: associator 5 3 4 0,1,1,1,2 +24576: y 4 0 4 3,1,1,1,2 +24576: x 9 0 9 1,1,1,1,2 +NO CLASH, using fixed ground order +24577: Facts: +24577: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +NO CLASH, using fixed ground order +24578: Facts: +24578: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +24578: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +24578: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +24578: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +24578: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +24578: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +24578: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +24578: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +24578: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +24578: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +24578: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +24578: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +24578: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +24578: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +24578: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +24578: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +24578: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +24578: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +24578: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +24578: Id : 21, {_}: + associator ?59 ?60 ?61 + =>= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +24578: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +24578: Goal: +24578: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +24578: Order: +24578: lpo +24578: Leaf order: +24578: commutator 1 2 0 +24578: add 24 2 0 +24578: additive_inverse 22 1 0 +24578: additive_identity 9 0 1 3 +24578: multiply 40 2 4 0,2add +24578: associator 5 3 4 0,1,1,1,2 +24578: y 4 0 4 3,1,1,1,2 +24578: x 9 0 9 1,1,1,1,2 +24577: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +24577: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +24577: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +24577: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +24577: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +24577: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +24577: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +24577: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +24577: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +24577: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +24577: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +24577: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +24577: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +24577: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +24577: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +24577: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +24577: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +24577: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +24577: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +24577: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +24577: Goal: +24577: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +24577: Order: +24577: kbo +24577: Leaf order: +24577: commutator 1 2 0 +24577: add 24 2 0 +24577: additive_inverse 22 1 0 +24577: additive_identity 9 0 1 3 +24577: multiply 40 2 4 0,2add +24577: associator 5 3 4 0,1,1,1,2 +24577: y 4 0 4 3,1,1,1,2 +24577: x 9 0 9 1,1,1,1,2 +% SZS status Timeout for RNG031-7.p +NO CLASH, using fixed ground order +24609: Facts: +24609: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3 +24609: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5 +24609: Goal: +24609: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1 +24609: Order: +24609: nrkbo +24609: Leaf order: +24609: f 2 1 0 +24609: g2 2 1 1 0,3 +24609: g1 2 1 1 0,2 +NO CLASH, using fixed ground order +24610: Facts: +24610: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3 +24610: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5 +24610: Goal: +24610: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1 +24610: Order: +24610: kbo +24610: Leaf order: +24610: f 2 1 0 +24610: g2 2 1 1 0,3 +24610: g1 2 1 1 0,2 +NO CLASH, using fixed ground order +24611: Facts: +24611: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3 +24611: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5 +24611: Goal: +24611: Id : 1, {_}: g1 ?1 =>= g2 ?1 [1] by clause3 ?1 +24611: Order: +24611: lpo +24611: Leaf order: +24611: f 2 1 0 +24611: g2 2 1 1 0,3 +24611: g1 2 1 1 0,2 +24609: status GaveUp for SYN305-1.p +24610: status GaveUp for SYN305-1.p +24611: status GaveUp for SYN305-1.p +% SZS status Timeout for SYN305-1.p +CLASH, statistics insufficient +24616: Facts: +24616: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +24616: Id : 3, {_}: + apply (apply (apply h ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?8) ?9) ?8 + [9, 8, 7] by h_definition ?7 ?8 ?9 +24616: Goal: +24616: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +24616: Order: +24616: nrkbo +24616: Leaf order: +24616: h 1 0 0 +24616: b 1 0 0 +24616: apply 14 2 3 0,2 +24616: f 3 1 3 0,2,2 +CLASH, statistics insufficient +24617: Facts: +24617: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +24617: Id : 3, {_}: + apply (apply (apply h ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?8) ?9) ?8 + [9, 8, 7] by h_definition ?7 ?8 ?9 +24617: Goal: +24617: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +24617: Order: +24617: kbo +24617: Leaf order: +24617: h 1 0 0 +24617: b 1 0 0 +24617: apply 14 2 3 0,2 +24617: f 3 1 3 0,2,2 +CLASH, statistics insufficient +24618: Facts: +24618: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +24618: Id : 3, {_}: + apply (apply (apply h ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?8) ?9) ?8 + [9, 8, 7] by h_definition ?7 ?8 ?9 +24618: Goal: +24618: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +24618: Order: +24618: lpo +24618: Leaf order: +24618: h 1 0 0 +24618: b 1 0 0 +24618: apply 14 2 3 0,2 +24618: f 3 1 3 0,2,2 +% SZS status Timeout for COL043-1.p +CLASH, statistics insufficient +24654: Facts: +CLASH, statistics insufficient +24655: Facts: +24655: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +24655: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +24655: Id : 4, {_}: + apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12 + [12, 11] by w_definition ?11 ?12 +24655: Goal: +24655: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1) + =<= + apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1)) + [1] by prove_p_combinator ?1 +24655: Order: +24655: kbo +24655: Leaf order: +24655: w 1 0 0 +24655: q 1 0 0 +24655: b 1 0 0 +24655: h 2 1 2 0,2,2 +24655: g 4 1 4 0,2,1,1,2 +24655: apply 22 2 8 0,2 +24655: f 3 1 3 0,2,1,1,1,2 +CLASH, statistics insufficient +24656: Facts: +24656: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +24656: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +24656: Id : 4, {_}: + apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12 + [12, 11] by w_definition ?11 ?12 +24656: Goal: +24656: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1)) + [1] by prove_p_combinator ?1 +24656: Order: +24656: lpo +24656: Leaf order: +24656: w 1 0 0 +24656: q 1 0 0 +24656: b 1 0 0 +24656: h 2 1 2 0,2,2 +24656: g 4 1 4 0,2,1,1,2 +24656: apply 22 2 8 0,2 +24656: f 3 1 3 0,2,1,1,1,2 +24654: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +24654: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +24654: Id : 4, {_}: + apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12 + [12, 11] by w_definition ?11 ?12 +24654: Goal: +24654: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1) + =<= + apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1)) + [1] by prove_p_combinator ?1 +24654: Order: +24654: nrkbo +24654: Leaf order: +24654: w 1 0 0 +24654: q 1 0 0 +24654: b 1 0 0 +24654: h 2 1 2 0,2,2 +24654: g 4 1 4 0,2,1,1,2 +24654: apply 22 2 8 0,2 +24654: f 3 1 3 0,2,1,1,1,2 +% SZS status Timeout for COL066-1.p +NO CLASH, using fixed ground order +24759: Facts: +24759: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +24759: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +24759: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +24759: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +24759: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +24759: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +24759: Id : 8, {_}: + join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +24759: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +24759: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +24759: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +24759: Goal: +24759: Id : 1, {_}: + join + (complement + (join + (join (meet (complement a) b) + (meet (complement a) (complement b))) + (meet a (join (complement a) b)))) (join (complement a) b) + =>= + n1 + [] by prove_e3 +24759: Order: +24759: nrkbo +24759: Leaf order: +24759: n0 1 0 0 +24759: n1 2 0 1 3 +24759: join 17 2 5 0,2 +24759: meet 12 2 3 0,1,1,1,1,2 +24759: b 4 0 4 2,1,1,1,1,2 +24759: complement 15 1 6 0,1,2 +24759: a 5 0 5 1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +24760: Facts: +24760: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +24760: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +24760: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +24760: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +24760: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +24760: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +24760: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +24760: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +24760: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +24760: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +24760: Goal: +24760: Id : 1, {_}: + join + (complement + (join + (join (meet (complement a) b) + (meet (complement a) (complement b))) + (meet a (join (complement a) b)))) (join (complement a) b) + =>= + n1 + [] by prove_e3 +24760: Order: +24760: kbo +24760: Leaf order: +24760: n0 1 0 0 +24760: n1 2 0 1 3 +24760: join 17 2 5 0,2 +24760: meet 12 2 3 0,1,1,1,1,2 +24760: b 4 0 4 2,1,1,1,1,2 +24760: complement 15 1 6 0,1,2 +24760: a 5 0 5 1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +24761: Facts: +24761: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +24761: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +24761: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +24761: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +24761: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +24761: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +24761: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +24761: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +24761: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +24761: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +24761: Goal: +24761: Id : 1, {_}: + join + (complement + (join + (join (meet (complement a) b) + (meet (complement a) (complement b))) + (meet a (join (complement a) b)))) (join (complement a) b) + =>= + n1 + [] by prove_e3 +24761: Order: +24761: lpo +24761: Leaf order: +24761: n0 1 0 0 +24761: n1 2 0 1 3 +24761: join 17 2 5 0,2 +24761: meet 12 2 3 0,1,1,1,1,2 +24761: b 4 0 4 2,1,1,1,1,2 +24761: complement 15 1 6 0,1,2 +24761: a 5 0 5 1,1,1,1,1,1,2 +% SZS status Timeout for LAT018-1.p +NO CLASH, using fixed ground order +24778: Facts: +24778: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +24778: Goal: +24778: Id : 1, {_}: + meet (meet a b) c =>= meet a (meet b c) + [] by prove_normal_axioms_3 +24778: Order: +24778: nrkbo +24778: Leaf order: +24778: join 20 2 0 +24778: c 2 0 2 2,2 +24778: meet 22 2 4 0,2 +24778: b 2 0 2 2,1,2 +24778: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +24779: Facts: +24779: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +24779: Goal: +24779: Id : 1, {_}: + meet (meet a b) c =>= meet a (meet b c) + [] by prove_normal_axioms_3 +24779: Order: +24779: kbo +24779: Leaf order: +24779: join 20 2 0 +24779: c 2 0 2 2,2 +24779: meet 22 2 4 0,2 +24779: b 2 0 2 2,1,2 +24779: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +24780: Facts: +24780: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +24780: Goal: +24780: Id : 1, {_}: + meet (meet a b) c =>= meet a (meet b c) + [] by prove_normal_axioms_3 +24780: Order: +24780: lpo +24780: Leaf order: +24780: join 20 2 0 +24780: c 2 0 2 2,2 +24780: meet 22 2 4 0,2 +24780: b 2 0 2 2,1,2 +24780: a 2 0 2 1,1,2 +% SZS status Timeout for LAT082-1.p +NO CLASH, using fixed ground order +24809: Facts: +24809: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +24809: Goal: +24809: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_normal_axioms_6 +24809: Order: +24809: kbo +24809: Leaf order: +24809: meet 18 2 0 +24809: c 2 0 2 2,2 +24809: join 24 2 4 0,2 +24809: b 2 0 2 2,1,2 +24809: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +24810: Facts: +24810: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +24810: Goal: +24810: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_normal_axioms_6 +24810: Order: +24810: lpo +24810: Leaf order: +24810: meet 18 2 0 +24810: c 2 0 2 2,2 +24810: join 24 2 4 0,2 +24810: b 2 0 2 2,1,2 +24810: a 2 0 2 1,1,2 +NO CLASH, using fixed ground order +24808: Facts: +24808: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +24808: Goal: +24808: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_normal_axioms_6 +24808: Order: +24808: nrkbo +24808: Leaf order: +24808: meet 18 2 0 +24808: c 2 0 2 2,2 +24808: join 24 2 4 0,2 +24808: b 2 0 2 2,1,2 +24808: a 2 0 2 1,1,2 +% SZS status Timeout for LAT085-1.p +NO CLASH, using fixed ground order +24831: Facts: +24831: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24831: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24831: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24831: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24831: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24831: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24831: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24831: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24831: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +24831: Goal: +24831: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +24831: Order: +24831: nrkbo +24831: Leaf order: +24831: join 16 2 4 0,2,2 +24831: meet 22 2 6 0,2 +24831: c 4 0 4 2,2,2,2 +24831: b 4 0 4 1,2,2 +24831: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24832: Facts: +24832: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24832: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24832: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24832: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24832: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24832: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24832: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24832: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24832: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +24832: Goal: +24832: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +24832: Order: +24832: kbo +24832: Leaf order: +24832: join 16 2 4 0,2,2 +24832: meet 22 2 6 0,2 +24832: c 4 0 4 2,2,2,2 +24832: b 4 0 4 1,2,2 +24832: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24833: Facts: +24833: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24833: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24833: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24833: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24833: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24833: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24833: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24833: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24833: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +24833: Goal: +24833: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +24833: Order: +24833: lpo +24833: Leaf order: +24833: join 16 2 4 0,2,2 +24833: meet 22 2 6 0,2 +24833: c 4 0 4 2,2,2,2 +24833: b 4 0 4 1,2,2 +24833: a 4 0 4 1,2 +% SZS status Timeout for LAT144-1.p +NO CLASH, using fixed ground order +24860: Facts: +24860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24860: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24860: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24860: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24860: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24860: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +24860: Goal: +24860: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +24860: Order: +24860: nrkbo +24860: Leaf order: +24860: meet 19 2 5 0,2 +24860: join 18 2 5 0,2,2 +24860: d 2 0 2 2,2,2,2,2 +24860: c 3 0 3 1,2,2,2 +24860: b 3 0 3 1,2,2 +24860: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24861: Facts: +24861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24861: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24861: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24861: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24861: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24861: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +24861: Goal: +24861: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +24861: Order: +24861: kbo +24861: Leaf order: +24861: meet 19 2 5 0,2 +24861: join 18 2 5 0,2,2 +24861: d 2 0 2 2,2,2,2,2 +24861: c 3 0 3 1,2,2,2 +24861: b 3 0 3 1,2,2 +24861: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24862: Facts: +24862: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24862: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24862: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24862: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24862: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24862: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24862: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24862: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24862: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +24862: Goal: +24862: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +24862: Order: +24862: lpo +24862: Leaf order: +24862: meet 19 2 5 0,2 +24862: join 18 2 5 0,2,2 +24862: d 2 0 2 2,2,2,2,2 +24862: c 3 0 3 1,2,2,2 +24862: b 3 0 3 1,2,2 +24862: a 4 0 4 1,2 +% SZS status Timeout for LAT150-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +24889: Facts: +24889: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24889: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24889: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24889: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24889: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24889: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24889: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24889: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24889: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +24889: Goal: +24889: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +24889: Order: +24889: kbo +24889: Leaf order: +24889: meet 19 2 5 0,2 +24889: join 18 2 5 0,2,2 +24889: d 2 0 2 2,2,2,2,2 +24889: c 3 0 3 1,2,2,2 +24889: b 3 0 3 1,2,2 +24889: a 4 0 4 1,2 +24888: Facts: +24888: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24888: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24888: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24888: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24888: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24888: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24888: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24888: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24888: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +24888: Goal: +24888: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +24888: Order: +24888: nrkbo +24888: Leaf order: +24888: meet 19 2 5 0,2 +24888: join 18 2 5 0,2,2 +24888: d 2 0 2 2,2,2,2,2 +24888: c 3 0 3 1,2,2,2 +24888: b 3 0 3 1,2,2 +24888: a 4 0 4 1,2 +NO CLASH, using fixed ground order +24890: Facts: +24890: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24890: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24890: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24890: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24890: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24890: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24890: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24890: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24890: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +24890: Goal: +24890: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +24890: Order: +24890: lpo +24890: Leaf order: +24890: meet 19 2 5 0,2 +24890: join 18 2 5 0,2,2 +24890: d 2 0 2 2,2,2,2,2 +24890: c 3 0 3 1,2,2,2 +24890: b 3 0 3 1,2,2 +24890: a 4 0 4 1,2 +% SZS status Timeout for LAT151-1.p +NO CLASH, using fixed ground order +24921: Facts: +24921: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24921: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24921: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24921: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24921: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24921: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24921: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24921: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24921: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +24921: Goal: +24921: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24921: Order: +24921: nrkbo +24921: Leaf order: +24921: join 18 2 4 0,2,2 +24921: meet 20 2 6 0,2 +24921: c 3 0 3 2,2,2,2 +24921: b 3 0 3 1,2,2 +24921: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24922: Facts: +24922: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24922: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24922: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24922: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24922: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24922: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24922: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24922: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24922: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +24922: Goal: +24922: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24922: Order: +24922: kbo +24922: Leaf order: +24922: join 18 2 4 0,2,2 +24922: meet 20 2 6 0,2 +24922: c 3 0 3 2,2,2,2 +24922: b 3 0 3 1,2,2 +24922: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24923: Facts: +24923: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24923: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24923: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24923: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24923: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24923: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24923: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24923: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24923: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +24923: Goal: +24923: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24923: Order: +24923: lpo +24923: Leaf order: +24923: join 18 2 4 0,2,2 +24923: meet 20 2 6 0,2 +24923: c 3 0 3 2,2,2,2 +24923: b 3 0 3 1,2,2 +24923: a 6 0 6 1,2 +% SZS status Timeout for LAT152-1.p +NO CLASH, using fixed ground order +24939: Facts: +24939: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24939: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24939: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24939: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24939: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24939: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24939: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24939: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24939: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +24939: Goal: +24939: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +24939: Order: +24939: nrkbo +24939: Leaf order: +24939: join 18 2 4 0,2,2 +24939: meet 20 2 6 0,2 +24939: c 2 0 2 2,2,2,2 +24939: b 4 0 4 1,2,2 +24939: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24940: Facts: +24940: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24940: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24940: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24940: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24940: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24940: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24940: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24940: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24940: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +24940: Goal: +24940: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +24940: Order: +24940: kbo +24940: Leaf order: +24940: join 18 2 4 0,2,2 +24940: meet 20 2 6 0,2 +24940: c 2 0 2 2,2,2,2 +24940: b 4 0 4 1,2,2 +24940: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24941: Facts: +24941: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24941: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24941: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24941: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24941: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24941: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24941: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24941: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24941: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +24941: Goal: +24941: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +24941: Order: +24941: lpo +24941: Leaf order: +24941: join 18 2 4 0,2,2 +24941: meet 20 2 6 0,2 +24941: c 2 0 2 2,2,2,2 +24941: b 4 0 4 1,2,2 +24941: a 6 0 6 1,2 +% SZS status Timeout for LAT159-1.p +NO CLASH, using fixed ground order +24972: Facts: +24972: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24972: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24972: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +NO CLASH, using fixed ground order +24972: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24972: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24972: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24972: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24972: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24972: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +24972: Goal: +24972: Id : 1, {_}: + meet a (meet b (join c d)) + =<= + meet a (meet b (join c (meet a (join d (meet b c))))) + [] by prove_H73 +24972: Order: +24972: nrkbo +24972: Leaf order: +24972: meet 19 2 6 0,2 +24972: join 15 2 3 0,2,2,2 +24972: d 2 0 2 2,2,2,2 +24972: c 3 0 3 1,2,2,2 +24972: b 3 0 3 1,2,2 +24972: a 3 0 3 1,2 +24973: Facts: +24973: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24973: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24973: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24973: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24973: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24973: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24973: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24973: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24973: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +24973: Goal: +24973: Id : 1, {_}: + meet a (meet b (join c d)) + =<= + meet a (meet b (join c (meet a (join d (meet b c))))) + [] by prove_H73 +24973: Order: +24973: kbo +24973: Leaf order: +24973: meet 19 2 6 0,2 +24973: join 15 2 3 0,2,2,2 +24973: d 2 0 2 2,2,2,2 +24973: c 3 0 3 1,2,2,2 +24973: b 3 0 3 1,2,2 +24973: a 3 0 3 1,2 +NO CLASH, using fixed ground order +24974: Facts: +24974: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24974: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24974: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24974: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24974: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24974: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24974: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24974: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24974: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +24974: Goal: +24974: Id : 1, {_}: + meet a (meet b (join c d)) + =<= + meet a (meet b (join c (meet a (join d (meet b c))))) + [] by prove_H73 +24974: Order: +24974: lpo +24974: Leaf order: +24974: meet 19 2 6 0,2 +24974: join 15 2 3 0,2,2,2 +24974: d 2 0 2 2,2,2,2 +24974: c 3 0 3 1,2,2,2 +24974: b 3 0 3 1,2,2 +24974: a 3 0 3 1,2 +% SZS status Timeout for LAT162-1.p +NO CLASH, using fixed ground order +24990: Facts: +24990: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24990: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24990: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24990: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24990: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24990: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24990: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24990: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24990: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +24990: Goal: +24990: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24990: Order: +24990: nrkbo +24990: Leaf order: +24990: join 17 2 4 0,2,2 +24990: meet 20 2 6 0,2 +24990: c 3 0 3 2,2,2,2 +24990: b 3 0 3 1,2,2 +24990: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24991: Facts: +24991: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24991: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24991: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24991: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24991: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24991: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24991: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24991: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24991: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +24991: Goal: +24991: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24991: Order: +24991: kbo +24991: Leaf order: +24991: join 17 2 4 0,2,2 +24991: meet 20 2 6 0,2 +24991: c 3 0 3 2,2,2,2 +24991: b 3 0 3 1,2,2 +24991: a 6 0 6 1,2 +NO CLASH, using fixed ground order +24992: Facts: +24992: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24992: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24992: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24992: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24992: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24992: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24992: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24992: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24992: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +24992: Goal: +24992: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +24992: Order: +24992: lpo +24992: Leaf order: +24992: join 17 2 4 0,2,2 +24992: meet 20 2 6 0,2 +24992: c 3 0 3 2,2,2,2 +24992: b 3 0 3 1,2,2 +24992: a 6 0 6 1,2 +% SZS status Timeout for LAT164-1.p +NO CLASH, using fixed ground order +25019: Facts: +NO CLASH, using fixed ground order +25020: Facts: +25020: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25020: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25020: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25020: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25020: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25020: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25020: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25020: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25020: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +25020: Goal: +25020: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +25020: Order: +25020: kbo +25020: Leaf order: +25020: meet 17 2 4 0,2 +25020: join 19 2 4 0,2,2 +25020: c 2 0 2 2,2,2 +25020: b 4 0 4 1,2,2 +25020: a 4 0 4 1,2 +25019: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25019: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25019: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25019: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25019: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25019: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25019: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +NO CLASH, using fixed ground order +25019: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25019: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +25019: Goal: +25019: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +25019: Order: +25019: nrkbo +25019: Leaf order: +25019: meet 17 2 4 0,2 +25019: join 19 2 4 0,2,2 +25019: c 2 0 2 2,2,2 +25019: b 4 0 4 1,2,2 +25019: a 4 0 4 1,2 +25021: Facts: +25021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25021: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25021: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25021: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25021: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25021: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +25021: Goal: +25021: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +25021: Order: +25021: lpo +25021: Leaf order: +25021: meet 17 2 4 0,2 +25021: join 19 2 4 0,2,2 +25021: c 2 0 2 2,2,2 +25021: b 4 0 4 1,2,2 +25021: a 4 0 4 1,2 +% SZS status Timeout for LAT169-1.p +NO CLASH, using fixed ground order +25071: Facts: +25071: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25071: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25071: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25071: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25071: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25071: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25071: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25071: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25071: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +25071: Goal: +25071: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25071: Order: +25071: nrkbo +25071: Leaf order: +25071: join 18 2 4 0,2,2 +25071: meet 19 2 6 0,2 +25071: c 3 0 3 2,2,2,2 +25071: b 3 0 3 1,2,2 +25071: a 6 0 6 1,2 +NO CLASH, using fixed ground order +25072: Facts: +25072: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25072: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25072: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25072: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25072: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25072: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25072: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25072: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25072: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +25072: Goal: +25072: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25072: Order: +25072: kbo +25072: Leaf order: +25072: join 18 2 4 0,2,2 +25072: meet 19 2 6 0,2 +25072: c 3 0 3 2,2,2,2 +25072: b 3 0 3 1,2,2 +25072: a 6 0 6 1,2 +NO CLASH, using fixed ground order +25073: Facts: +25073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25073: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25073: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25073: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25073: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25073: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +25073: Goal: +25073: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25073: Order: +25073: lpo +25073: Leaf order: +25073: join 18 2 4 0,2,2 +25073: meet 19 2 6 0,2 +25073: c 3 0 3 2,2,2,2 +25073: b 3 0 3 1,2,2 +25073: a 6 0 6 1,2 +% SZS status Timeout for LAT174-1.p +NO CLASH, using fixed ground order +25101: Facts: +25101: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25101: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25101: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25101: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25101: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25101: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25101: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25101: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25101: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25101: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25101: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25101: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25101: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25101: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25101: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25101: Goal: +25101: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +25101: Order: +25101: nrkbo +25101: Leaf order: +25101: commutator 1 2 0 +25101: associator 1 3 0 +25101: additive_inverse 6 1 0 +25101: add 16 2 0 +25101: additive_identity 8 0 0 +25101: multiply 28 2 6 0,2 +25101: cy 2 0 2 1,2,2,2 +25101: cx 4 0 4 1,2,2 +25101: cz 2 0 2 1,2 +NO CLASH, using fixed ground order +25102: Facts: +25102: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25102: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25102: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25102: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25102: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25102: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25102: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25102: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25102: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25102: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +NO CLASH, using fixed ground order +25103: Facts: +25103: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25103: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25103: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25103: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25103: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25103: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25103: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25103: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25103: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25102: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25102: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25102: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25102: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25102: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25102: Goal: +25102: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +25102: Order: +25102: kbo +25102: Leaf order: +25102: commutator 1 2 0 +25102: associator 1 3 0 +25102: additive_inverse 6 1 0 +25102: add 16 2 0 +25102: additive_identity 8 0 0 +25102: multiply 28 2 6 0,2 +25102: cy 2 0 2 1,2,2,2 +25102: cx 4 0 4 1,2,2 +25102: cz 2 0 2 1,2 +25103: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25103: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25103: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25103: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25103: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25103: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25103: Goal: +25103: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +25103: Order: +25103: lpo +25103: Leaf order: +25103: commutator 1 2 0 +25103: associator 1 3 0 +25103: additive_inverse 6 1 0 +25103: add 16 2 0 +25103: additive_identity 8 0 0 +25103: multiply 28 2 6 0,2 +25103: cy 2 0 2 1,2,2,2 +25103: cx 4 0 4 1,2,2 +25103: cz 2 0 2 1,2 +% SZS status Timeout for RNG027-5.p +NO CLASH, using fixed ground order +25119: Facts: +25119: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25119: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25119: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25119: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25119: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25119: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25119: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25119: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25119: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25119: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25119: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25119: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25119: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25119: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25119: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25119: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25119: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25119: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25119: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25119: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25119: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25119: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25119: Goal: +25119: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +25119: Order: +25119: nrkbo +25119: Leaf order: +25119: commutator 1 2 0 +25119: associator 1 3 0 +25119: additive_inverse 22 1 0 +25119: add 24 2 0 +25119: additive_identity 8 0 0 +25119: multiply 46 2 6 0,2 +25119: cy 2 0 2 1,2,2,2 +25119: cx 4 0 4 1,2,2 +25119: cz 2 0 2 1,2 +NO CLASH, using fixed ground order +25120: Facts: +25120: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25120: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25120: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25120: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25120: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25120: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25120: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25120: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25120: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25120: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25120: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25120: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25120: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25120: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25120: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25120: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25120: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25120: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25120: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25120: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25120: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25120: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25120: Goal: +25120: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +25120: Order: +25120: kbo +25120: Leaf order: +25120: commutator 1 2 0 +25120: associator 1 3 0 +25120: additive_inverse 22 1 0 +25120: add 24 2 0 +25120: additive_identity 8 0 0 +25120: multiply 46 2 6 0,2 +25120: cy 2 0 2 1,2,2,2 +25120: cx 4 0 4 1,2,2 +25120: cz 2 0 2 1,2 +NO CLASH, using fixed ground order +25121: Facts: +25121: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25121: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25121: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25121: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25121: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25121: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25121: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25121: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25121: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25121: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25121: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25121: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25121: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25121: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25121: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25121: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25121: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25121: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25121: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25121: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25121: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25121: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25121: Goal: +25121: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +25121: Order: +25121: lpo +25121: Leaf order: +25121: commutator 1 2 0 +25121: associator 1 3 0 +25121: additive_inverse 22 1 0 +25121: add 24 2 0 +25121: additive_identity 8 0 0 +25121: multiply 46 2 6 0,2 +25121: cy 2 0 2 1,2,2,2 +25121: cx 4 0 4 1,2,2 +25121: cz 2 0 2 1,2 +% SZS status Timeout for RNG027-7.p +NO CLASH, using fixed ground order +25148: Facts: +25148: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25148: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25148: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25148: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25148: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25148: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25148: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25148: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25148: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25148: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25148: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25148: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25148: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25148: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25148: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25148: Goal: +25148: Id : 1, {_}: + associator x (multiply x y) z =<= multiply (associator x y z) x + [] by prove_right_moufang +25148: Order: +25148: nrkbo +25148: Leaf order: +25148: commutator 1 2 0 +25148: additive_inverse 6 1 0 +25148: add 16 2 0 +25148: additive_identity 8 0 0 +25148: associator 3 3 2 0,2 +25148: z 2 0 2 3,2 +25148: multiply 24 2 2 0,2,2 +25148: y 2 0 2 2,2,2 +25148: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25149: Facts: +25149: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25149: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25149: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25149: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25149: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25149: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25149: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25149: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25149: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25149: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25149: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25149: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25149: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25149: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25149: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25149: Goal: +25149: Id : 1, {_}: + associator x (multiply x y) z =<= multiply (associator x y z) x + [] by prove_right_moufang +25149: Order: +25149: kbo +25149: Leaf order: +25149: commutator 1 2 0 +25149: additive_inverse 6 1 0 +25149: add 16 2 0 +25149: additive_identity 8 0 0 +25149: associator 3 3 2 0,2 +25149: z 2 0 2 3,2 +25149: multiply 24 2 2 0,2,2 +25149: y 2 0 2 2,2,2 +25149: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25150: Facts: +25150: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25150: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25150: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25150: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25150: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25150: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25150: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25150: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25150: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25150: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25150: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25150: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25150: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25150: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25150: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25150: Goal: +25150: Id : 1, {_}: + associator x (multiply x y) z =<= multiply (associator x y z) x + [] by prove_right_moufang +25150: Order: +25150: lpo +25150: Leaf order: +25150: commutator 1 2 0 +25150: additive_inverse 6 1 0 +25150: add 16 2 0 +25150: additive_identity 8 0 0 +25150: associator 3 3 2 0,2 +25150: z 2 0 2 3,2 +25150: multiply 24 2 2 0,2,2 +25150: y 2 0 2 2,2,2 +25150: x 4 0 4 1,2 +% SZS status Timeout for RNG027-8.p +NO CLASH, using fixed ground order +25166: Facts: +25166: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25166: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25166: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25166: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25166: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25166: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25166: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25166: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25166: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25166: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25166: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25166: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25166: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25166: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25166: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25166: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25166: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25166: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25166: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25166: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25166: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25166: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25166: Goal: +25166: Id : 1, {_}: + associator x (multiply x y) z =<= multiply (associator x y z) x + [] by prove_right_moufang +25166: Order: +25166: nrkbo +25166: Leaf order: +25166: commutator 1 2 0 +25166: additive_inverse 22 1 0 +25166: add 24 2 0 +25166: additive_identity 8 0 0 +25166: associator 3 3 2 0,2 +25166: z 2 0 2 3,2 +25166: multiply 42 2 2 0,2,2 +25166: y 2 0 2 2,2,2 +25166: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25168: Facts: +25168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25168: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25168: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25168: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25168: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25168: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25168: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25168: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25168: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25168: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25168: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25168: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25168: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25168: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25168: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25168: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25168: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25168: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25168: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25168: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25168: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25168: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25168: Goal: +25168: Id : 1, {_}: + associator x (multiply x y) z =<= multiply (associator x y z) x + [] by prove_right_moufang +25168: Order: +25168: lpo +25168: Leaf order: +25168: commutator 1 2 0 +25168: additive_inverse 22 1 0 +25168: add 24 2 0 +25168: additive_identity 8 0 0 +25168: associator 3 3 2 0,2 +25168: z 2 0 2 3,2 +25168: multiply 42 2 2 0,2,2 +25168: y 2 0 2 2,2,2 +25168: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25167: Facts: +25167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25167: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25167: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25167: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25167: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25167: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25167: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25167: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25167: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25167: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25167: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25167: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25167: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25167: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25167: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25167: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25167: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25167: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25167: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25167: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25167: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25167: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25167: Goal: +25167: Id : 1, {_}: + associator x (multiply x y) z =<= multiply (associator x y z) x + [] by prove_right_moufang +25167: Order: +25167: kbo +25167: Leaf order: +25167: commutator 1 2 0 +25167: additive_inverse 22 1 0 +25167: add 24 2 0 +25167: additive_identity 8 0 0 +25167: associator 3 3 2 0,2 +25167: z 2 0 2 3,2 +25167: multiply 42 2 2 0,2,2 +25167: y 2 0 2 2,2,2 +25167: x 4 0 4 1,2 +% SZS status Timeout for RNG027-9.p +NO CLASH, using fixed ground order +25195: Facts: +25195: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25195: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25195: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25195: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25195: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25195: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25195: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25195: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25195: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25195: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25195: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25195: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25195: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25195: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25195: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25195: Goal: +25195: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +25195: Order: +25195: nrkbo +25195: Leaf order: +25195: commutator 1 2 0 +25195: associator 1 3 0 +25195: additive_inverse 6 1 0 +25195: add 16 2 0 +25195: additive_identity 8 0 0 +25195: cz 2 0 2 2,2 +25195: multiply 28 2 6 0,2 +25195: cy 2 0 2 1,2,1,2 +25195: cx 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25196: Facts: +25196: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25196: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25196: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25196: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25196: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25196: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25196: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25196: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25196: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25196: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25196: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25196: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25196: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25196: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25196: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25196: Goal: +25196: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +25196: Order: +25196: kbo +25196: Leaf order: +25196: commutator 1 2 0 +25196: associator 1 3 0 +25196: additive_inverse 6 1 0 +25196: add 16 2 0 +25196: additive_identity 8 0 0 +25196: cz 2 0 2 2,2 +25196: multiply 28 2 6 0,2 +25196: cy 2 0 2 1,2,1,2 +25196: cx 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25197: Facts: +25197: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25197: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25197: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25197: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25197: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25197: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25197: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25197: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25197: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25197: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25197: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25197: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25197: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25197: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25197: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25197: Goal: +25197: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +25197: Order: +25197: lpo +25197: Leaf order: +25197: commutator 1 2 0 +25197: associator 1 3 0 +25197: additive_inverse 6 1 0 +25197: add 16 2 0 +25197: additive_identity 8 0 0 +25197: cz 2 0 2 2,2 +25197: multiply 28 2 6 0,2 +25197: cy 2 0 2 1,2,1,2 +25197: cx 4 0 4 1,1,2 +% SZS status Timeout for RNG028-5.p +NO CLASH, using fixed ground order +25213: Facts: +25213: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25213: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25213: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25213: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25213: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25213: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25213: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25213: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25213: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25213: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25213: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25213: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25213: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25213: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25213: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25213: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25213: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25213: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25213: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25213: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25213: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25213: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25213: Goal: +25213: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +25213: Order: +25213: nrkbo +25213: Leaf order: +25213: commutator 1 2 0 +25213: associator 1 3 0 +25213: additive_inverse 22 1 0 +25213: add 24 2 0 +25213: additive_identity 8 0 0 +25213: cz 2 0 2 2,2 +25213: multiply 46 2 6 0,2 +25213: cy 2 0 2 1,2,1,2 +25213: cx 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25214: Facts: +25214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25214: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25214: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25214: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25214: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25214: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25214: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25214: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25214: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25214: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25214: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25214: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25214: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25214: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25214: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25214: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25214: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25214: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25214: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25214: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25214: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25214: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25214: Goal: +25214: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +25214: Order: +25214: kbo +25214: Leaf order: +25214: commutator 1 2 0 +25214: associator 1 3 0 +25214: additive_inverse 22 1 0 +25214: add 24 2 0 +25214: additive_identity 8 0 0 +25214: cz 2 0 2 2,2 +25214: multiply 46 2 6 0,2 +25214: cy 2 0 2 1,2,1,2 +25214: cx 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25215: Facts: +25215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25215: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25215: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25215: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25215: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25215: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25215: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25215: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25215: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25215: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25215: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25215: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25215: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25215: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25215: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25215: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25215: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25215: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25215: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25215: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25215: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25215: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25215: Goal: +25215: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +25215: Order: +25215: lpo +25215: Leaf order: +25215: commutator 1 2 0 +25215: associator 1 3 0 +25215: additive_inverse 22 1 0 +25215: add 24 2 0 +25215: additive_identity 8 0 0 +25215: cz 2 0 2 2,2 +25215: multiply 46 2 6 0,2 +25215: cy 2 0 2 1,2,1,2 +25215: cx 4 0 4 1,1,2 +% SZS status Timeout for RNG028-7.p +NO CLASH, using fixed ground order +25251: Facts: +25251: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25251: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25251: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25251: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25251: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25251: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25251: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25251: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25251: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25251: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25251: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25251: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25251: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25251: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25251: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25251: Goal: +25251: Id : 1, {_}: + associator x (multiply y x) z =<= multiply x (associator x y z) + [] by prove_left_moufang +25251: Order: +25251: nrkbo +25251: Leaf order: +25251: commutator 1 2 0 +25251: additive_inverse 6 1 0 +25251: add 16 2 0 +25251: additive_identity 8 0 0 +25251: associator 3 3 2 0,2 +25251: z 2 0 2 3,2 +25251: multiply 24 2 2 0,2,2 +25251: y 2 0 2 1,2,2 +25251: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25252: Facts: +25252: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25252: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25252: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25252: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25252: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25252: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25252: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25252: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25252: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25252: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25252: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25252: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25252: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25252: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25252: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25252: Goal: +25252: Id : 1, {_}: + associator x (multiply y x) z =<= multiply x (associator x y z) + [] by prove_left_moufang +25252: Order: +25252: kbo +25252: Leaf order: +25252: commutator 1 2 0 +25252: additive_inverse 6 1 0 +25252: add 16 2 0 +25252: additive_identity 8 0 0 +25252: associator 3 3 2 0,2 +25252: z 2 0 2 3,2 +25252: multiply 24 2 2 0,2,2 +25252: y 2 0 2 1,2,2 +25252: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25253: Facts: +25253: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25253: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25253: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25253: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25253: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25253: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25253: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25253: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25253: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25253: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25253: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25253: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25253: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25253: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25253: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25253: Goal: +25253: Id : 1, {_}: + associator x (multiply y x) z =<= multiply x (associator x y z) + [] by prove_left_moufang +25253: Order: +25253: lpo +25253: Leaf order: +25253: commutator 1 2 0 +25253: additive_inverse 6 1 0 +25253: add 16 2 0 +25253: additive_identity 8 0 0 +25253: associator 3 3 2 0,2 +25253: z 2 0 2 3,2 +25253: multiply 24 2 2 0,2,2 +25253: y 2 0 2 1,2,2 +25253: x 4 0 4 1,2 +% SZS status Timeout for RNG028-8.p +NO CLASH, using fixed ground order +25289: Facts: +25289: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25289: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25289: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25289: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25289: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25289: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25289: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25289: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25289: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25289: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25289: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25289: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25289: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25289: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25289: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25289: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25289: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25289: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25289: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25289: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25289: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25289: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25289: Goal: +25289: Id : 1, {_}: + associator x (multiply y x) z =<= multiply x (associator x y z) + [] by prove_left_moufang +25289: Order: +25289: nrkbo +25289: Leaf order: +25289: commutator 1 2 0 +25289: additive_inverse 22 1 0 +25289: add 24 2 0 +25289: additive_identity 8 0 0 +25289: associator 3 3 2 0,2 +25289: z 2 0 2 3,2 +25289: multiply 42 2 2 0,2,2 +25289: y 2 0 2 1,2,2 +25289: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25290: Facts: +25290: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25290: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25290: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25290: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25290: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25290: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25290: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25290: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25290: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25290: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25290: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25290: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25290: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25290: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25290: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25290: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25290: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25290: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25290: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25290: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25290: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25290: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25290: Goal: +25290: Id : 1, {_}: + associator x (multiply y x) z =<= multiply x (associator x y z) + [] by prove_left_moufang +25290: Order: +25290: kbo +25290: Leaf order: +25290: commutator 1 2 0 +25290: additive_inverse 22 1 0 +25290: add 24 2 0 +25290: additive_identity 8 0 0 +25290: associator 3 3 2 0,2 +25290: z 2 0 2 3,2 +25290: multiply 42 2 2 0,2,2 +25290: y 2 0 2 1,2,2 +25290: x 4 0 4 1,2 +NO CLASH, using fixed ground order +25291: Facts: +25291: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25291: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25291: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25291: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25291: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25291: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25291: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25291: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25291: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25291: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25291: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25291: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25291: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25291: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25291: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25291: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25291: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25291: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25291: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25291: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25291: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25291: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25291: Goal: +25291: Id : 1, {_}: + associator x (multiply y x) z =<= multiply x (associator x y z) + [] by prove_left_moufang +25291: Order: +25291: lpo +25291: Leaf order: +25291: commutator 1 2 0 +25291: additive_inverse 22 1 0 +25291: add 24 2 0 +25291: additive_identity 8 0 0 +25291: associator 3 3 2 0,2 +25291: z 2 0 2 3,2 +25291: multiply 42 2 2 0,2,2 +25291: y 2 0 2 1,2,2 +25291: x 4 0 4 1,2 +% SZS status Timeout for RNG028-9.p +NO CLASH, using fixed ground order +25318: Facts: +25318: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25318: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25318: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25318: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25318: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25318: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25318: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25318: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25318: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25318: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25318: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25318: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25318: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25318: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25318: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25318: Goal: +25318: Id : 1, {_}: + multiply (multiply cx cy) (multiply cz cx) + =>= + multiply cx (multiply (multiply cy cz) cx) + [] by prove_middle_law +25318: Order: +25318: nrkbo +25318: Leaf order: +25318: commutator 1 2 0 +25318: associator 1 3 0 +25318: additive_inverse 6 1 0 +25318: add 16 2 0 +25318: additive_identity 8 0 0 +25318: cz 2 0 2 1,2,2 +25318: multiply 28 2 6 0,2 +25318: cy 2 0 2 2,1,2 +25318: cx 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25320: Facts: +25320: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25320: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25320: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25320: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25320: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25320: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25320: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25320: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25320: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25320: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25320: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25320: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25320: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25320: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25320: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25320: Goal: +25320: Id : 1, {_}: + multiply (multiply cx cy) (multiply cz cx) + =>= + multiply cx (multiply (multiply cy cz) cx) + [] by prove_middle_law +25320: Order: +25320: lpo +25320: Leaf order: +25320: commutator 1 2 0 +25320: associator 1 3 0 +25320: additive_inverse 6 1 0 +25320: add 16 2 0 +25320: additive_identity 8 0 0 +25320: cz 2 0 2 1,2,2 +25320: multiply 28 2 6 0,2 +25320: cy 2 0 2 2,1,2 +25320: cx 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25319: Facts: +25319: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25319: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25319: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25319: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25319: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25319: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25319: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25319: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25319: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25319: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25319: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25319: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25319: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25319: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25319: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25319: Goal: +25319: Id : 1, {_}: + multiply (multiply cx cy) (multiply cz cx) + =>= + multiply cx (multiply (multiply cy cz) cx) + [] by prove_middle_law +25319: Order: +25319: kbo +25319: Leaf order: +25319: commutator 1 2 0 +25319: associator 1 3 0 +25319: additive_inverse 6 1 0 +25319: add 16 2 0 +25319: additive_identity 8 0 0 +25319: cz 2 0 2 1,2,2 +25319: multiply 28 2 6 0,2 +25319: cy 2 0 2 2,1,2 +25319: cx 4 0 4 1,1,2 +% SZS status Timeout for RNG029-5.p +NO CLASH, using fixed ground order +25337: Facts: +25337: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25337: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25337: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25337: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25337: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25337: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25337: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25337: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25337: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25337: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25337: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25337: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25337: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25337: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25337: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25337: Goal: +25337: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +25337: Order: +25337: nrkbo +25337: Leaf order: +25337: commutator 1 2 0 +25337: associator 1 3 0 +25337: additive_inverse 6 1 0 +25337: add 16 2 0 +25337: additive_identity 8 0 0 +25337: z 2 0 2 1,2,2 +25337: multiply 28 2 6 0,2 +25337: y 2 0 2 2,1,2 +25337: x 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25338: Facts: +25338: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25338: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25338: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25338: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25338: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25338: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25338: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25338: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25338: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25338: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25338: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25338: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25338: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25338: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25338: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25338: Goal: +25338: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +25338: Order: +25338: kbo +25338: Leaf order: +25338: commutator 1 2 0 +25338: associator 1 3 0 +25338: additive_inverse 6 1 0 +25338: add 16 2 0 +25338: additive_identity 8 0 0 +25338: z 2 0 2 1,2,2 +25338: multiply 28 2 6 0,2 +25338: y 2 0 2 2,1,2 +25338: x 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25339: Facts: +25339: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25339: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25339: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25339: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25339: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25339: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25339: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25339: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25339: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25339: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25339: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25339: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25339: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25339: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25339: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25339: Goal: +25339: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +25339: Order: +25339: lpo +25339: Leaf order: +25339: commutator 1 2 0 +25339: associator 1 3 0 +25339: additive_inverse 6 1 0 +25339: add 16 2 0 +25339: additive_identity 8 0 0 +25339: z 2 0 2 1,2,2 +25339: multiply 28 2 6 0,2 +25339: y 2 0 2 2,1,2 +25339: x 4 0 4 1,1,2 +% SZS status Timeout for RNG029-6.p +NO CLASH, using fixed ground order +25367: Facts: +25367: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25367: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25367: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25367: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25367: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25367: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25367: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25367: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25367: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25367: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25367: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25367: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25367: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25367: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25367: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25367: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25367: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25367: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25367: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25367: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25367: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25367: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25367: Goal: +25367: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +25367: Order: +25367: nrkbo +25367: Leaf order: +25367: commutator 1 2 0 +25367: associator 1 3 0 +25367: additive_inverse 22 1 0 +25367: add 24 2 0 +25367: additive_identity 8 0 0 +25367: z 2 0 2 1,2,2 +25367: multiply 46 2 6 0,2 +25367: y 2 0 2 2,1,2 +25367: x 4 0 4 1,1,2 +NO CLASH, using fixed ground order +25368: Facts: +25368: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25368: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25368: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +NO CLASH, using fixed ground order +25369: Facts: +25369: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25369: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25369: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25369: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25369: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25369: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25369: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25369: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25369: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25369: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25369: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25369: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25369: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25369: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25369: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25369: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25369: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25369: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25369: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25369: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25369: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25369: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25369: Goal: +25369: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +25369: Order: +25369: lpo +25369: Leaf order: +25369: commutator 1 2 0 +25369: associator 1 3 0 +25369: additive_inverse 22 1 0 +25369: add 24 2 0 +25369: additive_identity 8 0 0 +25369: z 2 0 2 1,2,2 +25369: multiply 46 2 6 0,2 +25369: y 2 0 2 2,1,2 +25369: x 4 0 4 1,1,2 +25368: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25368: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25368: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25368: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25368: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25368: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25368: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25368: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25368: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25368: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25368: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25368: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25368: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25368: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25368: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25368: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25368: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25368: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25368: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25368: Goal: +25368: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +25368: Order: +25368: kbo +25368: Leaf order: +25368: commutator 1 2 0 +25368: associator 1 3 0 +25368: additive_inverse 22 1 0 +25368: add 24 2 0 +25368: additive_identity 8 0 0 +25368: z 2 0 2 1,2,2 +25368: multiply 46 2 6 0,2 +25368: y 2 0 2 2,1,2 +25368: x 4 0 4 1,1,2 +% SZS status Timeout for RNG029-7.p +NO CLASH, using fixed ground order +25651: Facts: +25651: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +25651: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +25651: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +25651: Id : 5, {_}: add c d =>= d [] by absorbtion +25651: Goal: +NO CLASH, using fixed ground order +25652: Facts: +25652: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +25652: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +25652: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +25652: Id : 5, {_}: add c d =>= d [] by absorbtion +25652: Goal: +25652: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +25652: Order: +25652: kbo +25652: Leaf order: +25652: d 2 0 0 +25652: c 1 0 0 +25652: add 13 2 3 0,2 +25652: negate 9 1 5 0,1,2 +25652: b 3 0 3 1,2,1,1,2 +25652: a 2 0 2 1,1,1,2 +25651: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +25651: Order: +25651: nrkbo +25651: Leaf order: +25651: d 2 0 0 +25651: c 1 0 0 +25651: add 13 2 3 0,2 +25651: negate 9 1 5 0,1,2 +25651: b 3 0 3 1,2,1,1,2 +25651: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +25653: Facts: +25653: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +25653: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +25653: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +25653: Id : 5, {_}: add c d =>= d [] by absorbtion +25653: Goal: +25653: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +25653: Order: +25653: lpo +25653: Leaf order: +25653: d 2 0 0 +25653: c 1 0 0 +25653: add 13 2 3 0,2 +25653: negate 9 1 5 0,1,2 +25653: b 3 0 3 1,2,1,1,2 +25653: a 2 0 2 1,1,1,2 +% SZS status Timeout for ROB006-1.p +NO CLASH, using fixed ground order +25684: Facts: +25684: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +25684: Id : 3, {_}: + add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +25684: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +25684: Id : 5, {_}: add c d =>= d [] by absorbtion +25684: Goal: +25684: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +25684: Order: +25684: nrkbo +25684: Leaf order: +25684: d 2 0 0 +25684: c 1 0 0 +25684: negate 4 1 0 +25684: add 11 2 1 0,2 +NO CLASH, using fixed ground order +25685: Facts: +25685: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +25685: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +25685: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +25685: Id : 5, {_}: add c d =>= d [] by absorbtion +25685: Goal: +25685: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +25685: Order: +25685: kbo +25685: Leaf order: +25685: d 2 0 0 +25685: c 1 0 0 +25685: negate 4 1 0 +25685: add 11 2 1 0,2 +NO CLASH, using fixed ground order +25686: Facts: +25686: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +25686: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +25686: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +25686: Id : 5, {_}: add c d =>= d [] by absorbtion +25686: Goal: +25686: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +25686: Order: +25686: lpo +25686: Leaf order: +25686: d 2 0 0 +25686: c 1 0 0 +25686: negate 4 1 0 +25686: add 11 2 1 0,2 +% SZS status Timeout for ROB006-2.p +NO CLASH, using fixed ground order +25702: Facts: +25702: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +25702: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +25702: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +25702: Id : 5, {_}: add c d =>= c [] by identity_constant +25702: Goal: +25702: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +25702: Order: +25702: nrkbo +25702: Leaf order: +25702: d 1 0 0 +25702: c 2 0 0 +25702: add 13 2 3 0,2 +25702: negate 9 1 5 0,1,2 +25702: b 3 0 3 1,2,1,1,2 +25702: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +25704: Facts: +25704: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +25704: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +25704: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +25704: Id : 5, {_}: add c d =>= c [] by identity_constant +25704: Goal: +25704: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +25704: Order: +25704: lpo +25704: Leaf order: +25704: d 1 0 0 +25704: c 2 0 0 +25704: add 13 2 3 0,2 +25704: negate 9 1 5 0,1,2 +25704: b 3 0 3 1,2,1,1,2 +25704: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +25703: Facts: +25703: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +25703: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +25703: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +25703: Id : 5, {_}: add c d =>= c [] by identity_constant +25703: Goal: +25703: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +25703: Order: +25703: kbo +25703: Leaf order: +25703: d 1 0 0 +25703: c 2 0 0 +25703: add 13 2 3 0,2 +25703: negate 9 1 5 0,1,2 +25703: b 3 0 3 1,2,1,1,2 +25703: a 2 0 2 1,1,1,2 +% SZS status Timeout for ROB026-1.p +NO CLASH, using fixed ground order +25731: Facts: +25731: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25731: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25731: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25731: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25731: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25731: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25731: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25731: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25731: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25731: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25731: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25731: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25731: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25731: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25731: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25731: Goal: +25731: Id : 1, {_}: + least_upper_bound a (greatest_lower_bound b c) + =<= + greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c) + [] by prove_distrnu +25731: Order: +25731: nrkbo +25731: Leaf order: +25731: inverse 1 1 0 +25731: multiply 18 2 0 +25731: identity 2 0 0 +25731: least_upper_bound 16 2 3 0,2 +25731: greatest_lower_bound 15 2 2 0,2,2 +25731: c 2 0 2 2,2,2 +25731: b 2 0 2 1,2,2 +25731: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25732: Facts: +25732: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25732: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25732: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25732: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25732: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25732: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25732: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25732: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25732: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25732: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25732: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25732: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25732: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25732: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25732: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25732: Goal: +25732: Id : 1, {_}: + least_upper_bound a (greatest_lower_bound b c) + =<= + greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c) + [] by prove_distrnu +25732: Order: +25732: kbo +25732: Leaf order: +25732: inverse 1 1 0 +25732: multiply 18 2 0 +25732: identity 2 0 0 +25732: least_upper_bound 16 2 3 0,2 +25732: greatest_lower_bound 15 2 2 0,2,2 +25732: c 2 0 2 2,2,2 +25732: b 2 0 2 1,2,2 +25732: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25733: Facts: +25733: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25733: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25733: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25733: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25733: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25733: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25733: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25733: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25733: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25733: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25733: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25733: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25733: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25733: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25733: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25733: Goal: +25733: Id : 1, {_}: + least_upper_bound a (greatest_lower_bound b c) + =<= + greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c) + [] by prove_distrnu +25733: Order: +25733: lpo +25733: Leaf order: +25733: inverse 1 1 0 +25733: multiply 18 2 0 +25733: identity 2 0 0 +25733: least_upper_bound 16 2 3 0,2 +25733: greatest_lower_bound 15 2 2 0,2,2 +25733: c 2 0 2 2,2,2 +25733: b 2 0 2 1,2,2 +25733: a 3 0 3 1,2 +% SZS status Timeout for GRP164-1.p +NO CLASH, using fixed ground order +25749: Facts: +25749: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25749: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25749: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25749: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25749: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25749: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25749: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25749: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25749: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25749: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25749: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25749: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25749: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25749: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25749: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25749: Goal: +25749: Id : 1, {_}: + greatest_lower_bound a (least_upper_bound b c) + =<= + least_upper_bound (greatest_lower_bound a b) + (greatest_lower_bound a c) + [] by prove_distrun +25749: Order: +25749: nrkbo +25749: Leaf order: +25749: inverse 1 1 0 +25749: multiply 18 2 0 +25749: identity 2 0 0 +25749: greatest_lower_bound 16 2 3 0,2 +25749: least_upper_bound 15 2 2 0,2,2 +25749: c 2 0 2 2,2,2 +25749: b 2 0 2 1,2,2 +25749: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25750: Facts: +25750: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25750: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25750: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25750: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25750: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25750: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25750: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25750: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25750: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25750: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25750: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +NO CLASH, using fixed ground order +25751: Facts: +25751: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25751: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25751: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25751: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25751: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25751: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25751: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25751: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25751: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25751: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25751: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25751: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25751: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25751: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25751: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25751: Goal: +25751: Id : 1, {_}: + greatest_lower_bound a (least_upper_bound b c) + =<= + least_upper_bound (greatest_lower_bound a b) + (greatest_lower_bound a c) + [] by prove_distrun +25751: Order: +25751: lpo +25751: Leaf order: +25751: inverse 1 1 0 +25751: multiply 18 2 0 +25751: identity 2 0 0 +25751: greatest_lower_bound 16 2 3 0,2 +25751: least_upper_bound 15 2 2 0,2,2 +25751: c 2 0 2 2,2,2 +25751: b 2 0 2 1,2,2 +25751: a 3 0 3 1,2 +25750: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25750: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25750: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25750: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25750: Goal: +25750: Id : 1, {_}: + greatest_lower_bound a (least_upper_bound b c) + =<= + least_upper_bound (greatest_lower_bound a b) + (greatest_lower_bound a c) + [] by prove_distrun +25750: Order: +25750: kbo +25750: Leaf order: +25750: inverse 1 1 0 +25750: multiply 18 2 0 +25750: identity 2 0 0 +25750: greatest_lower_bound 16 2 3 0,2 +25750: least_upper_bound 15 2 2 0,2,2 +25750: c 2 0 2 2,2,2 +25750: b 2 0 2 1,2,2 +25750: a 3 0 3 1,2 +% SZS status Timeout for GRP164-2.p +NO CLASH, using fixed ground order +25782: Facts: +25782: Id : 2, {_}: + multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4) + [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4 +25782: Id : 3, {_}: + multiply ?6 (multiply ?7 (multiply ?7 ?7)) + =?= + multiply ?7 (multiply ?7 (multiply ?7 ?6)) + [7, 6] by condition ?6 ?7 +25782: Goal: +25782: Id : 1, {_}: + multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a (multiply b (multiply a b)))))))))))))))) + =<= + multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b (multiply b (multiply b b)))))))))))))))) + [] by prove_this +25782: Order: +25782: nrkbo +25782: Leaf order: +25782: multiply 44 2 34 0,2 +25782: b 18 0 18 1,2,2 +25782: a 18 0 18 1,2 +NO CLASH, using fixed ground order +25783: Facts: +25783: Id : 2, {_}: + multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4) + [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4 +25783: Id : 3, {_}: + multiply ?6 (multiply ?7 (multiply ?7 ?7)) + =?= + multiply ?7 (multiply ?7 (multiply ?7 ?6)) + [7, 6] by condition ?6 ?7 +25783: Goal: +25783: Id : 1, {_}: + multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a (multiply b (multiply a b)))))))))))))))) + =?= + multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b (multiply b (multiply b b)))))))))))))))) + [] by prove_this +25783: Order: +25783: kbo +25783: Leaf order: +25783: multiply 44 2 34 0,2 +25783: b 18 0 18 1,2,2 +25783: a 18 0 18 1,2 +NO CLASH, using fixed ground order +% SZS status Timeout for GRP196-1.p +NO CLASH, using fixed ground order +25809: Facts: +25809: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5 +25809: Goal: +25809: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25809: Order: +25809: nrkbo +25809: Leaf order: +25809: f 18 2 8 0,2 +25809: c 3 0 3 2,1,2,2 +25809: b 4 0 4 1,1,2,2 +25809: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25810: Facts: +25810: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5 +25810: Goal: +25810: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25810: Order: +25810: kbo +25810: Leaf order: +25810: f 18 2 8 0,2 +25810: c 3 0 3 2,1,2,2 +25810: b 4 0 4 1,1,2,2 +25810: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25811: Facts: +25811: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5 +25811: Goal: +25811: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25811: Order: +25811: lpo +25811: Leaf order: +25811: f 18 2 8 0,2 +25811: c 3 0 3 2,1,2,2 +25811: b 4 0 4 1,1,2,2 +25811: a 3 0 3 1,2 +% SZS status Timeout for LAT070-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +25843: Facts: +25843: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25843: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25843: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25843: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25843: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25843: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25843: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25843: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25843: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +25843: Goal: +25843: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25843: Order: +25843: kbo +25843: Leaf order: +25843: join 17 2 4 0,2,2 +25843: meet 21 2 6 0,2 +25843: c 3 0 3 2,2,2,2 +25843: b 3 0 3 1,2,2 +25843: a 6 0 6 1,2 +NO CLASH, using fixed ground order +25844: Facts: +25844: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25844: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25844: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25844: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25844: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25844: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25844: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25844: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25844: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +25844: Goal: +25844: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25844: Order: +25844: lpo +25844: Leaf order: +25844: join 17 2 4 0,2,2 +25844: meet 21 2 6 0,2 +25844: c 3 0 3 2,2,2,2 +25844: b 3 0 3 1,2,2 +25844: a 6 0 6 1,2 +25842: Facts: +25842: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25842: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25842: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25842: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25842: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25842: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25842: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25842: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25842: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +25842: Goal: +25842: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25842: Order: +25842: nrkbo +25842: Leaf order: +25842: join 17 2 4 0,2,2 +25842: meet 21 2 6 0,2 +25842: c 3 0 3 2,2,2,2 +25842: b 3 0 3 1,2,2 +25842: a 6 0 6 1,2 +% SZS status Timeout for LAT138-1.p +NO CLASH, using fixed ground order +25866: Facts: +25866: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25866: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25866: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25866: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25866: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25866: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25866: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25866: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25866: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +25866: Goal: +25866: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +25866: Order: +25866: nrkbo +25866: Leaf order: +25866: join 17 2 4 0,2,2 +25866: meet 21 2 6 0,2 +25866: c 4 0 4 2,2,2,2 +25866: b 4 0 4 1,2,2 +25866: a 4 0 4 1,2 +NO CLASH, using fixed ground order +25867: Facts: +25867: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25867: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25867: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25867: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25867: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25867: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25867: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25867: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25867: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +25867: Goal: +25867: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +25867: Order: +25867: kbo +25867: Leaf order: +25867: join 17 2 4 0,2,2 +25867: meet 21 2 6 0,2 +25867: c 4 0 4 2,2,2,2 +25867: b 4 0 4 1,2,2 +25867: a 4 0 4 1,2 +NO CLASH, using fixed ground order +25868: Facts: +25868: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25868: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25868: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25868: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25868: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25868: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25868: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25868: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25868: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +25868: Goal: +25868: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +25868: Order: +25868: lpo +25868: Leaf order: +25868: join 17 2 4 0,2,2 +25868: meet 21 2 6 0,2 +25868: c 4 0 4 2,2,2,2 +25868: b 4 0 4 1,2,2 +25868: a 4 0 4 1,2 +% SZS status Timeout for LAT140-1.p +NO CLASH, using fixed ground order +25928: Facts: +25928: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25928: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25928: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25928: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25928: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25928: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25928: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25928: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25928: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +25928: Goal: +NO CLASH, using fixed ground order +25929: Facts: +25929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25929: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25929: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25929: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25929: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25929: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +25929: Goal: +25929: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25929: Order: +25929: kbo +25929: Leaf order: +25929: join 16 2 4 0,2,2 +25929: meet 22 2 6 0,2 +25929: c 3 0 3 2,2,2,2 +25929: b 3 0 3 1,2,2 +25929: a 6 0 6 1,2 +25928: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25928: Order: +25928: nrkbo +25928: Leaf order: +25928: join 16 2 4 0,2,2 +25928: meet 22 2 6 0,2 +25928: c 3 0 3 2,2,2,2 +25928: b 3 0 3 1,2,2 +25928: a 6 0 6 1,2 +NO CLASH, using fixed ground order +25930: Facts: +25930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25930: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25930: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25930: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25930: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25930: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +25930: Goal: +25930: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25930: Order: +25930: lpo +25930: Leaf order: +25930: join 16 2 4 0,2,2 +25930: meet 22 2 6 0,2 +25930: c 3 0 3 2,2,2,2 +25930: b 3 0 3 1,2,2 +25930: a 6 0 6 1,2 +% SZS status Timeout for LAT145-1.p +NO CLASH, using fixed ground order +25948: Facts: +25948: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25948: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25948: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25948: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25948: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25948: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25948: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25948: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25948: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +25948: Goal: +25948: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (join b d))))) + [] by prove_H43 +25948: Order: +25948: nrkbo +25948: Leaf order: +25948: meet 19 2 5 0,2 +25948: join 19 2 5 0,2,2 +25948: d 3 0 3 2,2,2,2,2 +25948: c 2 0 2 1,2,2,2 +25948: b 4 0 4 1,2,2 +25948: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25949: Facts: +25949: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25949: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25949: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25949: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25949: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25949: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25949: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25949: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25949: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +25949: Goal: +25949: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (join b d))))) + [] by prove_H43 +25949: Order: +25949: kbo +25949: Leaf order: +25949: meet 19 2 5 0,2 +25949: join 19 2 5 0,2,2 +25949: d 3 0 3 2,2,2,2,2 +25949: c 2 0 2 1,2,2,2 +25949: b 4 0 4 1,2,2 +25949: a 3 0 3 1,2 +NO CLASH, using fixed ground order +25950: Facts: +25950: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25950: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25950: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25950: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25950: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25950: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25950: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25950: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25950: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +25950: Goal: +25950: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (join b d))))) + [] by prove_H43 +25950: Order: +25950: lpo +25950: Leaf order: +25950: meet 19 2 5 0,2 +25950: join 19 2 5 0,2,2 +25950: d 3 0 3 2,2,2,2,2 +25950: c 2 0 2 1,2,2,2 +25950: b 4 0 4 1,2,2 +25950: a 3 0 3 1,2 +% SZS status Timeout for LAT149-1.p +NO CLASH, using fixed ground order +26495: Facts: +26495: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26495: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26495: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26495: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26495: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26495: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26495: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26495: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26495: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +26495: Goal: +26495: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +26495: Order: +26495: nrkbo +26495: Leaf order: +26495: join 18 2 4 0,2,2 +26495: meet 20 2 6 0,2 +26495: c 2 0 2 2,2,2,2 +26495: b 4 0 4 1,2,2 +26495: a 6 0 6 1,2 +NO CLASH, using fixed ground order +26496: Facts: +26496: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26496: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26496: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26496: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26496: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26496: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26496: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26496: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26496: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +26496: Goal: +26496: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +26496: Order: +26496: kbo +26496: Leaf order: +26496: join 18 2 4 0,2,2 +26496: meet 20 2 6 0,2 +26496: c 2 0 2 2,2,2,2 +26496: b 4 0 4 1,2,2 +26496: a 6 0 6 1,2 +NO CLASH, using fixed ground order +26497: Facts: +26497: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26497: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26497: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26497: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26497: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26497: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26497: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26497: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26497: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +26497: Goal: +26497: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +26497: Order: +26497: lpo +26497: Leaf order: +26497: join 18 2 4 0,2,2 +26497: meet 20 2 6 0,2 +26497: c 2 0 2 2,2,2,2 +26497: b 4 0 4 1,2,2 +26497: a 6 0 6 1,2 +% SZS status Timeout for LAT153-1.p +NO CLASH, using fixed ground order +26513: Facts: +26513: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26513: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26513: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26513: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26513: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26513: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26513: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26513: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26513: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +26513: Goal: +26513: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +26513: Order: +26513: nrkbo +26513: Leaf order: +26513: join 18 2 4 0,2,2 +26513: meet 20 2 6 0,2 +26513: c 4 0 4 2,2,2,2 +26513: b 4 0 4 1,2,2 +26513: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26514: Facts: +26514: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26514: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26514: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26514: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26514: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26514: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26514: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26514: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26514: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +26514: Goal: +26514: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +26514: Order: +26514: kbo +26514: Leaf order: +26514: join 18 2 4 0,2,2 +26514: meet 20 2 6 0,2 +26514: c 4 0 4 2,2,2,2 +26514: b 4 0 4 1,2,2 +26514: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26515: Facts: +26515: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26515: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26515: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26515: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26515: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26515: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26515: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26515: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26515: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +26515: Goal: +26515: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +26515: Order: +26515: lpo +26515: Leaf order: +26515: join 18 2 4 0,2,2 +26515: meet 20 2 6 0,2 +26515: c 4 0 4 2,2,2,2 +26515: b 4 0 4 1,2,2 +26515: a 4 0 4 1,2 +% SZS status Timeout for LAT157-1.p +NO CLASH, using fixed ground order +26542: Facts: +26542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26542: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26542: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26542: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26542: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26542: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +26542: Goal: +26542: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c (join b d)))) + [] by prove_H49 +26542: Order: +26542: nrkbo +26542: Leaf order: +26542: meet 19 2 5 0,2 +26542: join 19 2 5 0,2,2 +26542: d 2 0 2 2,2,2,2,2 +26542: c 3 0 3 1,2,2,2 +26542: b 3 0 3 1,2,2 +26542: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26543: Facts: +26543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26543: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26543: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26543: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26543: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26543: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +26543: Goal: +26543: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c (join b d)))) + [] by prove_H49 +26543: Order: +26543: kbo +26543: Leaf order: +26543: meet 19 2 5 0,2 +26543: join 19 2 5 0,2,2 +26543: d 2 0 2 2,2,2,2,2 +26543: c 3 0 3 1,2,2,2 +26543: b 3 0 3 1,2,2 +26543: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26544: Facts: +26544: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26544: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26544: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26544: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26544: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26544: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26544: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26544: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26544: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +26544: Goal: +26544: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c (join b d)))) + [] by prove_H49 +26544: Order: +26544: lpo +26544: Leaf order: +26544: meet 19 2 5 0,2 +26544: join 19 2 5 0,2,2 +26544: d 2 0 2 2,2,2,2,2 +26544: c 3 0 3 1,2,2,2 +26544: b 3 0 3 1,2,2 +26544: a 4 0 4 1,2 +% SZS status Timeout for LAT158-1.p +NO CLASH, using fixed ground order +26561: Facts: +26561: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26561: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26561: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26561: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26561: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26561: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26561: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26561: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26561: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +26561: Goal: +26561: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26561: Order: +26561: nrkbo +26561: Leaf order: +26561: join 16 2 3 0,2,2 +26561: meet 21 2 7 0,2 +26561: d 3 0 3 2,2,2,2,2 +26561: c 2 0 2 1,2,2,2,2 +26561: b 3 0 3 1,2,2 +26561: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26562: Facts: +26562: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26562: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26562: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26562: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26562: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26562: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26562: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26562: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26562: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +26562: Goal: +26562: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26562: Order: +26562: kbo +26562: Leaf order: +26562: join 16 2 3 0,2,2 +26562: meet 21 2 7 0,2 +26562: d 3 0 3 2,2,2,2,2 +26562: c 2 0 2 1,2,2,2,2 +26562: b 3 0 3 1,2,2 +26562: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26563: Facts: +26563: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26563: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26563: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26563: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26563: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26563: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26563: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26563: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26563: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +26563: Goal: +26563: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26563: Order: +26563: lpo +26563: Leaf order: +26563: join 16 2 3 0,2,2 +26563: meet 21 2 7 0,2 +26563: d 3 0 3 2,2,2,2,2 +26563: c 2 0 2 1,2,2,2,2 +26563: b 3 0 3 1,2,2 +26563: a 4 0 4 1,2 +% SZS status Timeout for LAT163-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +26595: Facts: +26595: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26595: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26595: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26595: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26595: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26595: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26595: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26595: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26595: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +26595: Goal: +26595: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +26595: Order: +26595: kbo +26595: Leaf order: +26595: meet 20 2 6 0,2 +26595: join 17 2 4 0,2,2 +26595: d 2 0 2 2,2,2,2,2 +26595: c 3 0 3 1,2,2,2 +26595: b 4 0 4 1,2,2 +26595: a 3 0 3 1,2 +26594: Facts: +26594: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26594: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26594: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26594: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26594: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26594: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26594: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26594: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26594: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +26594: Goal: +26594: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +26594: Order: +26594: nrkbo +26594: Leaf order: +26594: meet 20 2 6 0,2 +26594: join 17 2 4 0,2,2 +26594: d 2 0 2 2,2,2,2,2 +26594: c 3 0 3 1,2,2,2 +26594: b 4 0 4 1,2,2 +26594: a 3 0 3 1,2 +NO CLASH, using fixed ground order +26596: Facts: +26596: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26596: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26596: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26596: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26596: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26596: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26596: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26596: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26596: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +26596: Goal: +26596: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =>= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +26596: Order: +26596: lpo +26596: Leaf order: +26596: meet 20 2 6 0,2 +26596: join 17 2 4 0,2,2 +26596: d 2 0 2 2,2,2,2,2 +26596: c 3 0 3 1,2,2,2 +26596: b 4 0 4 1,2,2 +26596: a 3 0 3 1,2 +% SZS status Timeout for LAT165-1.p +NO CLASH, using fixed ground order +26645: Facts: +26645: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26645: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26645: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26645: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26645: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26645: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26645: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26645: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26645: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29 +26645: Goal: +26645: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet b (join a d))))) + [] by prove_H78 +26645: Order: +26645: nrkbo +26645: Leaf order: +26645: meet 20 2 5 0,2 +26645: join 18 2 5 0,2,2 +26645: d 3 0 3 2,2,2,2,2 +26645: c 2 0 2 1,2,2,2 +26645: b 4 0 4 1,2,2 +26645: a 3 0 3 1,2 +NO CLASH, using fixed ground order +26646: Facts: +26646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26646: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26646: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26646: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26646: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26646: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29 +26646: Goal: +26646: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet b (join a d))))) + [] by prove_H78 +26646: Order: +26646: kbo +26646: Leaf order: +26646: meet 20 2 5 0,2 +26646: join 18 2 5 0,2,2 +26646: d 3 0 3 2,2,2,2,2 +26646: c 2 0 2 1,2,2,2 +26646: b 4 0 4 1,2,2 +26646: a 3 0 3 1,2 +NO CLASH, using fixed ground order +26647: Facts: +26647: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26647: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26647: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26647: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26647: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26647: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26647: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26647: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26647: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29 +26647: Goal: +26647: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet b (join a d))))) + [] by prove_H78 +26647: Order: +26647: lpo +26647: Leaf order: +26647: meet 20 2 5 0,2 +26647: join 18 2 5 0,2,2 +26647: d 3 0 3 2,2,2,2,2 +26647: c 2 0 2 1,2,2,2 +26647: b 4 0 4 1,2,2 +26647: a 3 0 3 1,2 +% SZS status Timeout for LAT166-1.p +NO CLASH, using fixed ground order +26677: Facts: +26677: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26677: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26677: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26677: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26677: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26677: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26677: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26677: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26677: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29))))) + [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29 +26677: Goal: +26677: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +26677: Order: +26677: kbo +26677: Leaf order: +26677: meet 20 2 6 0,2 +26677: join 18 2 4 0,2,2 +26677: d 2 0 2 2,2,2,2,2 +26677: c 3 0 3 1,2,2,2 +26677: b 4 0 4 1,2,2 +26677: a 3 0 3 1,2 +NO CLASH, using fixed ground order +26676: Facts: +26676: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26676: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26676: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26676: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26676: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26676: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26676: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26676: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26676: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29))))) + [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29 +26676: Goal: +26676: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +26676: Order: +26676: nrkbo +26676: Leaf order: +26676: meet 20 2 6 0,2 +26676: join 18 2 4 0,2,2 +26676: d 2 0 2 2,2,2,2,2 +26676: c 3 0 3 1,2,2,2 +26676: b 4 0 4 1,2,2 +26676: a 3 0 3 1,2 +NO CLASH, using fixed ground order +26678: Facts: +26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26678: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26678: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26678: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26678: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26678: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29))))) + [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29 +26678: Goal: +26678: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =>= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +26678: Order: +26678: lpo +26678: Leaf order: +26678: meet 20 2 6 0,2 +26678: join 18 2 4 0,2,2 +26678: d 2 0 2 2,2,2,2,2 +26678: c 3 0 3 1,2,2,2 +26678: b 4 0 4 1,2,2 +26678: a 3 0 3 1,2 +% SZS status Timeout for LAT167-1.p +NO CLASH, using fixed ground order +26697: Facts: +26697: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26697: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26697: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26697: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26697: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26697: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26697: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26697: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26697: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +26697: Goal: +26697: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26697: Order: +26697: nrkbo +26697: Leaf order: +26697: join 17 2 3 0,2,2 +26697: meet 20 2 7 0,2 +26697: d 3 0 3 2,2,2,2,2 +26697: c 2 0 2 1,2,2,2,2 +26697: b 3 0 3 1,2,2 +26697: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26698: Facts: +26698: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26698: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26698: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26698: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26698: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26698: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26698: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26698: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26698: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +26698: Goal: +26698: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26698: Order: +26698: kbo +26698: Leaf order: +26698: join 17 2 3 0,2,2 +26698: meet 20 2 7 0,2 +26698: d 3 0 3 2,2,2,2,2 +26698: c 2 0 2 1,2,2,2,2 +26698: b 3 0 3 1,2,2 +26698: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26699: Facts: +26699: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26699: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26699: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26699: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26699: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26699: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26699: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26699: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26699: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +26699: Goal: +26699: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26699: Order: +26699: lpo +26699: Leaf order: +26699: join 17 2 3 0,2,2 +26699: meet 20 2 7 0,2 +26699: d 3 0 3 2,2,2,2,2 +26699: c 2 0 2 1,2,2,2,2 +26699: b 3 0 3 1,2,2 +26699: a 4 0 4 1,2 +% SZS status Timeout for LAT172-1.p +NO CLASH, using fixed ground order +26727: Facts: +26727: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26727: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26727: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26727: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26727: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26727: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26727: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26727: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26727: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +26727: Goal: +26727: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +26727: Order: +26727: nrkbo +26727: Leaf order: +26727: meet 18 2 5 0,2 +26727: join 19 2 5 0,2,2 +26727: d 2 0 2 2,2,2,2,2 +26727: c 3 0 3 1,2,2,2 +26727: b 3 0 3 1,2,2 +26727: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26728: Facts: +26728: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26728: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26728: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26728: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26728: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26728: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26728: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26728: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26728: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +26728: Goal: +26728: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +26728: Order: +26728: kbo +26728: Leaf order: +26728: meet 18 2 5 0,2 +26728: join 19 2 5 0,2,2 +26728: d 2 0 2 2,2,2,2,2 +26728: c 3 0 3 1,2,2,2 +26728: b 3 0 3 1,2,2 +26728: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26729: Facts: +26729: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26729: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26729: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26729: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26729: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26729: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26729: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26729: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26729: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +26729: Goal: +26729: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +26729: Order: +26729: lpo +26729: Leaf order: +26729: meet 18 2 5 0,2 +26729: join 19 2 5 0,2,2 +26729: d 2 0 2 2,2,2,2,2 +26729: c 3 0 3 1,2,2,2 +26729: b 3 0 3 1,2,2 +26729: a 4 0 4 1,2 +% SZS status Timeout for LAT173-1.p +NO CLASH, using fixed ground order +26747: Facts: +26747: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26747: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26747: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26747: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26747: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26747: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26747: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26747: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26747: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +26747: Goal: +26747: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26747: Order: +26747: kbo +26747: Leaf order: +26747: join 18 2 3 0,2,2 +26747: meet 20 2 7 0,2 +26747: d 3 0 3 2,2,2,2,2 +26747: c 2 0 2 1,2,2,2,2 +26747: b 3 0 3 1,2,2 +26747: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26746: Facts: +26746: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26746: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26746: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26746: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26746: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26746: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26746: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26746: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26746: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +26746: Goal: +26746: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26746: Order: +26746: nrkbo +26746: Leaf order: +26746: join 18 2 3 0,2,2 +26746: meet 20 2 7 0,2 +26746: d 3 0 3 2,2,2,2,2 +26746: c 2 0 2 1,2,2,2,2 +26746: b 3 0 3 1,2,2 +26746: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26748: Facts: +26748: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26748: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26748: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26748: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26748: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26748: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26748: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26748: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26748: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +26748: Goal: +26748: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +26748: Order: +26748: lpo +26748: Leaf order: +26748: join 18 2 3 0,2,2 +26748: meet 20 2 7 0,2 +26748: d 3 0 3 2,2,2,2,2 +26748: c 2 0 2 1,2,2,2,2 +26748: b 3 0 3 1,2,2 +26748: a 4 0 4 1,2 +% SZS status Timeout for LAT175-1.p +NO CLASH, using fixed ground order +26789: Facts: +26789: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26789: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26789: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26789: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26789: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26789: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26789: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26789: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26789: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +26789: Goal: +26789: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +26789: Order: +26789: nrkbo +26789: Leaf order: +26789: meet 18 2 5 0,2 +26789: join 20 2 5 0,2,2 +26789: d 2 0 2 2,2,2,2,2 +26789: c 3 0 3 1,2,2,2 +26789: b 3 0 3 1,2,2 +26789: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26790: Facts: +26790: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26790: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26790: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26790: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26790: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26790: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26790: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26790: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26790: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +26790: Goal: +26790: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +26790: Order: +26790: kbo +26790: Leaf order: +26790: meet 18 2 5 0,2 +26790: join 20 2 5 0,2,2 +26790: d 2 0 2 2,2,2,2,2 +26790: c 3 0 3 1,2,2,2 +26790: b 3 0 3 1,2,2 +26790: a 4 0 4 1,2 +NO CLASH, using fixed ground order +26791: Facts: +26791: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26791: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26791: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26791: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26791: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26791: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26791: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26791: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26791: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +26791: Goal: +26791: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +26791: Order: +26791: lpo +26791: Leaf order: +26791: meet 18 2 5 0,2 +26791: join 20 2 5 0,2,2 +26791: d 2 0 2 2,2,2,2,2 +26791: c 3 0 3 1,2,2,2 +26791: b 3 0 3 1,2,2 +26791: a 4 0 4 1,2 +% SZS status Timeout for LAT176-1.p +NO CLASH, using fixed ground order +27075: Facts: +27075: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +27075: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +27075: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +27075: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +27075: Id : 6, {_}: + add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +27075: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +27075: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +27075: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +27075: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +27075: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29 + [29] by x_fourthed_is_x ?29 +27075: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +27075: Goal: +27075: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +27075: Order: +27075: nrkbo +27075: Leaf order: +27075: additive_inverse 2 1 0 +27075: add 14 2 0 +27075: additive_identity 4 0 0 +27075: c 2 0 1 3 +27075: multiply 15 2 1 0,2 +27075: a 2 0 1 2,2 +27075: b 2 0 1 1,2 +NO CLASH, using fixed ground order +27077: Facts: +27077: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +27077: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +27077: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +27077: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +27077: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +27077: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +27077: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +27077: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +27077: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +27077: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29 + [29] by x_fourthed_is_x ?29 +27077: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +27077: Goal: +27077: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +27077: Order: +27077: lpo +27077: Leaf order: +27077: additive_inverse 2 1 0 +27077: add 14 2 0 +27077: additive_identity 4 0 0 +27077: c 2 0 1 3 +27077: multiply 15 2 1 0,2 +27077: a 2 0 1 2,2 +27077: b 2 0 1 1,2 +NO CLASH, using fixed ground order +27076: Facts: +27076: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +27076: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +27076: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +27076: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +27076: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +27076: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +27076: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +27076: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +27076: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +27076: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29 + [29] by x_fourthed_is_x ?29 +27076: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +27076: Goal: +27076: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +27076: Order: +27076: kbo +27076: Leaf order: +27076: additive_inverse 2 1 0 +27076: add 14 2 0 +27076: additive_identity 4 0 0 +27076: c 2 0 1 3 +27076: multiply 15 2 1 0,2 +27076: a 2 0 1 2,2 +27076: b 2 0 1 1,2 +% SZS status Timeout for RNG035-7.p +NO CLASH, using fixed ground order +27109: Facts: +27109: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +27109: Goal: +27109: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27109: Order: +27109: nrkbo +27109: Leaf order: +27109: b 1 0 1 1,2,2 +27109: nand 9 2 3 0,2 +27109: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27110: Facts: +27110: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +27110: Goal: +27110: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27110: Order: +27110: kbo +27110: Leaf order: +27110: b 1 0 1 1,2,2 +27110: nand 9 2 3 0,2 +27110: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27111: Facts: +27111: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +27111: Goal: +27111: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27111: Order: +27111: lpo +27111: Leaf order: +27111: b 1 0 1 1,2,2 +27111: nand 9 2 3 0,2 +27111: a 4 0 4 1,1,2 +% SZS status Timeout for BOO077-1.p +NO CLASH, using fixed ground order +27127: Facts: +27127: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +27127: Goal: +27127: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27127: Order: +27127: nrkbo +27127: Leaf order: +27127: nand 12 2 6 0,2 +27127: c 2 0 2 2,2,2,2 +27127: b 3 0 3 1,2,2 +27127: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27128: Facts: +27128: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +27128: Goal: +27128: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27128: Order: +27128: kbo +27128: Leaf order: +27128: nand 12 2 6 0,2 +27128: c 2 0 2 2,2,2,2 +27128: b 3 0 3 1,2,2 +27128: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27129: Facts: +27129: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +27129: Goal: +27129: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27129: Order: +27129: lpo +27129: Leaf order: +27129: nand 12 2 6 0,2 +27129: c 2 0 2 2,2,2,2 +27129: b 3 0 3 1,2,2 +27129: a 3 0 3 1,2 +% SZS status Timeout for BOO078-1.p +NO CLASH, using fixed ground order +27161: Facts: +27161: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +27161: Goal: +27161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27161: Order: +27161: kbo +27161: Leaf order: +27161: b 1 0 1 1,2,2 +27161: nand 9 2 3 0,2 +27161: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27162: Facts: +27162: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +27162: Goal: +27162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27162: Order: +27162: lpo +27162: Leaf order: +27162: b 1 0 1 1,2,2 +27162: nand 9 2 3 0,2 +27162: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27160: Facts: +27160: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +27160: Goal: +27160: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27160: Order: +27160: nrkbo +27160: Leaf order: +27160: b 1 0 1 1,2,2 +27160: nand 9 2 3 0,2 +27160: a 4 0 4 1,1,2 +% SZS status Timeout for BOO079-1.p +NO CLASH, using fixed ground order +27178: Facts: +27178: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +27178: Goal: +27178: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27178: Order: +27178: nrkbo +27178: Leaf order: +27178: nand 12 2 6 0,2 +27178: c 2 0 2 2,2,2,2 +27178: b 3 0 3 1,2,2 +27178: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27179: Facts: +27179: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +27179: Goal: +27179: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27179: Order: +27179: kbo +27179: Leaf order: +27179: nand 12 2 6 0,2 +27179: c 2 0 2 2,2,2,2 +27179: b 3 0 3 1,2,2 +27179: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27180: Facts: +27180: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +27180: Goal: +27180: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27180: Order: +27180: lpo +27180: Leaf order: +27180: nand 12 2 6 0,2 +27180: c 2 0 2 2,2,2,2 +27180: b 3 0 3 1,2,2 +27180: a 3 0 3 1,2 +% SZS status Timeout for BOO080-1.p +NO CLASH, using fixed ground order +27207: Facts: +27207: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +27207: Goal: +27207: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27207: Order: +27207: nrkbo +27207: Leaf order: +27207: b 1 0 1 1,2,2 +27207: nand 9 2 3 0,2 +27207: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27208: Facts: +27208: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +27208: Goal: +27208: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27208: Order: +27208: kbo +27208: Leaf order: +27208: b 1 0 1 1,2,2 +27208: nand 9 2 3 0,2 +27208: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27209: Facts: +27209: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +27209: Goal: +27209: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27209: Order: +27209: lpo +27209: Leaf order: +27209: b 1 0 1 1,2,2 +27209: nand 9 2 3 0,2 +27209: a 4 0 4 1,1,2 +% SZS status Timeout for BOO081-1.p +NO CLASH, using fixed ground order +27227: Facts: +27227: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +27227: Goal: +27227: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27227: Order: +27227: nrkbo +27227: Leaf order: +27227: nand 12 2 6 0,2 +27227: c 2 0 2 2,2,2,2 +27227: b 3 0 3 1,2,2 +27227: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27228: Facts: +27228: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +27228: Goal: +27228: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27228: Order: +27228: kbo +27228: Leaf order: +27228: nand 12 2 6 0,2 +27228: c 2 0 2 2,2,2,2 +27228: b 3 0 3 1,2,2 +27228: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27229: Facts: +27229: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +27229: Goal: +27229: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27229: Order: +27229: lpo +27229: Leaf order: +27229: nand 12 2 6 0,2 +27229: c 2 0 2 2,2,2,2 +27229: b 3 0 3 1,2,2 +27229: a 3 0 3 1,2 +% SZS status Timeout for BOO082-1.p +NO CLASH, using fixed ground order +27257: Facts: +27257: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +27257: Goal: +27257: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27257: Order: +27257: nrkbo +27257: Leaf order: +27257: b 1 0 1 1,2,2 +27257: nand 9 2 3 0,2 +27257: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27258: Facts: +27258: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +27258: Goal: +27258: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27258: Order: +27258: kbo +27258: Leaf order: +27258: b 1 0 1 1,2,2 +27258: nand 9 2 3 0,2 +27258: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27259: Facts: +27259: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +27259: Goal: +27259: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27259: Order: +27259: lpo +27259: Leaf order: +27259: b 1 0 1 1,2,2 +27259: nand 9 2 3 0,2 +27259: a 4 0 4 1,1,2 +% SZS status Timeout for BOO083-1.p +NO CLASH, using fixed ground order +27275: Facts: +27275: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +27275: Goal: +27275: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27275: Order: +27275: nrkbo +27275: Leaf order: +27275: nand 12 2 6 0,2 +27275: c 2 0 2 2,2,2,2 +27275: b 3 0 3 1,2,2 +27275: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27276: Facts: +27276: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +27276: Goal: +27276: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27276: Order: +27276: kbo +27276: Leaf order: +27276: nand 12 2 6 0,2 +27276: c 2 0 2 2,2,2,2 +27276: b 3 0 3 1,2,2 +27276: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27277: Facts: +27277: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +27277: Goal: +27277: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27277: Order: +27277: lpo +27277: Leaf order: +27277: nand 12 2 6 0,2 +27277: c 2 0 2 2,2,2,2 +27277: b 3 0 3 1,2,2 +27277: a 3 0 3 1,2 +% SZS status Timeout for BOO084-1.p +NO CLASH, using fixed ground order +27304: Facts: +27304: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +27304: Goal: +27304: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27304: Order: +27304: nrkbo +27304: Leaf order: +27304: b 1 0 1 1,2,2 +27304: nand 9 2 3 0,2 +27304: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27305: Facts: +27305: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +27305: Goal: +27305: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27305: Order: +27305: kbo +27305: Leaf order: +27305: b 1 0 1 1,2,2 +27305: nand 9 2 3 0,2 +27305: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27306: Facts: +27306: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +27306: Goal: +27306: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27306: Order: +27306: lpo +27306: Leaf order: +27306: b 1 0 1 1,2,2 +27306: nand 9 2 3 0,2 +27306: a 4 0 4 1,1,2 +% SZS status Timeout for BOO085-1.p +NO CLASH, using fixed ground order +27328: Facts: +27328: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +27328: Goal: +27328: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27328: Order: +27328: nrkbo +27328: Leaf order: +27328: nand 12 2 6 0,2 +27328: c 2 0 2 2,2,2,2 +27328: b 3 0 3 1,2,2 +27328: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27331: Facts: +27331: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +27331: Goal: +27331: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27331: Order: +27331: lpo +27331: Leaf order: +27331: nand 12 2 6 0,2 +27331: c 2 0 2 2,2,2,2 +27331: b 3 0 3 1,2,2 +27331: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27329: Facts: +27329: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +27329: Goal: +27329: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27329: Order: +27329: kbo +27329: Leaf order: +27329: nand 12 2 6 0,2 +27329: c 2 0 2 2,2,2,2 +27329: b 3 0 3 1,2,2 +27329: a 3 0 3 1,2 +% SZS status Timeout for BOO086-1.p +NO CLASH, using fixed ground order +27408: Facts: +27408: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +27408: Goal: +27408: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27408: Order: +27408: kbo +27408: Leaf order: +27408: b 1 0 1 1,2,2 +27408: nand 9 2 3 0,2 +27408: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27407: Facts: +27407: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +27407: Goal: +27407: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27407: Order: +27407: nrkbo +27407: Leaf order: +27407: b 1 0 1 1,2,2 +27407: nand 9 2 3 0,2 +27407: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27409: Facts: +27409: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +27409: Goal: +27409: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27409: Order: +27409: lpo +27409: Leaf order: +27409: b 1 0 1 1,2,2 +27409: nand 9 2 3 0,2 +27409: a 4 0 4 1,1,2 +% SZS status Timeout for BOO087-1.p +NO CLASH, using fixed ground order +27425: Facts: +27425: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +27425: Goal: +27425: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27425: Order: +27425: nrkbo +27425: Leaf order: +27425: nand 12 2 6 0,2 +27425: c 2 0 2 2,2,2,2 +27425: b 3 0 3 1,2,2 +27425: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27426: Facts: +27426: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +27426: Goal: +27426: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27426: Order: +27426: kbo +27426: Leaf order: +27426: nand 12 2 6 0,2 +27426: c 2 0 2 2,2,2,2 +27426: b 3 0 3 1,2,2 +27426: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27427: Facts: +27427: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +27427: Goal: +27427: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27427: Order: +27427: lpo +27427: Leaf order: +27427: nand 12 2 6 0,2 +27427: c 2 0 2 2,2,2,2 +27427: b 3 0 3 1,2,2 +27427: a 3 0 3 1,2 +% SZS status Timeout for BOO088-1.p +NO CLASH, using fixed ground order +27458: Facts: +27458: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +27458: Goal: +27458: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27458: Order: +27458: nrkbo +27458: Leaf order: +27458: b 1 0 1 1,2,2 +27458: nand 9 2 3 0,2 +27458: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27459: Facts: +27459: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +27459: Goal: +27459: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27459: Order: +27459: kbo +27459: Leaf order: +27459: b 1 0 1 1,2,2 +27459: nand 9 2 3 0,2 +27459: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27460: Facts: +27460: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +27460: Goal: +27460: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27460: Order: +27460: lpo +27460: Leaf order: +27460: b 1 0 1 1,2,2 +27460: nand 9 2 3 0,2 +27460: a 4 0 4 1,1,2 +% SZS status Timeout for BOO089-1.p +NO CLASH, using fixed ground order +27496: Facts: +27496: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +27496: Goal: +27496: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27496: Order: +27496: nrkbo +27496: Leaf order: +27496: nand 12 2 6 0,2 +27496: c 2 0 2 2,2,2,2 +27496: b 3 0 3 1,2,2 +27496: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27497: Facts: +27497: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +27497: Goal: +27497: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27497: Order: +27497: kbo +27497: Leaf order: +27497: nand 12 2 6 0,2 +27497: c 2 0 2 2,2,2,2 +27497: b 3 0 3 1,2,2 +27497: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27498: Facts: +27498: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +27498: Goal: +27498: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27498: Order: +27498: lpo +27498: Leaf order: +27498: nand 12 2 6 0,2 +27498: c 2 0 2 2,2,2,2 +27498: b 3 0 3 1,2,2 +27498: a 3 0 3 1,2 +% SZS status Timeout for BOO090-1.p +NO CLASH, using fixed ground order +27534: Facts: +27534: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +27534: Goal: +27534: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27534: Order: +27534: nrkbo +27534: Leaf order: +27534: b 1 0 1 1,2,2 +27534: nand 9 2 3 0,2 +27534: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27535: Facts: +27535: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +27535: Goal: +27535: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27535: Order: +27535: kbo +27535: Leaf order: +27535: b 1 0 1 1,2,2 +27535: nand 9 2 3 0,2 +27535: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27536: Facts: +27536: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +27536: Goal: +27536: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27536: Order: +27536: lpo +27536: Leaf order: +27536: b 1 0 1 1,2,2 +27536: nand 9 2 3 0,2 +27536: a 4 0 4 1,1,2 +% SZS status Timeout for BOO091-1.p +NO CLASH, using fixed ground order +27553: Facts: +27553: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +27553: Goal: +27553: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27553: Order: +27553: nrkbo +27553: Leaf order: +27553: nand 12 2 6 0,2 +27553: c 2 0 2 2,2,2,2 +27553: b 3 0 3 1,2,2 +27553: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27554: Facts: +27554: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +27554: Goal: +27554: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27554: Order: +27554: kbo +27554: Leaf order: +27554: nand 12 2 6 0,2 +27554: c 2 0 2 2,2,2,2 +27554: b 3 0 3 1,2,2 +27554: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27555: Facts: +27555: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +27555: Goal: +27555: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27555: Order: +27555: lpo +27555: Leaf order: +27555: nand 12 2 6 0,2 +27555: c 2 0 2 2,2,2,2 +27555: b 3 0 3 1,2,2 +27555: a 3 0 3 1,2 +% SZS status Timeout for BOO092-1.p +NO CLASH, using fixed ground order +27585: Facts: +27585: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +27585: Goal: +27585: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27585: Order: +27585: kbo +27585: Leaf order: +27585: b 1 0 1 1,2,2 +27585: nand 9 2 3 0,2 +27585: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27584: Facts: +27584: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +27584: Goal: +27584: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27584: Order: +27584: nrkbo +27584: Leaf order: +27584: b 1 0 1 1,2,2 +27584: nand 9 2 3 0,2 +27584: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27586: Facts: +27586: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +27586: Goal: +27586: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27586: Order: +27586: lpo +27586: Leaf order: +27586: b 1 0 1 1,2,2 +27586: nand 9 2 3 0,2 +27586: a 4 0 4 1,1,2 +% SZS status Timeout for BOO093-1.p +NO CLASH, using fixed ground order +27602: Facts: +27602: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +27602: Goal: +27602: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27602: Order: +27602: nrkbo +27602: Leaf order: +27602: nand 12 2 6 0,2 +27602: c 2 0 2 2,2,2,2 +27602: b 3 0 3 1,2,2 +27602: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27603: Facts: +27603: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +27603: Goal: +27603: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27603: Order: +27603: kbo +27603: Leaf order: +27603: nand 12 2 6 0,2 +27603: c 2 0 2 2,2,2,2 +27603: b 3 0 3 1,2,2 +27603: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27604: Facts: +27604: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +27604: Goal: +27604: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27604: Order: +27604: lpo +27604: Leaf order: +27604: nand 12 2 6 0,2 +27604: c 2 0 2 2,2,2,2 +27604: b 3 0 3 1,2,2 +27604: a 3 0 3 1,2 +% SZS status Timeout for BOO094-1.p +NO CLASH, using fixed ground order +27635: Facts: +27635: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +27635: Goal: +27635: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27635: Order: +27635: nrkbo +27635: Leaf order: +27635: b 1 0 1 1,2,2 +27635: nand 9 2 3 0,2 +27635: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27636: Facts: +27636: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +27636: Goal: +27636: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27636: Order: +27636: kbo +27636: Leaf order: +27636: b 1 0 1 1,2,2 +27636: nand 9 2 3 0,2 +27636: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27637: Facts: +27637: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +27637: Goal: +27637: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27637: Order: +27637: lpo +27637: Leaf order: +27637: b 1 0 1 1,2,2 +27637: nand 9 2 3 0,2 +27637: a 4 0 4 1,1,2 +% SZS status Timeout for BOO095-1.p +NO CLASH, using fixed ground order +27662: Facts: +27662: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +27662: Goal: +27662: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27662: Order: +27662: nrkbo +27662: Leaf order: +27662: nand 12 2 6 0,2 +27662: c 2 0 2 2,2,2,2 +27662: b 3 0 3 1,2,2 +27662: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27663: Facts: +27663: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +27663: Goal: +27663: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27663: Order: +27663: kbo +27663: Leaf order: +27663: nand 12 2 6 0,2 +27663: c 2 0 2 2,2,2,2 +27663: b 3 0 3 1,2,2 +27663: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27664: Facts: +27664: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +27664: Goal: +27664: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27664: Order: +27664: lpo +27664: Leaf order: +27664: nand 12 2 6 0,2 +27664: c 2 0 2 2,2,2,2 +27664: b 3 0 3 1,2,2 +27664: a 3 0 3 1,2 +% SZS status Timeout for BOO096-1.p +NO CLASH, using fixed ground order +27691: Facts: +27691: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +27691: Goal: +27691: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27691: Order: +27691: nrkbo +27691: Leaf order: +27691: b 1 0 1 1,2,2 +27691: nand 9 2 3 0,2 +27691: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27692: Facts: +27692: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +27692: Goal: +27692: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27692: Order: +27692: kbo +27692: Leaf order: +27692: b 1 0 1 1,2,2 +27692: nand 9 2 3 0,2 +27692: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27693: Facts: +27693: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +27693: Goal: +27693: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27693: Order: +27693: lpo +27693: Leaf order: +27693: b 1 0 1 1,2,2 +27693: nand 9 2 3 0,2 +27693: a 4 0 4 1,1,2 +% SZS status Timeout for BOO097-1.p +NO CLASH, using fixed ground order +27766: Facts: +27766: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +27766: Goal: +27766: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27766: Order: +27766: nrkbo +27766: Leaf order: +27766: nand 12 2 6 0,2 +27766: c 2 0 2 2,2,2,2 +27766: b 3 0 3 1,2,2 +27766: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27767: Facts: +27767: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +27767: Goal: +27767: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27767: Order: +27767: kbo +27767: Leaf order: +27767: nand 12 2 6 0,2 +27767: c 2 0 2 2,2,2,2 +27767: b 3 0 3 1,2,2 +27767: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27768: Facts: +27768: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +27768: Goal: +27768: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27768: Order: +27768: lpo +27768: Leaf order: +27768: nand 12 2 6 0,2 +27768: c 2 0 2 2,2,2,2 +27768: b 3 0 3 1,2,2 +27768: a 3 0 3 1,2 +% SZS status Timeout for BOO098-1.p +NO CLASH, using fixed ground order +27800: Facts: +27800: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +27800: Goal: +27800: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27800: Order: +27800: nrkbo +27800: Leaf order: +27800: b 1 0 1 1,2,2 +27800: nand 9 2 3 0,2 +27800: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27801: Facts: +27801: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +27801: Goal: +27801: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27801: Order: +27801: kbo +27801: Leaf order: +27801: b 1 0 1 1,2,2 +27801: nand 9 2 3 0,2 +27801: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27802: Facts: +27802: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +27802: Goal: +27802: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27802: Order: +27802: lpo +27802: Leaf order: +27802: b 1 0 1 1,2,2 +27802: nand 9 2 3 0,2 +27802: a 4 0 4 1,1,2 +% SZS status Timeout for BOO099-1.p +NO CLASH, using fixed ground order +27864: Facts: +27864: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +27864: Goal: +27864: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27864: Order: +27864: nrkbo +27864: Leaf order: +27864: nand 12 2 6 0,2 +27864: c 2 0 2 2,2,2,2 +27864: b 3 0 3 1,2,2 +27864: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27865: Facts: +27865: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +27865: Goal: +27865: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27865: Order: +27865: kbo +27865: Leaf order: +27865: nand 12 2 6 0,2 +27865: c 2 0 2 2,2,2,2 +27865: b 3 0 3 1,2,2 +27865: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27866: Facts: +27866: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +27866: Goal: +27866: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27866: Order: +27866: lpo +27866: Leaf order: +27866: nand 12 2 6 0,2 +27866: c 2 0 2 2,2,2,2 +27866: b 3 0 3 1,2,2 +27866: a 3 0 3 1,2 +% SZS status Timeout for BOO100-1.p +NO CLASH, using fixed ground order +27893: Facts: +27893: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +27893: Goal: +27893: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27893: Order: +27893: nrkbo +27893: Leaf order: +27893: b 1 0 1 1,2,2 +27893: nand 9 2 3 0,2 +27893: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27894: Facts: +27894: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +27894: Goal: +27894: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27894: Order: +27894: kbo +27894: Leaf order: +27894: b 1 0 1 1,2,2 +27894: nand 9 2 3 0,2 +27894: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27895: Facts: +27895: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +27895: Goal: +27895: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27895: Order: +27895: lpo +27895: Leaf order: +27895: b 1 0 1 1,2,2 +27895: nand 9 2 3 0,2 +27895: a 4 0 4 1,1,2 +% SZS status Timeout for BOO101-1.p +NO CLASH, using fixed ground order +27912: Facts: +27912: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +27912: Goal: +27912: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27912: Order: +27912: nrkbo +27912: Leaf order: +27912: nand 12 2 6 0,2 +27912: c 2 0 2 2,2,2,2 +27912: b 3 0 3 1,2,2 +27912: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27913: Facts: +27913: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +27913: Goal: +27913: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27913: Order: +27913: kbo +27913: Leaf order: +27913: nand 12 2 6 0,2 +27913: c 2 0 2 2,2,2,2 +27913: b 3 0 3 1,2,2 +27913: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27914: Facts: +27914: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +27914: Goal: +27914: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27914: Order: +27914: lpo +27914: Leaf order: +27914: nand 12 2 6 0,2 +27914: c 2 0 2 2,2,2,2 +27914: b 3 0 3 1,2,2 +27914: a 3 0 3 1,2 +% SZS status Timeout for BOO102-1.p +NO CLASH, using fixed ground order +27942: Facts: +27942: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +27942: Goal: +27942: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27942: Order: +27942: nrkbo +27942: Leaf order: +27942: b 1 0 1 1,2,2 +27942: nand 9 2 3 0,2 +27942: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27943: Facts: +27943: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +27943: Goal: +27943: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27943: Order: +27943: kbo +27943: Leaf order: +27943: b 1 0 1 1,2,2 +27943: nand 9 2 3 0,2 +27943: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27944: Facts: +27944: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +27944: Goal: +27944: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27944: Order: +27944: lpo +27944: Leaf order: +27944: b 1 0 1 1,2,2 +27944: nand 9 2 3 0,2 +27944: a 4 0 4 1,1,2 +% SZS status Timeout for BOO103-1.p +NO CLASH, using fixed ground order +27963: Facts: +27963: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +27963: Goal: +27963: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27963: Order: +27963: nrkbo +27963: Leaf order: +27963: nand 12 2 6 0,2 +27963: c 2 0 2 2,2,2,2 +27963: b 3 0 3 1,2,2 +27963: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27964: Facts: +27964: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +27964: Goal: +27964: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27964: Order: +27964: kbo +27964: Leaf order: +27964: nand 12 2 6 0,2 +27964: c 2 0 2 2,2,2,2 +27964: b 3 0 3 1,2,2 +27964: a 3 0 3 1,2 +NO CLASH, using fixed ground order +27965: Facts: +27965: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +27965: Goal: +27965: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +27965: Order: +27965: lpo +27965: Leaf order: +27965: nand 12 2 6 0,2 +27965: c 2 0 2 2,2,2,2 +27965: b 3 0 3 1,2,2 +27965: a 3 0 3 1,2 +% SZS status Timeout for BOO104-1.p +NO CLASH, using fixed ground order +27992: Facts: +27992: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +27992: Goal: +27992: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27992: Order: +27992: nrkbo +27992: Leaf order: +27992: b 1 0 1 1,2,2 +27992: nand 9 2 3 0,2 +27992: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27993: Facts: +27993: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +27993: Goal: +27993: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27993: Order: +27993: kbo +27993: Leaf order: +27993: b 1 0 1 1,2,2 +27993: nand 9 2 3 0,2 +27993: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +27994: Facts: +27994: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +27994: Goal: +27994: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +27994: Order: +27994: lpo +27994: Leaf order: +27994: b 1 0 1 1,2,2 +27994: nand 9 2 3 0,2 +27994: a 4 0 4 1,1,2 +% SZS status Timeout for BOO105-1.p +NO CLASH, using fixed ground order +28010: Facts: +28010: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +28010: Goal: +28010: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +28010: Order: +28010: nrkbo +28010: Leaf order: +28010: nand 12 2 6 0,2 +28010: c 2 0 2 2,2,2,2 +28010: b 3 0 3 1,2,2 +28010: a 3 0 3 1,2 +NO CLASH, using fixed ground order +28011: Facts: +28011: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +28011: Goal: +28011: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +28011: Order: +28011: kbo +28011: Leaf order: +28011: nand 12 2 6 0,2 +28011: c 2 0 2 2,2,2,2 +28011: b 3 0 3 1,2,2 +28011: a 3 0 3 1,2 +NO CLASH, using fixed ground order +28012: Facts: +28012: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +28012: Goal: +28012: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +28012: Order: +28012: lpo +28012: Leaf order: +28012: nand 12 2 6 0,2 +28012: c 2 0 2 2,2,2,2 +28012: b 3 0 3 1,2,2 +28012: a 3 0 3 1,2 +% SZS status Timeout for BOO106-1.p +NO CLASH, using fixed ground order +28046: Facts: +28046: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +28046: Goal: +28046: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +28046: Order: +28046: nrkbo +28046: Leaf order: +28046: b 1 0 1 1,2,2 +28046: nand 9 2 3 0,2 +28046: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +28047: Facts: +28047: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +28047: Goal: +28047: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +28047: Order: +28047: kbo +28047: Leaf order: +28047: b 1 0 1 1,2,2 +28047: nand 9 2 3 0,2 +28047: a 4 0 4 1,1,2 +NO CLASH, using fixed ground order +28048: Facts: +28048: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +28048: Goal: +28048: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +28048: Order: +28048: lpo +28048: Leaf order: +28048: b 1 0 1 1,2,2 +28048: nand 9 2 3 0,2 +28048: a 4 0 4 1,1,2 +% SZS status Timeout for BOO107-1.p +NO CLASH, using fixed ground order +28069: Facts: +28069: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +28069: Goal: +28069: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +28069: Order: +28069: nrkbo +28069: Leaf order: +28069: nand 12 2 6 0,2 +28069: c 2 0 2 2,2,2,2 +28069: b 3 0 3 1,2,2 +28069: a 3 0 3 1,2 +NO CLASH, using fixed ground order +28070: Facts: +28070: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +28070: Goal: +28070: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +28070: Order: +28070: kbo +28070: Leaf order: +28070: nand 12 2 6 0,2 +28070: c 2 0 2 2,2,2,2 +28070: b 3 0 3 1,2,2 +28070: a 3 0 3 1,2 +NO CLASH, using fixed ground order +28071: Facts: +28071: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +28071: Goal: +28071: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +28071: Order: +28071: lpo +28071: Leaf order: +28071: nand 12 2 6 0,2 +28071: c 2 0 2 2,2,2,2 +28071: b 3 0 3 1,2,2 +28071: a 3 0 3 1,2 +% SZS status Timeout for BOO108-1.p +CLASH, statistics insufficient +28456: Facts: +28456: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +28456: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +28456: Goal: +28456: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +28456: Order: +28456: nrkbo +28456: Leaf order: +28456: b 1 0 0 +28456: s 1 0 0 +28456: apply 14 2 3 0,2 +28456: f 3 1 3 0,2,2 +CLASH, statistics insufficient +28457: Facts: +28457: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +28457: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +28457: Goal: +28457: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +28457: Order: +28457: kbo +28457: Leaf order: +28457: b 1 0 0 +28457: s 1 0 0 +28457: apply 14 2 3 0,2 +28457: f 3 1 3 0,2,2 +CLASH, statistics insufficient +28458: Facts: +28458: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +28458: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +28458: Goal: +28458: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +28458: Order: +28458: lpo +28458: Leaf order: +28458: b 1 0 0 +28458: s 1 0 0 +28458: apply 14 2 3 0,2 +28458: f 3 1 3 0,2,2 +% SZS status Timeout for COL067-1.p +CLASH, statistics insufficient +28873: Facts: +28873: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +28873: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +28873: Goal: +28873: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +28873: Order: +28873: nrkbo +28873: Leaf order: +28873: b 1 0 0 +28873: s 1 0 0 +28873: apply 12 2 1 0,3 +28873: combinator 1 0 1 1,3 +CLASH, statistics insufficient +28874: Facts: +28874: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +28874: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +28874: Goal: +28874: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +28874: Order: +28874: kbo +28874: Leaf order: +28874: b 1 0 0 +28874: s 1 0 0 +28874: apply 12 2 1 0,3 +28874: combinator 1 0 1 1,3 +CLASH, statistics insufficient +28875: Facts: +28875: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +28875: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +28875: Goal: +28875: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +28875: Order: +28875: lpo +28875: Leaf order: +28875: b 1 0 0 +28875: s 1 0 0 +28875: apply 12 2 1 0,3 +28875: combinator 1 0 1 1,3 +% SZS status Timeout for COL068-1.p +CLASH, statistics insufficient +28902: Facts: +28902: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +28902: Id : 3, {_}: + apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8) + [8, 7] by l_definition ?7 ?8 +28902: Goal: +28902: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +28902: Order: +28902: nrkbo +28902: Leaf order: +28902: l 1 0 0 +28902: b 1 0 0 +28902: apply 12 2 3 0,2 +28902: f 3 1 3 0,2,2 +CLASH, statistics insufficient +28903: Facts: +28903: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +28903: Id : 3, {_}: + apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8) + [8, 7] by l_definition ?7 ?8 +28903: Goal: +28903: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +28903: Order: +28903: kbo +28903: Leaf order: +28903: l 1 0 0 +28903: b 1 0 0 +28903: apply 12 2 3 0,2 +28903: f 3 1 3 0,2,2 +CLASH, statistics insufficient +28904: Facts: +28904: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +28904: Id : 3, {_}: + apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8) + [8, 7] by l_definition ?7 ?8 +28904: Goal: +28904: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +28904: Order: +28904: lpo +28904: Leaf order: +28904: l 1 0 0 +28904: b 1 0 0 +28904: apply 12 2 3 0,2 +28904: f 3 1 3 0,2,2 +% SZS status Timeout for COL069-1.p +CLASH, statistics insufficient +28921: Facts: +28921: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by definition_B ?3 ?4 ?5 +28921: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7 +28921: Goal: +28921: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by strong_fixpoint ?1 +28921: Order: +28921: nrkbo +28921: Leaf order: +28921: m 1 0 0 +28921: b 1 0 0 +28921: apply 10 2 3 0,2 +28921: f 3 1 3 0,2,2 +CLASH, statistics insufficient +28922: Facts: +28922: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by definition_B ?3 ?4 ?5 +28922: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7 +28922: Goal: +28922: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by strong_fixpoint ?1 +28922: Order: +28922: kbo +28922: Leaf order: +28922: m 1 0 0 +28922: b 1 0 0 +28922: apply 10 2 3 0,2 +28922: f 3 1 3 0,2,2 +CLASH, statistics insufficient +28923: Facts: +28923: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by definition_B ?3 ?4 ?5 +28923: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7 +28923: Goal: +28923: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by strong_fixpoint ?1 +28923: Order: +28923: lpo +28923: Leaf order: +28923: m 1 0 0 +28923: b 1 0 0 +28923: apply 10 2 3 0,2 +28923: f 3 1 3 0,2,2 +% SZS status Timeout for COL087-1.p +NO CLASH, using fixed ground order +28951: Facts: +28951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +28951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +28951: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +28951: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +28951: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +28951: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +28951: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +28951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +28951: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +28951: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +28951: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +28951: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +28951: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +28951: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +28951: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +28951: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1 +28951: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2 +28951: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3 +28951: Goal: +28951: Id : 1, {_}: + least_upper_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + multiply (greatest_lower_bound a b) (greatest_lower_bound a c) + [] by prove_p08a +28951: Order: +28951: nrkbo +28951: Leaf order: +28951: inverse 1 1 0 +28951: identity 5 0 0 +28951: least_upper_bound 17 2 1 0,2 +28951: greatest_lower_bound 18 2 5 0,1,2 +28951: multiply 21 2 3 0,2,1,2 +28951: c 5 0 3 2,2,1,2 +28951: b 5 0 3 1,2,1,2 +28951: a 7 0 5 1,1,2 +NO CLASH, using fixed ground order +28952: Facts: +28952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +28952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +28952: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +28952: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +28952: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +28952: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +28952: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +28952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +28952: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +28952: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +28952: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +28952: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +28952: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +28952: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +28952: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +28952: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1 +28952: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2 +28952: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3 +28952: Goal: +28952: Id : 1, {_}: + least_upper_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + multiply (greatest_lower_bound a b) (greatest_lower_bound a c) + [] by prove_p08a +28952: Order: +28952: kbo +28952: Leaf order: +28952: inverse 1 1 0 +28952: identity 5 0 0 +28952: least_upper_bound 17 2 1 0,2 +28952: greatest_lower_bound 18 2 5 0,1,2 +28952: multiply 21 2 3 0,2,1,2 +28952: c 5 0 3 2,2,1,2 +28952: b 5 0 3 1,2,1,2 +28952: a 7 0 5 1,1,2 +NO CLASH, using fixed ground order +28953: Facts: +28953: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +28953: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +28953: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +28953: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +28953: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +28953: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +28953: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +28953: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +28953: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +28953: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +28953: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +28953: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +28953: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +28953: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +28953: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +28953: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1 +28953: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2 +28953: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3 +28953: Goal: +28953: Id : 1, {_}: + least_upper_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + multiply (greatest_lower_bound a b) (greatest_lower_bound a c) + [] by prove_p08a +28953: Order: +28953: lpo +28953: Leaf order: +28953: inverse 1 1 0 +28953: identity 5 0 0 +28953: least_upper_bound 17 2 1 0,2 +28953: greatest_lower_bound 18 2 5 0,1,2 +28953: multiply 21 2 3 0,2,1,2 +28953: c 5 0 3 2,2,1,2 +28953: b 5 0 3 1,2,1,2 +28953: a 7 0 5 1,1,2 +% SZS status Timeout for GRP177-1.p +NO CLASH, using fixed ground order +28970: Facts: +28970: Id : 2, {_}: + f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5)) + =>= + ?3 + [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5 +28970: Goal: +28970: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +28970: Order: +28970: nrkbo +28970: Leaf order: +28970: f 17 2 8 0,2 +28970: c 3 0 3 2,1,2,2 +28970: b 4 0 4 1,1,2,2 +28970: a 3 0 3 1,2 +NO CLASH, using fixed ground order +28971: Facts: +28971: Id : 2, {_}: + f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5)) + =>= + ?3 + [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5 +28971: Goal: +28971: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +28971: Order: +28971: kbo +28971: Leaf order: +28971: f 17 2 8 0,2 +28971: c 3 0 3 2,1,2,2 +28971: b 4 0 4 1,1,2,2 +28971: a 3 0 3 1,2 +NO CLASH, using fixed ground order +28972: Facts: +28972: Id : 2, {_}: + f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5)) + =>= + ?3 + [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5 +28972: Goal: +28972: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +28972: Order: +28972: lpo +28972: Leaf order: +28972: f 17 2 8 0,2 +28972: c 3 0 3 2,1,2,2 +28972: b 4 0 4 1,1,2,2 +28972: a 3 0 3 1,2 +% SZS status Timeout for LAT071-1.p +NO CLASH, using fixed ground order +29000: Facts: +29000: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5 +29000: Goal: +29000: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29000: Order: +29000: nrkbo +29000: Leaf order: +29000: f 18 2 8 0,2 +29000: c 3 0 3 2,1,2,2 +29000: b 4 0 4 1,1,2,2 +29000: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29001: Facts: +29001: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5 +29001: Goal: +29001: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29001: Order: +29001: kbo +29001: Leaf order: +29001: f 18 2 8 0,2 +29001: c 3 0 3 2,1,2,2 +29001: b 4 0 4 1,1,2,2 +29001: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29002: Facts: +29002: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5 +29002: Goal: +29002: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +29002: Order: +29002: lpo +29002: Leaf order: +29002: f 18 2 8 0,2 +29002: c 3 0 3 2,1,2,2 +29002: b 4 0 4 1,1,2,2 +29002: a 3 0 3 1,2 +% SZS status Timeout for LAT072-1.p +NO CLASH, using fixed ground order +29018: Facts: +29018: Id : 2, {_}: + f (f (f ?2 (f ?3 ?2)) ?2) + (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5)))) + =>= + ?3 + [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5 +29018: Goal: +29018: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +29018: Order: +29018: nrkbo +29018: Leaf order: +29018: f 18 2 8 0,2 +29018: c 3 0 3 1,2,2,2,2 +29018: b 3 0 3 1,2,2 +29018: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29019: Facts: +29019: Id : 2, {_}: + f (f (f ?2 (f ?3 ?2)) ?2) + (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5)))) + =>= + ?3 + [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5 +29019: Goal: +29019: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +29019: Order: +29019: kbo +29019: Leaf order: +29019: f 18 2 8 0,2 +29019: c 3 0 3 1,2,2,2,2 +29019: b 3 0 3 1,2,2 +29019: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29020: Facts: +29020: Id : 2, {_}: + f (f (f ?2 (f ?3 ?2)) ?2) + (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5)))) + =>= + ?3 + [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5 +29020: Goal: +29020: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +29020: Order: +29020: lpo +29020: Leaf order: +29020: f 18 2 8 0,2 +29020: c 3 0 3 1,2,2,2,2 +29020: b 3 0 3 1,2,2 +29020: a 4 0 4 1,2 +% SZS status Timeout for LAT073-1.p +NO CLASH, using fixed ground order +29047: Facts: +29047: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +29047: Goal: +29047: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29047: Order: +29047: nrkbo +29047: Leaf order: +29047: f 19 2 8 0,2 +29047: c 3 0 3 2,1,2,2 +29047: b 4 0 4 1,1,2,2 +29047: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29048: Facts: +29048: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +29048: Goal: +29048: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29048: Order: +29048: kbo +29048: Leaf order: +29048: f 19 2 8 0,2 +29048: c 3 0 3 2,1,2,2 +29048: b 4 0 4 1,1,2,2 +29048: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29049: Facts: +29049: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +29049: Goal: +29049: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +29049: Order: +29049: lpo +29049: Leaf order: +29049: f 19 2 8 0,2 +29049: c 3 0 3 2,1,2,2 +29049: b 4 0 4 1,1,2,2 +29049: a 3 0 3 1,2 +% SZS status Timeout for LAT074-1.p +NO CLASH, using fixed ground order +29065: Facts: +29065: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +29065: Goal: +29065: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +29065: Order: +29065: nrkbo +29065: Leaf order: +29065: f 19 2 8 0,2 +29065: c 3 0 3 1,2,2,2,2 +29065: b 3 0 3 1,2,2 +29065: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29066: Facts: +29066: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +29066: Goal: +29066: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +29066: Order: +29066: kbo +29066: Leaf order: +29066: f 19 2 8 0,2 +29066: c 3 0 3 1,2,2,2,2 +29066: b 3 0 3 1,2,2 +29066: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29067: Facts: +29067: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +29067: Goal: +29067: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +29067: Order: +29067: lpo +29067: Leaf order: +29067: f 19 2 8 0,2 +29067: c 3 0 3 1,2,2,2,2 +29067: b 3 0 3 1,2,2 +29067: a 4 0 4 1,2 +% SZS status Timeout for LAT075-1.p +NO CLASH, using fixed ground order +29098: Facts: +29098: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +29098: Goal: +29098: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29098: Order: +29098: nrkbo +29098: Leaf order: +29098: f 20 2 8 0,2 +29098: c 3 0 3 2,1,2,2 +29098: b 4 0 4 1,1,2,2 +29098: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29099: Facts: +29099: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +29099: Goal: +29099: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29099: Order: +29099: kbo +29099: Leaf order: +29099: f 20 2 8 0,2 +29099: c 3 0 3 2,1,2,2 +29099: b 4 0 4 1,1,2,2 +29099: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29100: Facts: +29100: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +29100: Goal: +29100: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +29100: Order: +29100: lpo +29100: Leaf order: +29100: f 20 2 8 0,2 +29100: c 3 0 3 2,1,2,2 +29100: b 4 0 4 1,1,2,2 +29100: a 3 0 3 1,2 +% SZS status Timeout for LAT076-1.p +NO CLASH, using fixed ground order +29161: Facts: +NO CLASH, using fixed ground order +29162: Facts: +29162: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +29162: Goal: +29162: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +29162: Order: +29162: kbo +29162: Leaf order: +29162: f 20 2 8 0,2 +29162: c 3 0 3 1,2,2,2,2 +29162: b 3 0 3 1,2,2 +29162: a 4 0 4 1,2 +29161: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +29161: Goal: +29161: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +29161: Order: +29161: nrkbo +29161: Leaf order: +29161: f 20 2 8 0,2 +29161: c 3 0 3 1,2,2,2,2 +29161: b 3 0 3 1,2,2 +29161: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29163: Facts: +29163: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +29163: Goal: +29163: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +29163: Order: +29163: lpo +29163: Leaf order: +29163: f 20 2 8 0,2 +29163: c 3 0 3 1,2,2,2,2 +29163: b 3 0 3 1,2,2 +29163: a 4 0 4 1,2 +% SZS status Timeout for LAT077-1.p +NO CLASH, using fixed ground order +29191: Facts: +29191: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +29191: Goal: +29191: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29191: Order: +29191: nrkbo +29191: Leaf order: +29191: f 20 2 8 0,2 +29191: c 3 0 3 2,1,2,2 +29191: b 4 0 4 1,1,2,2 +29191: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29192: Facts: +29192: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +29192: Goal: +29192: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +29192: Order: +29192: kbo +29192: Leaf order: +29192: f 20 2 8 0,2 +29192: c 3 0 3 2,1,2,2 +29192: b 4 0 4 1,1,2,2 +29192: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29193: Facts: +29193: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +29193: Goal: +29193: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +29193: Order: +29193: lpo +29193: Leaf order: +29193: f 20 2 8 0,2 +29193: c 3 0 3 2,1,2,2 +29193: b 4 0 4 1,1,2,2 +29193: a 3 0 3 1,2 +% SZS status Timeout for LAT078-1.p +NO CLASH, using fixed ground order +29210: Facts: +29210: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +29210: Goal: +29210: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +29210: Order: +29210: nrkbo +29210: Leaf order: +29210: f 20 2 8 0,2 +29210: c 3 0 3 1,2,2,2,2 +29210: b 3 0 3 1,2,2 +29210: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29211: Facts: +29211: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +29211: Goal: +29211: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +29211: Order: +29211: kbo +29211: Leaf order: +29211: f 20 2 8 0,2 +29211: c 3 0 3 1,2,2,2,2 +29211: b 3 0 3 1,2,2 +29211: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29212: Facts: +29212: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +29212: Goal: +29212: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +29212: Order: +29212: lpo +29212: Leaf order: +29212: f 20 2 8 0,2 +29212: c 3 0 3 1,2,2,2,2 +29212: b 3 0 3 1,2,2 +29212: a 4 0 4 1,2 +% SZS status Timeout for LAT079-1.p +NO CLASH, using fixed ground order +29240: Facts: +29240: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29240: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29240: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29240: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29240: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29240: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29240: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29240: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29240: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H11 ?26 ?27 ?28 +29240: Goal: +29240: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +29240: Order: +29240: nrkbo +29240: Leaf order: +29240: join 16 2 3 0,2,2 +29240: meet 20 2 5 0,2 +29240: c 3 0 3 2,2,2,2 +29240: b 3 0 3 1,2,2 +29240: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29241: Facts: +29241: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29241: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29241: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29241: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29241: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29241: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29241: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29241: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29241: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H11 ?26 ?27 ?28 +29241: Goal: +29241: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +29241: Order: +29241: kbo +29241: Leaf order: +29241: join 16 2 3 0,2,2 +29241: meet 20 2 5 0,2 +29241: c 3 0 3 2,2,2,2 +29241: b 3 0 3 1,2,2 +29241: a 4 0 4 1,2 +NO CLASH, using fixed ground order +29242: Facts: +29242: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29242: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29242: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29242: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29242: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29242: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29242: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29242: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29242: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =?= + meet ?26 + (join ?27 + (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H11 ?26 ?27 ?28 +29242: Goal: +29242: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +29242: Order: +29242: lpo +29242: Leaf order: +29242: join 16 2 3 0,2,2 +29242: meet 20 2 5 0,2 +29242: c 3 0 3 2,2,2,2 +29242: b 3 0 3 1,2,2 +29242: a 4 0 4 1,2 +% SZS status Timeout for LAT139-1.p +NO CLASH, using fixed ground order +29258: Facts: +29258: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29258: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29258: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29258: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29258: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29258: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29258: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29258: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29258: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +29258: Goal: +29258: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29258: Order: +29258: nrkbo +29258: Leaf order: +29258: join 17 2 4 0,2,2 +29258: meet 21 2 6 0,2 +29258: c 3 0 3 2,2,2,2 +29258: b 3 0 3 1,2,2 +29258: a 6 0 6 1,2 +NO CLASH, using fixed ground order +29259: Facts: +29259: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29259: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29259: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29259: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29259: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29259: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29259: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29259: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29259: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +29259: Goal: +29259: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29259: Order: +29259: kbo +29259: Leaf order: +29259: join 17 2 4 0,2,2 +29259: meet 21 2 6 0,2 +29259: c 3 0 3 2,2,2,2 +NO CLASH, using fixed ground order +29260: Facts: +29260: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29260: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29260: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29260: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29260: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29260: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29260: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29260: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29260: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +29260: Goal: +29260: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29260: Order: +29260: lpo +29260: Leaf order: +29260: join 17 2 4 0,2,2 +29260: meet 21 2 6 0,2 +29260: c 3 0 3 2,2,2,2 +29260: b 3 0 3 1,2,2 +29260: a 6 0 6 1,2 +29259: b 3 0 3 1,2,2 +29259: a 6 0 6 1,2 +% SZS status Timeout for LAT141-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +29297: Facts: +29297: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29297: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29297: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29297: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29297: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29297: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29297: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29297: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29297: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H58 ?26 ?27 ?28 +29297: Goal: +29297: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +29297: Order: +29297: kbo +29297: Leaf order: +29297: meet 18 2 5 0,2 +29297: d 2 0 2 2,2,2,2 +29297: join 18 2 5 0,1,2,2 +29297: c 2 0 2 2,1,2,2 +29297: b 5 0 5 1,1,2,2 +29297: a 3 0 3 1,2 +29296: Facts: +29296: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29296: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29296: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29296: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29296: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29296: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29296: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29296: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29296: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H58 ?26 ?27 ?28 +29296: Goal: +29296: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +29296: Order: +29296: nrkbo +29296: Leaf order: +29296: meet 18 2 5 0,2 +29296: d 2 0 2 2,2,2,2 +29296: join 18 2 5 0,1,2,2 +29296: c 2 0 2 2,1,2,2 +29296: b 5 0 5 1,1,2,2 +29296: a 3 0 3 1,2 +NO CLASH, using fixed ground order +29298: Facts: +29298: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29298: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29298: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29298: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29298: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29298: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29298: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29298: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29298: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H58 ?26 ?27 ?28 +29298: Goal: +29298: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +29298: Order: +29298: lpo +29298: Leaf order: +29298: meet 18 2 5 0,2 +29298: d 2 0 2 2,2,2,2 +29298: join 18 2 5 0,1,2,2 +29298: c 2 0 2 2,1,2,2 +29298: b 5 0 5 1,1,2,2 +29298: a 3 0 3 1,2 +% SZS status Timeout for LAT161-1.p +NO CLASH, using fixed ground order +29316: Facts: +29316: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29316: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29316: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29316: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29316: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29316: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29316: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29316: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29316: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +29316: Goal: +29316: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29316: Order: +29316: nrkbo +29316: Leaf order: +29316: join 19 2 4 0,2,2 +29316: meet 19 2 6 0,2 +29316: c 3 0 3 2,2,2,2 +29316: b 3 0 3 1,2,2 +29316: a 6 0 6 1,2 +NO CLASH, using fixed ground order +29317: Facts: +29317: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29317: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29317: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29317: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29317: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29317: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29317: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29317: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29317: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +29317: Goal: +29317: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29317: Order: +29317: kbo +29317: Leaf order: +29317: join 19 2 4 0,2,2 +29317: meet 19 2 6 0,2 +29317: c 3 0 3 2,2,2,2 +29317: b 3 0 3 1,2,2 +29317: a 6 0 6 1,2 +NO CLASH, using fixed ground order +29318: Facts: +29318: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29318: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29318: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29318: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29318: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29318: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29318: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29318: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29318: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +29318: Goal: +29318: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29318: Order: +29318: lpo +29318: Leaf order: +29318: join 19 2 4 0,2,2 +29318: meet 19 2 6 0,2 +29318: c 3 0 3 2,2,2,2 +29318: b 3 0 3 1,2,2 +29318: a 6 0 6 1,2 +% SZS status Timeout for LAT177-1.p +NO CLASH, using fixed ground order +29346: Facts: +29346: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3 +29346: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associative_addition ?5 ?6 ?7 +NO CLASH, using fixed ground order +29347: Facts: +29347: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3 +29347: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associative_addition ?5 ?6 ?7 +29347: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9 +29347: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11 +29347: Id : 6, {_}: + add ?13 (additive_inverse ?13) =>= additive_identity + [13] by right_additive_inverse ?13 +29347: Id : 7, {_}: + add (additive_inverse ?15) ?15 =>= additive_identity + [15] by left_additive_inverse ?15 +29347: Id : 8, {_}: + additive_inverse additive_identity =>= additive_identity + [] by additive_inverse_identity +29347: Id : 9, {_}: + add ?18 (add (additive_inverse ?18) ?19) =>= ?19 + [19, 18] by property_of_inverse_and_add ?18 ?19 +29347: Id : 10, {_}: + additive_inverse (add ?21 ?22) + =>= + add (additive_inverse ?21) (additive_inverse ?22) + [22, 21] by distribute_additive_inverse ?21 ?22 +29347: Id : 11, {_}: + additive_inverse (additive_inverse ?24) =>= ?24 + [24] by additive_inverse_additive_inverse ?24 +29347: Id : 12, {_}: + multiply ?26 additive_identity =>= additive_identity + [26] by multiply_additive_id1 ?26 +29347: Id : 13, {_}: + multiply additive_identity ?28 =>= additive_identity + [28] by multiply_additive_id2 ?28 +29347: Id : 14, {_}: + multiply (additive_inverse ?30) (additive_inverse ?31) + =>= + multiply ?30 ?31 + [31, 30] by product_of_inverse ?30 ?31 +NO CLASH, using fixed ground order +29346: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9 +29346: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11 +29346: Id : 6, {_}: + add ?13 (additive_inverse ?13) =>= additive_identity + [13] by right_additive_inverse ?13 +29346: Id : 7, {_}: + add (additive_inverse ?15) ?15 =>= additive_identity + [15] by left_additive_inverse ?15 +29346: Id : 8, {_}: + additive_inverse additive_identity =>= additive_identity + [] by additive_inverse_identity +29345: Facts: +29346: Id : 9, {_}: + add ?18 (add (additive_inverse ?18) ?19) =>= ?19 + [19, 18] by property_of_inverse_and_add ?18 ?19 +29346: Id : 10, {_}: + additive_inverse (add ?21 ?22) + =<= + add (additive_inverse ?21) (additive_inverse ?22) + [22, 21] by distribute_additive_inverse ?21 ?22 +29345: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3 +29345: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associative_addition ?5 ?6 ?7 +29346: Id : 11, {_}: + additive_inverse (additive_inverse ?24) =>= ?24 + [24] by additive_inverse_additive_inverse ?24 +29345: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9 +29346: Id : 12, {_}: + multiply ?26 additive_identity =>= additive_identity + [26] by multiply_additive_id1 ?26 +29345: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11 +29346: Id : 13, {_}: + multiply additive_identity ?28 =>= additive_identity + [28] by multiply_additive_id2 ?28 +29346: Id : 14, {_}: + multiply (additive_inverse ?30) (additive_inverse ?31) + =>= + multiply ?30 ?31 + [31, 30] by product_of_inverse ?30 ?31 +29346: Id : 15, {_}: + multiply ?33 (additive_inverse ?34) + =<= + additive_inverse (multiply ?33 ?34) + [34, 33] by multiply_additive_inverse1 ?33 ?34 +29345: Id : 6, {_}: + add ?13 (additive_inverse ?13) =>= additive_identity + [13] by right_additive_inverse ?13 +29345: Id : 7, {_}: + add (additive_inverse ?15) ?15 =>= additive_identity + [15] by left_additive_inverse ?15 +29345: Id : 8, {_}: + additive_inverse additive_identity =>= additive_identity + [] by additive_inverse_identity +29346: Id : 16, {_}: + multiply (additive_inverse ?36) ?37 + =<= + additive_inverse (multiply ?36 ?37) + [37, 36] by multiply_additive_inverse2 ?36 ?37 +29345: Id : 9, {_}: + add ?18 (add (additive_inverse ?18) ?19) =>= ?19 + [19, 18] by property_of_inverse_and_add ?18 ?19 +29346: Id : 17, {_}: + multiply ?39 (add ?40 ?41) + =<= + add (multiply ?39 ?40) (multiply ?39 ?41) + [41, 40, 39] by distribute1 ?39 ?40 ?41 +29345: Id : 10, {_}: + additive_inverse (add ?21 ?22) + =<= + add (additive_inverse ?21) (additive_inverse ?22) + [22, 21] by distribute_additive_inverse ?21 ?22 +29346: Id : 18, {_}: + multiply (add ?43 ?44) ?45 + =<= + add (multiply ?43 ?45) (multiply ?44 ?45) + [45, 44, 43] by distribute2 ?43 ?44 ?45 +29345: Id : 11, {_}: + additive_inverse (additive_inverse ?24) =>= ?24 + [24] by additive_inverse_additive_inverse ?24 +29345: Id : 12, {_}: + multiply ?26 additive_identity =>= additive_identity + [26] by multiply_additive_id1 ?26 +29345: Id : 13, {_}: + multiply additive_identity ?28 =>= additive_identity + [28] by multiply_additive_id2 ?28 +29345: Id : 14, {_}: + multiply (additive_inverse ?30) (additive_inverse ?31) + =>= + multiply ?30 ?31 + [31, 30] by product_of_inverse ?30 ?31 +29345: Id : 15, {_}: + multiply ?33 (additive_inverse ?34) + =<= + additive_inverse (multiply ?33 ?34) + [34, 33] by multiply_additive_inverse1 ?33 ?34 +29345: Id : 16, {_}: + multiply (additive_inverse ?36) ?37 + =<= + additive_inverse (multiply ?36 ?37) + [37, 36] by multiply_additive_inverse2 ?36 ?37 +29345: Id : 17, {_}: + multiply ?39 (add ?40 ?41) + =<= + add (multiply ?39 ?40) (multiply ?39 ?41) + [41, 40, 39] by distribute1 ?39 ?40 ?41 +29345: Id : 18, {_}: + multiply (add ?43 ?44) ?45 + =<= + add (multiply ?43 ?45) (multiply ?44 ?45) + [45, 44, 43] by distribute2 ?43 ?44 ?45 +29345: Id : 19, {_}: + multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48) + [48, 47] by right_alternative ?47 ?48 +29347: Id : 15, {_}: + multiply ?33 (additive_inverse ?34) + =<= + additive_inverse (multiply ?33 ?34) + [34, 33] by multiply_additive_inverse1 ?33 ?34 +29345: Id : 20, {_}: + associator ?50 ?51 ?52 + =<= + add (multiply (multiply ?50 ?51) ?52) + (additive_inverse (multiply ?50 (multiply ?51 ?52))) + [52, 51, 50] by associator ?50 ?51 ?52 +29345: Id : 21, {_}: + commutator ?54 ?55 + =<= + add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55)) + [55, 54] by commutator ?54 ?55 +29347: Id : 16, {_}: + multiply (additive_inverse ?36) ?37 + =<= + additive_inverse (multiply ?36 ?37) + [37, 36] by multiply_additive_inverse2 ?36 ?37 +29347: Id : 17, {_}: + multiply ?39 (add ?40 ?41) + =<= + add (multiply ?39 ?40) (multiply ?39 ?41) + [41, 40, 39] by distribute1 ?39 ?40 ?41 +29347: Id : 18, {_}: + multiply (add ?43 ?44) ?45 + =<= + add (multiply ?43 ?45) (multiply ?44 ?45) + [45, 44, 43] by distribute2 ?43 ?44 ?45 +29347: Id : 19, {_}: + multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48) + [48, 47] by right_alternative ?47 ?48 +29347: Id : 20, {_}: + associator ?50 ?51 ?52 + =<= + add (multiply (multiply ?50 ?51) ?52) + (additive_inverse (multiply ?50 (multiply ?51 ?52))) + [52, 51, 50] by associator ?50 ?51 ?52 +29347: Id : 21, {_}: + commutator ?54 ?55 + =<= + add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55)) + [55, 54] by commutator ?54 ?55 +29347: Id : 22, {_}: + multiply (multiply (associator ?57 ?57 ?58) ?57) + (associator ?57 ?57 ?58) + =>= + additive_identity + [58, 57] by middle_associator ?57 ?58 +29347: Id : 23, {_}: + multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61) + [61, 60] by left_alternative ?60 ?61 +29347: Id : 24, {_}: + s ?63 ?64 ?65 ?66 + =>= + add + (add (associator (multiply ?63 ?64) ?65 ?66) + (additive_inverse (multiply ?64 (associator ?63 ?65 ?66)))) + (additive_inverse (multiply (associator ?64 ?65 ?66) ?63)) + [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66 +29347: Id : 25, {_}: + multiply ?68 (multiply ?69 (multiply ?70 ?69)) + =<= + multiply (multiply (multiply ?68 ?69) ?70) ?69 + [70, 69, 68] by right_moufang ?68 ?69 ?70 +29347: Id : 26, {_}: + multiply (multiply ?72 (multiply ?73 ?72)) ?74 + =>= + multiply ?72 (multiply ?73 (multiply ?72 ?74)) + [74, 73, 72] by left_moufang ?72 ?73 ?74 +29347: Id : 27, {_}: + multiply (multiply ?76 ?77) (multiply ?78 ?76) + =<= + multiply (multiply ?76 (multiply ?77 ?78)) ?76 + [78, 77, 76] by middle_moufang ?76 ?77 ?78 +29347: Goal: +29347: Id : 1, {_}: + s a b c d =>= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29347: Order: +29347: lpo +29347: Leaf order: +29347: commutator 1 2 0 +29347: associator 6 3 0 +29347: multiply 51 2 0 +29347: additive_identity 11 0 0 +29347: add 22 2 0 +29347: additive_inverse 20 1 1 0,3 +29347: s 3 4 2 0,2 +29347: d 2 0 2 4,2 +29347: c 2 0 2 3,2 +29347: b 2 0 2 2,2 +29347: a 2 0 2 1,2 +29346: Id : 19, {_}: + multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48) + [48, 47] by right_alternative ?47 ?48 +29345: Id : 22, {_}: + multiply (multiply (associator ?57 ?57 ?58) ?57) + (associator ?57 ?57 ?58) + =>= + additive_identity + [58, 57] by middle_associator ?57 ?58 +29345: Id : 23, {_}: + multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61) + [61, 60] by left_alternative ?60 ?61 +29345: Id : 24, {_}: + s ?63 ?64 ?65 ?66 + =<= + add + (add (associator (multiply ?63 ?64) ?65 ?66) + (additive_inverse (multiply ?64 (associator ?63 ?65 ?66)))) + (additive_inverse (multiply (associator ?64 ?65 ?66) ?63)) + [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66 +29345: Id : 25, {_}: + multiply ?68 (multiply ?69 (multiply ?70 ?69)) + =?= + multiply (multiply (multiply ?68 ?69) ?70) ?69 + [70, 69, 68] by right_moufang ?68 ?69 ?70 +29345: Id : 26, {_}: + multiply (multiply ?72 (multiply ?73 ?72)) ?74 + =?= + multiply ?72 (multiply ?73 (multiply ?72 ?74)) + [74, 73, 72] by left_moufang ?72 ?73 ?74 +29345: Id : 27, {_}: + multiply (multiply ?76 ?77) (multiply ?78 ?76) + =?= + multiply (multiply ?76 (multiply ?77 ?78)) ?76 + [78, 77, 76] by middle_moufang ?76 ?77 ?78 +29345: Goal: +29345: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29345: Order: +29345: nrkbo +29345: Leaf order: +29345: commutator 1 2 0 +29345: associator 6 3 0 +29345: multiply 51 2 0 +29345: additive_identity 11 0 0 +29345: add 22 2 0 +29345: additive_inverse 20 1 1 0,3 +29345: s 3 4 2 0,2 +29345: d 2 0 2 4,2 +29345: c 2 0 2 3,2 +29345: b 2 0 2 2,2 +29345: a 2 0 2 1,2 +29346: Id : 20, {_}: + associator ?50 ?51 ?52 + =<= + add (multiply (multiply ?50 ?51) ?52) + (additive_inverse (multiply ?50 (multiply ?51 ?52))) + [52, 51, 50] by associator ?50 ?51 ?52 +29346: Id : 21, {_}: + commutator ?54 ?55 + =<= + add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55)) + [55, 54] by commutator ?54 ?55 +29346: Id : 22, {_}: + multiply (multiply (associator ?57 ?57 ?58) ?57) + (associator ?57 ?57 ?58) + =>= + additive_identity + [58, 57] by middle_associator ?57 ?58 +29346: Id : 23, {_}: + multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61) + [61, 60] by left_alternative ?60 ?61 +29346: Id : 24, {_}: + s ?63 ?64 ?65 ?66 + =<= + add + (add (associator (multiply ?63 ?64) ?65 ?66) + (additive_inverse (multiply ?64 (associator ?63 ?65 ?66)))) + (additive_inverse (multiply (associator ?64 ?65 ?66) ?63)) + [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66 +29346: Id : 25, {_}: + multiply ?68 (multiply ?69 (multiply ?70 ?69)) + =<= + multiply (multiply (multiply ?68 ?69) ?70) ?69 + [70, 69, 68] by right_moufang ?68 ?69 ?70 +29346: Id : 26, {_}: + multiply (multiply ?72 (multiply ?73 ?72)) ?74 + =>= + multiply ?72 (multiply ?73 (multiply ?72 ?74)) + [74, 73, 72] by left_moufang ?72 ?73 ?74 +29346: Id : 27, {_}: + multiply (multiply ?76 ?77) (multiply ?78 ?76) + =<= + multiply (multiply ?76 (multiply ?77 ?78)) ?76 + [78, 77, 76] by middle_moufang ?76 ?77 ?78 +29346: Goal: +29346: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29346: Order: +29346: kbo +29346: Leaf order: +29346: commutator 1 2 0 +29346: associator 6 3 0 +29346: multiply 51 2 0 +29346: additive_identity 11 0 0 +29346: add 22 2 0 +29346: additive_inverse 20 1 1 0,3 +29346: s 3 4 2 0,2 +29346: d 2 0 2 4,2 +29346: c 2 0 2 3,2 +29346: b 2 0 2 2,2 +29346: a 2 0 2 1,2 +% SZS status Timeout for RNG010-5.p +NO CLASH, using fixed ground order +29364: Facts: +29364: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29364: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29364: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29364: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29364: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29364: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29364: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29364: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29364: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29364: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29364: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29364: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29364: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29364: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29364: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29364: Id : 17, {_}: + s ?44 ?45 ?46 ?47 + =<= + add + (add (associator (multiply ?44 ?45) ?46 ?47) + (additive_inverse (multiply ?45 (associator ?44 ?46 ?47)))) + (additive_inverse (multiply (associator ?45 ?46 ?47) ?44)) + [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47 +29364: Id : 18, {_}: + multiply ?49 (multiply ?50 (multiply ?51 ?50)) + =<= + multiply (multiply (multiply ?49 ?50) ?51) ?50 + [51, 50, 49] by right_moufang ?49 ?50 ?51 +29364: Id : 19, {_}: + multiply (multiply ?53 (multiply ?54 ?53)) ?55 + =>= + multiply ?53 (multiply ?54 (multiply ?53 ?55)) + [55, 54, 53] by left_moufang ?53 ?54 ?55 +29364: Id : 20, {_}: + multiply (multiply ?57 ?58) (multiply ?59 ?57) + =<= + multiply (multiply ?57 (multiply ?58 ?59)) ?57 + [59, 58, 57] by middle_moufang ?57 ?58 ?59 +29364: Goal: +29364: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29364: Order: +29364: kbo +29364: Leaf order: +29364: commutator 1 2 0 +29364: associator 4 3 0 +29364: multiply 43 2 0 +29364: add 18 2 0 +29364: additive_identity 8 0 0 +29364: additive_inverse 9 1 1 0,3 +29364: s 3 4 2 0,2 +29364: d 2 0 2 4,2 +29364: c 2 0 2 3,2 +29364: b 2 0 2 2,2 +29364: a 2 0 2 1,2 +NO CLASH, using fixed ground order +29363: Facts: +29363: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29363: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29363: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29363: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29363: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29363: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29363: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29363: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29363: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29363: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29363: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29363: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29363: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29363: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29363: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29363: Id : 17, {_}: + s ?44 ?45 ?46 ?47 + =<= + add + (add (associator (multiply ?44 ?45) ?46 ?47) + (additive_inverse (multiply ?45 (associator ?44 ?46 ?47)))) + (additive_inverse (multiply (associator ?45 ?46 ?47) ?44)) + [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47 +29363: Id : 18, {_}: + multiply ?49 (multiply ?50 (multiply ?51 ?50)) + =?= + multiply (multiply (multiply ?49 ?50) ?51) ?50 + [51, 50, 49] by right_moufang ?49 ?50 ?51 +29363: Id : 19, {_}: + multiply (multiply ?53 (multiply ?54 ?53)) ?55 + =?= + multiply ?53 (multiply ?54 (multiply ?53 ?55)) + [55, 54, 53] by left_moufang ?53 ?54 ?55 +29363: Id : 20, {_}: + multiply (multiply ?57 ?58) (multiply ?59 ?57) + =?= + multiply (multiply ?57 (multiply ?58 ?59)) ?57 + [59, 58, 57] by middle_moufang ?57 ?58 ?59 +29363: Goal: +29363: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29363: Order: +29363: nrkbo +29363: Leaf order: +29363: commutator 1 2 0 +29363: associator 4 3 0 +29363: multiply 43 2 0 +29363: add 18 2 0 +29363: additive_identity 8 0 0 +29363: additive_inverse 9 1 1 0,3 +29363: s 3 4 2 0,2 +29363: d 2 0 2 4,2 +29363: c 2 0 2 3,2 +29363: b 2 0 2 2,2 +29363: a 2 0 2 1,2 +NO CLASH, using fixed ground order +29365: Facts: +29365: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29365: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29365: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29365: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29365: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29365: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29365: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29365: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29365: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29365: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29365: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29365: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29365: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29365: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29365: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29365: Id : 17, {_}: + s ?44 ?45 ?46 ?47 + =>= + add + (add (associator (multiply ?44 ?45) ?46 ?47) + (additive_inverse (multiply ?45 (associator ?44 ?46 ?47)))) + (additive_inverse (multiply (associator ?45 ?46 ?47) ?44)) + [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47 +29365: Id : 18, {_}: + multiply ?49 (multiply ?50 (multiply ?51 ?50)) + =<= + multiply (multiply (multiply ?49 ?50) ?51) ?50 + [51, 50, 49] by right_moufang ?49 ?50 ?51 +29365: Id : 19, {_}: + multiply (multiply ?53 (multiply ?54 ?53)) ?55 + =>= + multiply ?53 (multiply ?54 (multiply ?53 ?55)) + [55, 54, 53] by left_moufang ?53 ?54 ?55 +29365: Id : 20, {_}: + multiply (multiply ?57 ?58) (multiply ?59 ?57) + =<= + multiply (multiply ?57 (multiply ?58 ?59)) ?57 + [59, 58, 57] by middle_moufang ?57 ?58 ?59 +29365: Goal: +29365: Id : 1, {_}: + s a b c d =>= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29365: Order: +29365: lpo +29365: Leaf order: +29365: commutator 1 2 0 +29365: associator 4 3 0 +29365: multiply 43 2 0 +29365: add 18 2 0 +29365: additive_identity 8 0 0 +29365: additive_inverse 9 1 1 0,3 +29365: s 3 4 2 0,2 +29365: d 2 0 2 4,2 +29365: c 2 0 2 3,2 +29365: b 2 0 2 2,2 +29365: a 2 0 2 1,2 +% SZS status Timeout for RNG010-6.p +NO CLASH, using fixed ground order +29396: Facts: +29396: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29396: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29396: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29396: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29396: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29396: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29396: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29396: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29396: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29396: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29396: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29396: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29396: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29396: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29396: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29396: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29396: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =<= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29396: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =<= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29396: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29396: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29396: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29396: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29396: Id : 24, {_}: + s ?69 ?70 ?71 ?72 + =<= + add + (add (associator (multiply ?69 ?70) ?71 ?72) + (additive_inverse (multiply ?70 (associator ?69 ?71 ?72)))) + (additive_inverse (multiply (associator ?70 ?71 ?72) ?69)) + [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72 +29396: Id : 25, {_}: + multiply ?74 (multiply ?75 (multiply ?76 ?75)) + =?= + multiply (multiply (multiply ?74 ?75) ?76) ?75 + [76, 75, 74] by right_moufang ?74 ?75 ?76 +29396: Id : 26, {_}: + multiply (multiply ?78 (multiply ?79 ?78)) ?80 + =?= + multiply ?78 (multiply ?79 (multiply ?78 ?80)) + [80, 79, 78] by left_moufang ?78 ?79 ?80 +29396: Id : 27, {_}: + multiply (multiply ?82 ?83) (multiply ?84 ?82) + =?= + multiply (multiply ?82 (multiply ?83 ?84)) ?82 + [84, 83, 82] by middle_moufang ?82 ?83 ?84 +29396: Goal: +29396: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29396: Order: +29396: nrkbo +29396: Leaf order: +29396: commutator 1 2 0 +29396: associator 4 3 0 +29396: multiply 61 2 0 +29396: add 26 2 0 +29396: additive_identity 8 0 0 +29396: additive_inverse 25 1 1 0,3 +29396: s 3 4 2 0,2 +29396: d 2 0 2 4,2 +29396: c 2 0 2 3,2 +29396: b 2 0 2 2,2 +29396: a 2 0 2 1,2 +NO CLASH, using fixed ground order +29397: Facts: +29397: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29397: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29397: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29397: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29397: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29397: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29397: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29397: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29397: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29397: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29397: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29397: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29397: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29397: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29397: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29397: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29397: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =<= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29397: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =<= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29397: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29397: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29397: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29397: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29397: Id : 24, {_}: + s ?69 ?70 ?71 ?72 + =<= + add + (add (associator (multiply ?69 ?70) ?71 ?72) + (additive_inverse (multiply ?70 (associator ?69 ?71 ?72)))) + (additive_inverse (multiply (associator ?70 ?71 ?72) ?69)) + [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72 +29397: Id : 25, {_}: + multiply ?74 (multiply ?75 (multiply ?76 ?75)) + =<= + multiply (multiply (multiply ?74 ?75) ?76) ?75 + [76, 75, 74] by right_moufang ?74 ?75 ?76 +29397: Id : 26, {_}: + multiply (multiply ?78 (multiply ?79 ?78)) ?80 + =>= + multiply ?78 (multiply ?79 (multiply ?78 ?80)) + [80, 79, 78] by left_moufang ?78 ?79 ?80 +29397: Id : 27, {_}: + multiply (multiply ?82 ?83) (multiply ?84 ?82) + =<= + multiply (multiply ?82 (multiply ?83 ?84)) ?82 + [84, 83, 82] by middle_moufang ?82 ?83 ?84 +29397: Goal: +29397: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29397: Order: +29397: kbo +29397: Leaf order: +29397: commutator 1 2 0 +29397: associator 4 3 0 +29397: multiply 61 2 0 +29397: add 26 2 0 +29397: additive_identity 8 0 0 +29397: additive_inverse 25 1 1 0,3 +29397: s 3 4 2 0,2 +29397: d 2 0 2 4,2 +29397: c 2 0 2 3,2 +29397: b 2 0 2 2,2 +29397: a 2 0 2 1,2 +NO CLASH, using fixed ground order +29398: Facts: +29398: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29398: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29398: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29398: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29398: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29398: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29398: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29398: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29398: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29398: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29398: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29398: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29398: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29398: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29398: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29398: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29398: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =<= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29398: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =<= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29398: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29398: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29398: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29398: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29398: Id : 24, {_}: + s ?69 ?70 ?71 ?72 + =>= + add + (add (associator (multiply ?69 ?70) ?71 ?72) + (additive_inverse (multiply ?70 (associator ?69 ?71 ?72)))) + (additive_inverse (multiply (associator ?70 ?71 ?72) ?69)) + [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72 +29398: Id : 25, {_}: + multiply ?74 (multiply ?75 (multiply ?76 ?75)) + =<= + multiply (multiply (multiply ?74 ?75) ?76) ?75 + [76, 75, 74] by right_moufang ?74 ?75 ?76 +29398: Id : 26, {_}: + multiply (multiply ?78 (multiply ?79 ?78)) ?80 + =>= + multiply ?78 (multiply ?79 (multiply ?78 ?80)) + [80, 79, 78] by left_moufang ?78 ?79 ?80 +29398: Id : 27, {_}: + multiply (multiply ?82 ?83) (multiply ?84 ?82) + =<= + multiply (multiply ?82 (multiply ?83 ?84)) ?82 + [84, 83, 82] by middle_moufang ?82 ?83 ?84 +29398: Goal: +29398: Id : 1, {_}: + s a b c d =>= additive_inverse (s b a c d) + [] by prove_skew_symmetry +29398: Order: +29398: lpo +29398: Leaf order: +29398: commutator 1 2 0 +29398: associator 4 3 0 +29398: multiply 61 2 0 +29398: add 26 2 0 +29398: additive_identity 8 0 0 +29398: additive_inverse 25 1 1 0,3 +29398: s 3 4 2 0,2 +29398: d 2 0 2 4,2 +29398: c 2 0 2 3,2 +29398: b 2 0 2 2,2 +29398: a 2 0 2 1,2 +% SZS status Timeout for RNG010-7.p +NO CLASH, using fixed ground order +29437: Facts: +29437: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29437: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29437: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29437: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29437: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29437: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29437: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29437: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29437: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29437: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29437: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29437: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29437: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +29437: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +29437: Goal: +29437: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +29437: Order: +29437: nrkbo +29437: Leaf order: +29437: commutator 1 2 0 +29437: additive_inverse 6 1 0 +29437: additive_identity 9 0 1 3 +29437: add 17 2 1 0,2 +29437: multiply 22 2 4 0,1,2 +29437: associator 7 3 6 0,1,1,2 +29437: y 6 0 6 3,1,1,2 +29437: x 12 0 12 1,1,1,2 +NO CLASH, using fixed ground order +29438: Facts: +29438: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29438: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29438: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29438: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29438: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29438: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29438: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29438: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29438: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29438: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29438: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29438: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29438: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +29438: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +29438: Goal: +29438: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +29438: Order: +29438: kbo +29438: Leaf order: +29438: commutator 1 2 0 +29438: additive_inverse 6 1 0 +29438: additive_identity 9 0 1 3 +29438: add 17 2 1 0,2 +29438: multiply 22 2 4 0,1,2 +29438: associator 7 3 6 0,1,1,2 +29438: y 6 0 6 3,1,1,2 +29438: x 12 0 12 1,1,1,2 +NO CLASH, using fixed ground order +29439: Facts: +29439: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29439: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29439: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29439: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29439: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29439: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29439: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29439: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29439: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29439: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29439: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29439: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29439: Id : 14, {_}: + associator ?34 ?35 ?36 + =>= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +29439: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +29439: Goal: +29439: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +29439: Order: +29439: lpo +29439: Leaf order: +29439: commutator 1 2 0 +29439: additive_inverse 6 1 0 +29439: additive_identity 9 0 1 3 +29439: add 17 2 1 0,2 +29439: multiply 22 2 4 0,1,2 +29439: associator 7 3 6 0,1,1,2 +29439: y 6 0 6 3,1,1,2 +29439: x 12 0 12 1,1,1,2 +% SZS status Timeout for RNG030-6.p +NO CLASH, using fixed ground order +29722: Facts: +29722: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29722: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29722: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29722: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29722: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29722: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29722: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29722: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29722: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29722: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29722: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29722: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29722: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29722: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29722: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29722: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29722: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29722: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29722: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29722: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +29722: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +29722: Goal: +29722: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +29722: Order: +29722: nrkbo +29722: Leaf order: +29722: commutator 1 2 0 +29722: additive_inverse 22 1 0 +29722: additive_identity 9 0 1 3 +29722: add 25 2 1 0,2 +29722: multiply 40 2 4 0,1,2add +29722: associator 7 3 6 0,1,1,2 +29722: y 6 0 6 3,1,1,2 +29722: x 12 0 12 1,1,1,2 +NO CLASH, using fixed ground order +29723: Facts: +29723: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29723: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29723: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29723: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29723: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29723: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29723: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29723: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29723: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29723: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29723: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29723: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29723: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29723: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29723: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29723: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29723: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29723: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29723: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29723: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +29723: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +29723: Goal: +29723: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +29723: Order: +29723: kbo +29723: Leaf order: +29723: commutator 1 2 0 +29723: additive_inverse 22 1 0 +29723: additive_identity 9 0 1 3 +29723: add 25 2 1 0,2 +29723: multiply 40 2 4 0,1,2add +29723: associator 7 3 6 0,1,1,2 +29723: y 6 0 6 3,1,1,2 +29723: x 12 0 12 1,1,1,2 +NO CLASH, using fixed ground order +29724: Facts: +29724: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29724: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29724: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29724: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29724: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29724: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29724: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29724: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29724: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29724: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29724: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29724: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29724: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29724: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29724: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29724: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29724: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29724: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29724: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29724: Id : 21, {_}: + associator ?59 ?60 ?61 + =>= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +29724: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +29724: Goal: +29724: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +29724: Order: +29724: lpo +29724: Leaf order: +29724: commutator 1 2 0 +29724: additive_inverse 22 1 0 +29724: additive_identity 9 0 1 3 +29724: add 25 2 1 0,2 +29724: multiply 40 2 4 0,1,2add +29724: associator 7 3 6 0,1,1,2 +29724: y 6 0 6 3,1,1,2 +29724: x 12 0 12 1,1,1,2 +% SZS status Timeout for RNG030-7.p +NO CLASH, using fixed ground order +29762: Facts: +29762: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29762: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29762: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29762: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29762: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29762: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29762: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29762: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29762: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29762: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29762: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29762: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29762: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +29762: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +29762: Goal: +29762: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +29762: Order: +29762: nrkbo +29762: Leaf order: +29762: commutator 1 2 0 +29762: additive_inverse 6 1 0 +29762: additive_identity 9 0 1 3 +29762: add 21 2 5 0,2 +29762: multiply 30 2 12 0,1,1,1,1,1,2 +29762: associator 19 3 18 0,1,1,1,1,1,1,2 +29762: y 18 0 18 3,1,1,1,1,1,1,2 +29762: x 36 0 36 1,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +29763: Facts: +29763: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29763: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29763: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29763: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29763: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29763: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29763: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +NO CLASH, using fixed ground order +29764: Facts: +29764: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29764: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29764: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29764: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29764: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29764: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29764: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29764: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29764: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29764: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29764: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29764: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29764: Id : 14, {_}: + associator ?34 ?35 ?36 + =>= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +29764: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +29764: Goal: +29764: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +29764: Order: +29764: lpo +29764: Leaf order: +29764: commutator 1 2 0 +29764: additive_inverse 6 1 0 +29764: additive_identity 9 0 1 3 +29764: add 21 2 5 0,2 +29764: multiply 30 2 12 0,1,1,1,1,1,2 +29764: associator 19 3 18 0,1,1,1,1,1,1,2 +29764: y 18 0 18 3,1,1,1,1,1,1,2 +29764: x 36 0 36 1,1,1,1,1,1,1,2 +29763: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29763: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29763: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29763: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29763: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29763: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +29763: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +29763: Goal: +29763: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +29763: Order: +29763: kbo +29763: Leaf order: +29763: commutator 1 2 0 +29763: additive_inverse 6 1 0 +29763: additive_identity 9 0 1 3 +29763: add 21 2 5 0,2 +29763: multiply 30 2 12 0,1,1,1,1,1,2 +29763: associator 19 3 18 0,1,1,1,1,1,1,2 +29763: y 18 0 18 3,1,1,1,1,1,1,2 +29763: x 36 0 36 1,1,1,1,1,1,1,2 +% SZS status Timeout for RNG032-6.p +NO CLASH, using fixed ground order +29792: Facts: +29792: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29792: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29792: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29792: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29792: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29792: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29792: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29792: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29792: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29792: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29792: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29792: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29792: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29792: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29792: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29792: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29792: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29792: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29792: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29792: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +29792: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +29792: Goal: +29792: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +29792: Order: +29792: nrkbo +29792: Leaf order: +29792: commutator 1 2 0 +29792: additive_inverse 22 1 0 +29792: additive_identity 9 0 1 3 +29792: add 29 2 5 0,2 +29792: multiply 48 2 12 0,1,1,1,1,1,2add +29792: associator 19 3 18 0,1,1,1,1,1,1,2 +29792: y 18 0 18 3,1,1,1,1,1,1,2 +29792: x 36 0 36 1,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +29793: Facts: +29793: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29793: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29793: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29793: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29793: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29793: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29793: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29793: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29793: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29793: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29793: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29793: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29793: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29793: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29793: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29793: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29793: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29793: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29793: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29793: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +29793: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +29793: Goal: +29793: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +29793: Order: +29793: kbo +29793: Leaf order: +29793: commutator 1 2 0 +29793: additive_inverse 22 1 0 +29793: additive_identity 9 0 1 3 +29793: add 29 2 5 0,2 +29793: multiply 48 2 12 0,1,1,1,1,1,2add +29793: associator 19 3 18 0,1,1,1,1,1,1,2 +29793: y 18 0 18 3,1,1,1,1,1,1,2 +29793: x 36 0 36 1,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +29794: Facts: +29794: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29794: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29794: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29794: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29794: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29794: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29794: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29794: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29794: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29794: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29794: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29794: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29794: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29794: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29794: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29794: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29794: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29794: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29794: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29794: Id : 21, {_}: + associator ?59 ?60 ?61 + =>= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +29794: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +29794: Goal: +29794: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +29794: Order: +29794: lpo +29794: Leaf order: +29794: commutator 1 2 0 +29794: additive_inverse 22 1 0 +29794: additive_identity 9 0 1 3 +29794: add 29 2 5 0,2 +29794: multiply 48 2 12 0,1,1,1,1,1,2add +29794: associator 19 3 18 0,1,1,1,1,1,1,2 +29794: y 18 0 18 3,1,1,1,1,1,1,2 +29794: x 36 0 36 1,1,1,1,1,1,1,2 +% SZS status Timeout for RNG032-7.p +NO CLASH, using fixed ground order +29810: Facts: +29810: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29810: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29810: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29810: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29810: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29810: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29810: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29810: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29810: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29810: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29810: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29810: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29810: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29810: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29810: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29810: Goal: +29810: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29810: Order: +29810: nrkbo +29810: Leaf order: +29810: additive_inverse 6 1 0 +29810: additive_identity 8 0 0 +29810: add 18 2 2 0,2 +29810: commutator 2 2 1 0,3,2,2 +29810: associator 5 3 4 0,1,2 +29810: w 4 0 4 3,1,2 +29810: z 4 0 4 2,1,2 +29810: multiply 25 2 3 0,1,1,2 +29810: y 4 0 4 2,1,1,2 +29810: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29811: Facts: +29811: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29811: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29811: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29811: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29811: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29811: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29811: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29811: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29811: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29811: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29811: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29811: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29811: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29811: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29811: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29811: Goal: +29811: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29811: Order: +29811: kbo +29811: Leaf order: +29811: additive_inverse 6 1 0 +29811: additive_identity 8 0 0 +29811: add 18 2 2 0,2 +29811: commutator 2 2 1 0,3,2,2 +29811: associator 5 3 4 0,1,2 +29811: w 4 0 4 3,1,2 +29811: z 4 0 4 2,1,2 +29811: multiply 25 2 3 0,1,1,2 +29811: y 4 0 4 2,1,1,2 +29811: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29812: Facts: +29812: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29812: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29812: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29812: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29812: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29812: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29812: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29812: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29812: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29812: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29812: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29812: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29812: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29812: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29812: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29812: Goal: +29812: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29812: Order: +29812: lpo +29812: Leaf order: +29812: additive_inverse 6 1 0 +29812: additive_identity 8 0 0 +29812: add 18 2 2 0,2 +29812: commutator 2 2 1 0,3,2,2 +29812: associator 5 3 4 0,1,2 +29812: w 4 0 4 3,1,2 +29812: z 4 0 4 2,1,2 +29812: multiply 25 2 3 0,1,1,2 +29812: y 4 0 4 2,1,1,2 +29812: x 4 0 4 1,1,1,2 +% SZS status Timeout for RNG033-6.p +NO CLASH, using fixed ground order +29844: Facts: +29844: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29844: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29844: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29844: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29844: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29844: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29844: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29844: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29844: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29844: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29844: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29844: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29844: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29844: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29844: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29844: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29844: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29844: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29844: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29844: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29844: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29844: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29844: Goal: +29844: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29844: Order: +29844: nrkbo +29844: Leaf order: +29844: additive_inverse 22 1 0 +29844: additive_identity 8 0 0 +29844: add 26 2 2 0,2 +29844: commutator 2 2 1 0,3,2,2 +29844: associator 5 3 4 0,1,2 +29844: w 4 0 4 3,1,2 +29844: z 4 0 4 2,1,2 +29844: multiply 43 2 3 0,1,1,2 +29844: y 4 0 4 2,1,1,2 +29844: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29846: Facts: +29846: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29846: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29846: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29846: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29846: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29846: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29846: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29846: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29846: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29846: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29846: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29846: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29846: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29846: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29846: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29846: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29846: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29846: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29846: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29846: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29846: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29846: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29846: Goal: +29846: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29846: Order: +29846: lpo +29846: Leaf order: +29846: additive_inverse 22 1 0 +29846: additive_identity 8 0 0 +29846: add 26 2 2 0,2 +29846: commutator 2 2 1 0,3,2,2 +29846: associator 5 3 4 0,1,2 +29846: w 4 0 4 3,1,2 +29846: z 4 0 4 2,1,2 +29846: multiply 43 2 3 0,1,1,2 +29846: y 4 0 4 2,1,1,2 +29846: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29845: Facts: +29845: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29845: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29845: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29845: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29845: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29845: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29845: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29845: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29845: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29845: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29845: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29845: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29845: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29845: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29845: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29845: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29845: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29845: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29845: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29845: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29845: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29845: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29845: Goal: +29845: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29845: Order: +29845: kbo +29845: Leaf order: +29845: additive_inverse 22 1 0 +29845: additive_identity 8 0 0 +29845: add 26 2 2 0,2 +29845: commutator 2 2 1 0,3,2,2 +29845: associator 5 3 4 0,1,2 +29845: w 4 0 4 3,1,2 +29845: z 4 0 4 2,1,2 +29845: multiply 43 2 3 0,1,1,2 +29845: y 4 0 4 2,1,1,2 +29845: x 4 0 4 1,1,1,2 +% SZS status Timeout for RNG033-7.p +NO CLASH, using fixed ground order +29862: Facts: +29862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29862: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29862: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29862: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29862: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29862: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29862: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29862: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29862: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29862: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29862: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29862: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29862: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29862: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29862: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29862: Id : 17, {_}: + multiply ?44 (multiply ?45 (multiply ?46 ?45)) + =?= + multiply (multiply (multiply ?44 ?45) ?46) ?45 + [46, 45, 44] by right_moufang ?44 ?45 ?46 +29862: Goal: +29862: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29862: Order: +29862: nrkbo +29862: Leaf order: +29862: additive_inverse 6 1 0 +29862: additive_identity 8 0 0 +29862: add 18 2 2 0,2 +29862: commutator 2 2 1 0,3,2,2 +29862: associator 5 3 4 0,1,2 +29862: w 4 0 4 3,1,2 +29862: z 4 0 4 2,1,2 +29862: multiply 31 2 3 0,1,1,2 +29862: y 4 0 4 2,1,1,2 +29862: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29863: Facts: +29863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29863: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29863: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29863: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29863: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29863: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29863: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29863: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29863: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29863: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29863: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29863: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29863: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29863: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29863: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29863: Id : 17, {_}: + multiply ?44 (multiply ?45 (multiply ?46 ?45)) + =<= + multiply (multiply (multiply ?44 ?45) ?46) ?45 + [46, 45, 44] by right_moufang ?44 ?45 ?46 +29863: Goal: +29863: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29863: Order: +29863: kbo +29863: Leaf order: +29863: additive_inverse 6 1 0 +29863: additive_identity 8 0 0 +29863: add 18 2 2 0,2 +29863: commutator 2 2 1 0,3,2,2 +29863: associator 5 3 4 0,1,2 +29863: w 4 0 4 3,1,2 +29863: z 4 0 4 2,1,2 +29863: multiply 31 2 3 0,1,1,2 +29863: y 4 0 4 2,1,1,2 +29863: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29864: Facts: +29864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29864: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29864: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29864: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29864: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29864: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29864: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29864: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29864: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29864: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29864: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29864: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29864: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29864: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29864: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29864: Id : 17, {_}: + multiply ?44 (multiply ?45 (multiply ?46 ?45)) + =<= + multiply (multiply (multiply ?44 ?45) ?46) ?45 + [46, 45, 44] by right_moufang ?44 ?45 ?46 +29864: Goal: +29864: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29864: Order: +29864: lpo +29864: Leaf order: +29864: additive_inverse 6 1 0 +29864: additive_identity 8 0 0 +29864: add 18 2 2 0,2 +29864: commutator 2 2 1 0,3,2,2 +29864: associator 5 3 4 0,1,2 +29864: w 4 0 4 3,1,2 +29864: z 4 0 4 2,1,2 +29864: multiply 31 2 3 0,1,1,2 +29864: y 4 0 4 2,1,1,2 +29864: x 4 0 4 1,1,1,2 +% SZS status Timeout for RNG033-8.p +NO CLASH, using fixed ground order +29900: Facts: +29900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29900: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29900: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29900: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29900: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29900: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29900: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29900: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29900: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29900: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29900: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29900: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29900: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29900: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29900: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29900: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29900: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29900: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29900: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29900: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29900: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29900: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29900: Id : 24, {_}: + multiply ?69 (multiply ?70 (multiply ?71 ?70)) + =?= + multiply (multiply (multiply ?69 ?70) ?71) ?70 + [71, 70, 69] by right_moufang ?69 ?70 ?71 +29900: Goal: +29900: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29900: Order: +29900: nrkbo +29900: Leaf order: +29900: additive_inverse 22 1 0 +29900: additive_identity 8 0 0 +29900: add 26 2 2 0,2 +29900: commutator 2 2 1 0,3,2,2 +29900: associator 5 3 4 0,1,2 +29900: w 4 0 4 3,1,2 +29900: z 4 0 4 2,1,2 +29900: multiply 49 2 3 0,1,1,2 +29900: y 4 0 4 2,1,1,2 +29900: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29901: Facts: +29901: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29901: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29901: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29901: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29901: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29901: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29901: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29901: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29901: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29901: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29901: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29901: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29901: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29901: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29901: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29901: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29901: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29901: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29901: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29901: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29901: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29901: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29901: Id : 24, {_}: + multiply ?69 (multiply ?70 (multiply ?71 ?70)) + =<= + multiply (multiply (multiply ?69 ?70) ?71) ?70 + [71, 70, 69] by right_moufang ?69 ?70 ?71 +29901: Goal: +29901: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29901: Order: +29901: kbo +29901: Leaf order: +29901: additive_inverse 22 1 0 +29901: additive_identity 8 0 0 +29901: add 26 2 2 0,2 +29901: commutator 2 2 1 0,3,2,2 +29901: associator 5 3 4 0,1,2 +29901: w 4 0 4 3,1,2 +29901: z 4 0 4 2,1,2 +29901: multiply 49 2 3 0,1,1,2 +29901: y 4 0 4 2,1,1,2 +29901: x 4 0 4 1,1,1,2 +NO CLASH, using fixed ground order +29902: Facts: +29902: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29902: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29902: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29902: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29902: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29902: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29902: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29902: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29902: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29902: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29902: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29902: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29902: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29902: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29902: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29902: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29902: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29902: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29902: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29902: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29902: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29902: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29902: Id : 24, {_}: + multiply ?69 (multiply ?70 (multiply ?71 ?70)) + =<= + multiply (multiply (multiply ?69 ?70) ?71) ?70 + [71, 70, 69] by right_moufang ?69 ?70 ?71 +29902: Goal: +29902: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =<= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +29902: Order: +29902: lpo +29902: Leaf order: +29902: additive_inverse 22 1 0 +29902: additive_identity 8 0 0 +29902: add 26 2 2 0,2 +29902: commutator 2 2 1 0,3,2,2 +29902: associator 5 3 4 0,1,2 +29902: w 4 0 4 3,1,2 +29902: z 4 0 4 2,1,2 +29902: multiply 49 2 3 0,1,1,2 +29902: y 4 0 4 2,1,1,2 +29902: x 4 0 4 1,1,1,2 +% SZS status Timeout for RNG033-9.p +NO CLASH, using fixed ground order +29918: Facts: +29918: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29918: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29918: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +29918: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +29918: Id : 6, {_}: + add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +29918: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +29918: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +29918: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29918: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29918: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29 + [29] by x_fifthed_is_x ?29 +29918: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +29918: Goal: +29918: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +29918: Order: +29918: nrkbo +29918: Leaf order: +29918: additive_inverse 2 1 0 +29918: add 14 2 0 +29918: additive_identity 4 0 0 +29918: c 2 0 1 3 +29918: multiply 16 2 1 0,2 +29918: a 2 0 1 2,2 +29918: b 2 0 1 1,2 +NO CLASH, using fixed ground order +29919: Facts: +29919: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29919: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29919: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +29919: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +29919: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +29919: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +29919: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +29919: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29919: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29919: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29 + [29] by x_fifthed_is_x ?29 +29919: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +29919: Goal: +29919: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +29919: Order: +29919: kbo +29919: Leaf order: +29919: additive_inverse 2 1 0 +29919: add 14 2 0 +29919: additive_identity 4 0 0 +NO CLASH, using fixed ground order +29920: Facts: +29920: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29920: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29920: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +29920: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +29920: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +29920: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +29920: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +29920: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29920: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29920: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29 + [29] by x_fifthed_is_x ?29 +29920: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +29920: Goal: +29920: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +29920: Order: +29920: lpo +29920: Leaf order: +29920: additive_inverse 2 1 0 +29920: add 14 2 0 +29920: additive_identity 4 0 0 +29920: c 2 0 1 3 +29920: multiply 16 2 1 0,2 +29920: a 2 0 1 2,2 +29920: b 2 0 1 1,2 +29919: c 2 0 1 3 +29919: multiply 16 2 1 0,2 +29919: a 2 0 1 2,2 +29919: b 2 0 1 1,2 +% SZS status Timeout for RNG036-7.p +NO CLASH, using fixed ground order +29951: Facts: +29951: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +29951: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +29951: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +29951: Goal: +29951: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +29951: Order: +29951: nrkbo +29951: Leaf order: +29951: add 12 2 3 0,2 +29951: negate 9 1 5 0,1,2 +29951: b 3 0 3 1,2,1,1,2 +29951: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +29952: Facts: +29952: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +29952: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +29952: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +29952: Goal: +29952: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +29952: Order: +29952: kbo +29952: Leaf order: +29952: add 12 2 3 0,2 +29952: negate 9 1 5 0,1,2 +29952: b 3 0 3 1,2,1,1,2 +29952: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +29953: Facts: +29953: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +29953: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +29953: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +29953: Goal: +29953: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +29953: Order: +29953: lpo +29953: Leaf order: +29953: add 12 2 3 0,2 +29953: negate 9 1 5 0,1,2 +29953: b 3 0 3 1,2,1,1,2 +29953: a 2 0 2 1,1,1,2 +% SZS status Timeout for ROB001-1.p +NO CLASH, using fixed ground order +29969: Facts: +29969: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +29969: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +29969: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +29969: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +29969: Goal: +29969: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +29969: Order: +29969: nrkbo +29969: Leaf order: +29969: add 13 2 3 0,2 +29969: negate 11 1 5 0,1,2 +29969: b 5 0 3 1,2,1,1,2 +29969: a 3 0 2 1,1,1,2 +NO CLASH, using fixed ground order +29970: Facts: +29970: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +29970: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +29970: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +29970: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +29970: Goal: +29970: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +29970: Order: +29970: kbo +29970: Leaf order: +29970: add 13 2 3 0,2 +29970: negate 11 1 5 0,1,2 +29970: b 5 0 3 1,2,1,1,2 +29970: a 3 0 2 1,1,1,2 +NO CLASH, using fixed ground order +29971: Facts: +29971: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +29971: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +29971: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +29971: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +29971: Goal: +29971: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +29971: Order: +29971: lpo +29971: Leaf order: +29971: add 13 2 3 0,2 +29971: negate 11 1 5 0,1,2 +29971: b 5 0 3 1,2,1,1,2 +29971: a 3 0 2 1,1,1,2 +% SZS status Timeout for ROB007-1.p +NO CLASH, using fixed ground order +29998: Facts: +29998: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +29998: Id : 3, {_}: + add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +29998: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +29998: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +29998: Goal: +29998: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +29998: Order: +29998: nrkbo +29998: Leaf order: +29998: b 2 0 0 +29998: a 1 0 0 +29998: negate 6 1 0 +29998: add 11 2 1 0,2 +NO CLASH, using fixed ground order +29999: Facts: +29999: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +29999: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +29999: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +29999: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +29999: Goal: +29999: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +29999: Order: +29999: kbo +29999: Leaf order: +29999: b 2 0 0 +29999: a 1 0 0 +29999: negate 6 1 0 +29999: add 11 2 1 0,2 +NO CLASH, using fixed ground order +30000: Facts: +30000: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30000: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30000: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30000: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +30000: Goal: +30000: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30000: Order: +30000: lpo +30000: Leaf order: +30000: b 2 0 0 +30000: a 1 0 0 +30000: negate 6 1 0 +30000: add 11 2 1 0,2 +% SZS status Timeout for ROB007-2.p +NO CLASH, using fixed ground order +30074: Facts: +30074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +NO CLASH, using fixed ground order +30075: Facts: +30075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30075: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30075: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30075: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +30075: Goal: +30075: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30075: Order: +30075: kbo +30075: Leaf order: +30075: add 13 2 3 0,2 +30075: negate 11 1 5 0,1,2 +30075: b 5 0 3 1,2,1,1,2 +30075: a 3 0 2 1,1,1,2 +30074: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30074: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30074: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +30074: Goal: +30074: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30074: Order: +30074: nrkbo +30074: Leaf order: +30074: add 13 2 3 0,2 +30074: negate 11 1 5 0,1,2 +30074: b 5 0 3 1,2,1,1,2 +30074: a 3 0 2 1,1,1,2 +NO CLASH, using fixed ground order +30076: Facts: +30076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30076: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30076: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30076: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +30076: Goal: +30076: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30076: Order: +30076: lpo +30076: Leaf order: +30076: add 13 2 3 0,2 +30076: negate 11 1 5 0,1,2 +30076: b 5 0 3 1,2,1,1,2 +30076: a 3 0 2 1,1,1,2 +% SZS status Timeout for ROB020-1.p +NO CLASH, using fixed ground order +30104: Facts: +30104: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30104: Id : 3, {_}: + add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30104: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30104: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +30104: Goal: +30104: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30104: Order: +30104: nrkbo +30104: Leaf order: +30104: b 2 0 0 +30104: a 1 0 0 +30104: negate 6 1 0 +30104: add 11 2 1 0,2 +NO CLASH, using fixed ground order +30105: Facts: +30105: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30105: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30105: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30105: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +30105: Goal: +30105: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30105: Order: +30105: kbo +30105: Leaf order: +30105: b 2 0 0 +30105: a 1 0 0 +30105: negate 6 1 0 +30105: add 11 2 1 0,2 +NO CLASH, using fixed ground order +30106: Facts: +30106: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30106: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30106: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30106: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +30106: Goal: +30106: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30106: Order: +30106: lpo +30106: Leaf order: +30106: b 2 0 0 +30106: a 1 0 0 +30106: negate 6 1 0 +30106: add 11 2 1 0,2 +% SZS status Timeout for ROB020-2.p +NO CLASH, using fixed ground order +30123: Facts: +30123: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30123: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30123: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30123: Id : 5, {_}: + negate (add (negate (add a (add a b))) (negate (add a (negate b)))) + =>= + a + [] by the_condition +30123: Goal: +30123: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30123: Order: +30123: nrkbo +30123: Leaf order: +30123: add 16 2 3 0,2 +30123: negate 13 1 5 0,1,2 +30123: b 5 0 3 1,2,1,1,2 +30123: a 6 0 2 1,1,1,2 +NO CLASH, using fixed ground order +30124: Facts: +30124: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30124: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30124: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30124: Id : 5, {_}: + negate (add (negate (add a (add a b))) (negate (add a (negate b)))) + =>= + a + [] by the_condition +30124: Goal: +30124: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30124: Order: +30124: kbo +30124: Leaf order: +30124: add 16 2 3 0,2 +30124: negate 13 1 5 0,1,2 +30124: b 5 0 3 1,2,1,1,2 +30124: a 6 0 2 1,1,1,2 +NO CLASH, using fixed ground order +30125: Facts: +30125: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30125: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30125: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30125: Id : 5, {_}: + negate (add (negate (add a (add a b))) (negate (add a (negate b)))) + =>= + a + [] by the_condition +30125: Goal: +30125: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30125: Order: +30125: lpo +30125: Leaf order: +30125: add 16 2 3 0,2 +30125: negate 13 1 5 0,1,2 +30125: b 5 0 3 1,2,1,1,2 +30125: a 6 0 2 1,1,1,2 +% SZS status Timeout for ROB024-1.p +NO CLASH, using fixed ground order +30152: Facts: +30152: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30152: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30152: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30152: Id : 5, {_}: negate (negate c) =>= c [] by double_negation +30152: Goal: +30152: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30152: Order: +30152: nrkbo +30152: Leaf order: +30152: c 2 0 0 +30152: add 12 2 3 0,2 +30152: negate 11 1 5 0,1,2 +30152: b 3 0 3 1,2,1,1,2 +30152: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +30153: Facts: +30153: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30153: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30153: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30153: Id : 5, {_}: negate (negate c) =>= c [] by double_negation +30153: Goal: +30153: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30153: Order: +30153: kbo +30153: Leaf order: +30153: c 2 0 0 +30153: add 12 2 3 0,2 +30153: negate 11 1 5 0,1,2 +30153: b 3 0 3 1,2,1,1,2 +30153: a 2 0 2 1,1,1,2 +NO CLASH, using fixed ground order +30154: Facts: +30154: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +30154: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +30154: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +30154: Id : 5, {_}: negate (negate c) =>= c [] by double_negation +30154: Goal: +30154: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +30154: Order: +30154: lpo +30154: Leaf order: +30154: c 2 0 0 +30154: add 12 2 3 0,2 +30154: negate 11 1 5 0,1,2 +30154: b 3 0 3 1,2,1,1,2 +30154: a 2 0 2 1,1,1,2 +% SZS status Timeout for ROB027-1.p +NO CLASH, using fixed ground order +30170: Facts: +30170: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +30170: Id : 3, {_}: + add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +30170: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +30170: Goal: +30170: Id : 1, {_}: + negate (add ?1 ?2) =>= negate ?2 + [2, 1] by prove_absorption_within_negation ?1 ?2 +30170: Order: +30170: nrkbo +30170: Leaf order: +30170: negate 6 1 2 0,2 +30170: add 10 2 1 0,1,2 +NO CLASH, using fixed ground order +30171: Facts: +30171: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +30171: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +30171: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +30171: Goal: +30171: Id : 1, {_}: + negate (add ?1 ?2) =>= negate ?2 + [2, 1] by prove_absorption_within_negation ?1 ?2 +30171: Order: +30171: kbo +30171: Leaf order: +30171: negate 6 1 2 0,2 +30171: add 10 2 1 0,1,2 +NO CLASH, using fixed ground order +30172: Facts: +30172: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +30172: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +30172: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +30172: Goal: +30172: Id : 1, {_}: + negate (add ?1 ?2) =>= negate ?2 + [2, 1] by prove_absorption_within_negation ?1 ?2 +30172: Order: +30172: lpo +30172: Leaf order: +30172: negate 6 1 2 0,2 +30172: add 10 2 1 0,1,2 +% SZS status Timeout for ROB031-1.p +NO CLASH, using fixed ground order +30204: Facts: +30204: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +NO CLASH, using fixed ground order +30205: Facts: +30205: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +30205: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +30205: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +30205: Goal: +30205: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2 +30205: Order: +30205: kbo +30205: Leaf order: +30205: negate 4 1 0 +30205: add 10 2 1 0,2 +30204: Id : 3, {_}: + add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +30204: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +30204: Goal: +30204: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2 +30204: Order: +30204: nrkbo +30204: Leaf order: +30204: negate 4 1 0 +30204: add 10 2 1 0,2 +NO CLASH, using fixed ground order +30206: Facts: +30206: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +30206: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +30206: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +30206: Goal: +30206: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2 +30206: Order: +30206: lpo +30206: Leaf order: +30206: negate 4 1 0 +30206: add 10 2 1 0,2 +% SZS status Timeout for ROB032-1.p diff --git a/helm/software/components/binaries/matitaprover/log.90.fixed-order.2 b/helm/software/components/binaries/matitaprover/log.90.fixed-order.2 new file mode 100644 index 000000000..1ee4169b6 --- /dev/null +++ b/helm/software/components/binaries/matitaprover/log.90.fixed-order.2 @@ -0,0 +1,46518 @@ +CLASH, statistics insufficient +CLASH, statistics insufficient +22279: Facts: +22279: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +22279: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +22279: Id : 4, {_}: + add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +22279: Id : 5, {_}: + add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +22279: Id : 6, {_}: + multiply (add ?16 ?17) ?18 + =<= + add (multiply ?16 ?18) (multiply ?17 ?18) + [18, 17, 16] by distributivity3 ?16 ?17 ?18 +22279: Id : 7, {_}: + multiply ?20 (add ?21 ?22) + =<= + add (multiply ?20 ?21) (multiply ?20 ?22) + [22, 21, 20] by distributivity4 ?20 ?21 ?22 +22279: Id : 8, {_}: + add ?24 (inverse ?24) =>= multiplicative_identity + [24] by additive_inverse1 ?24 +22279: Id : 9, {_}: + add (inverse ?26) ?26 =>= multiplicative_identity + [26] by additive_inverse2 ?26 +22279: Id : 10, {_}: + multiply ?28 (inverse ?28) =>= additive_identity + [28] by multiplicative_inverse1 ?28 +22279: Id : 11, {_}: + multiply (inverse ?30) ?30 =>= additive_identity + [30] by multiplicative_inverse2 ?30 +22279: Id : 12, {_}: + multiply ?32 multiplicative_identity =>= ?32 + [32] by multiplicative_id1 ?32 +22279: Id : 13, {_}: + multiply multiplicative_identity ?34 =>= ?34 + [34] by multiplicative_id2 ?34 +22279: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +22279: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +22279: Goal: +22279: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22279: Order: +22279: kbo +22279: Leaf order: +22279: a 2 0 2 1,2 +22279: b 2 0 2 1,2,2 +22279: c 2 0 2 2,2,2 +22279: multiplicative_identity 4 0 0 +22279: additive_identity 4 0 0 +22279: inverse 4 1 0 +22279: add 16 2 0 multiply +22279: multiply 20 2 4 0,2add +CLASH, statistics insufficient +22280: Facts: +22280: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +22280: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +22280: Id : 4, {_}: + add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +22280: Id : 5, {_}: + add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +22280: Id : 6, {_}: + multiply (add ?16 ?17) ?18 + =>= + add (multiply ?16 ?18) (multiply ?17 ?18) + [18, 17, 16] by distributivity3 ?16 ?17 ?18 +22280: Id : 7, {_}: + multiply ?20 (add ?21 ?22) + =>= + add (multiply ?20 ?21) (multiply ?20 ?22) + [22, 21, 20] by distributivity4 ?20 ?21 ?22 +22280: Id : 8, {_}: + add ?24 (inverse ?24) =>= multiplicative_identity + [24] by additive_inverse1 ?24 +22280: Id : 9, {_}: + add (inverse ?26) ?26 =>= multiplicative_identity + [26] by additive_inverse2 ?26 +22280: Id : 10, {_}: + multiply ?28 (inverse ?28) =>= additive_identity + [28] by multiplicative_inverse1 ?28 +22280: Id : 11, {_}: + multiply (inverse ?30) ?30 =>= additive_identity + [30] by multiplicative_inverse2 ?30 +22280: Id : 12, {_}: + multiply ?32 multiplicative_identity =>= ?32 + [32] by multiplicative_id1 ?32 +22280: Id : 13, {_}: + multiply multiplicative_identity ?34 =>= ?34 + [34] by multiplicative_id2 ?34 +22280: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +22280: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +22280: Goal: +22280: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22280: Order: +22280: lpo +22280: Leaf order: +22280: a 2 0 2 1,2 +22280: b 2 0 2 1,2,2 +22280: c 2 0 2 2,2,2 +22280: multiplicative_identity 4 0 0 +22280: additive_identity 4 0 0 +22280: inverse 4 1 0 +22280: add 16 2 0 multiply +22280: multiply 20 2 4 0,2add +22278: Facts: +22278: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +22278: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +22278: Id : 4, {_}: + add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +22278: Id : 5, {_}: + add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +22278: Id : 6, {_}: + multiply (add ?16 ?17) ?18 + =<= + add (multiply ?16 ?18) (multiply ?17 ?18) + [18, 17, 16] by distributivity3 ?16 ?17 ?18 +22278: Id : 7, {_}: + multiply ?20 (add ?21 ?22) + =<= + add (multiply ?20 ?21) (multiply ?20 ?22) + [22, 21, 20] by distributivity4 ?20 ?21 ?22 +22278: Id : 8, {_}: + add ?24 (inverse ?24) =>= multiplicative_identity + [24] by additive_inverse1 ?24 +22278: Id : 9, {_}: + add (inverse ?26) ?26 =>= multiplicative_identity + [26] by additive_inverse2 ?26 +22278: Id : 10, {_}: + multiply ?28 (inverse ?28) =>= additive_identity + [28] by multiplicative_inverse1 ?28 +22278: Id : 11, {_}: + multiply (inverse ?30) ?30 =>= additive_identity + [30] by multiplicative_inverse2 ?30 +22278: Id : 12, {_}: + multiply ?32 multiplicative_identity =>= ?32 + [32] by multiplicative_id1 ?32 +22278: Id : 13, {_}: + multiply multiplicative_identity ?34 =>= ?34 + [34] by multiplicative_id2 ?34 +22278: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +22278: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +22278: Goal: +22278: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22278: Order: +22278: nrkbo +22278: Leaf order: +22278: a 2 0 2 1,2 +22278: b 2 0 2 1,2,2 +22278: c 2 0 2 2,2,2 +22278: multiplicative_identity 4 0 0 +22278: additive_identity 4 0 0 +22278: inverse 4 1 0 +22278: add 16 2 0 multiply +22278: multiply 20 2 4 0,2add +Statistics : +Max weight : 22 +Found proof, 16.771241s +% SZS status Unsatisfiable for BOO007-2.p +% SZS output start CNFRefutation for BOO007-2.p +Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32 +Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22 +Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38 +Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36 +Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28 +Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34 +Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24 +Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +Id : 31, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80 +Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14 +Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6 +Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18 +Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10 +Id : 65, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3 +Id : 46, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3 +Id : 58, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 46 with 5 at 2 +Id : 32, {_}: add (multiply ?82 ?83) ?84 =<= multiply (add ?82 ?84) (add ?84 ?83) [84, 83, 82] by Super 31 with 2 at 2,3 +Id : 121, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3 +Id : 2169, {_}: add ?2910 (multiply (inverse ?2910) ?2911) =>= add ?2910 ?2911 [2911, 2910] by Demod 121 with 13 at 3 +Id : 2179, {_}: add ?2938 additive_identity =<= add ?2938 (inverse (inverse ?2938)) [2938] by Super 2169 with 10 at 2,2 +Id : 2230, {_}: ?2938 =<= add ?2938 (inverse (inverse ?2938)) [2938] by Demod 2179 with 14 at 2 +Id : 2429, {_}: add (multiply ?3159 (inverse (inverse ?3160))) ?3160 =>= multiply (add ?3159 ?3160) ?3160 [3160, 3159] by Super 32 with 2230 at 2,3 +Id : 2455, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply (add ?3159 ?3160) ?3160 [3159, 3160] by Demod 2429 with 2 at 2 +Id : 2456, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= multiply ?3160 (add ?3159 ?3160) [3159, 3160] by Demod 2455 with 3 at 3 +Id : 248, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3 +Id : 2457, {_}: add ?3160 (multiply ?3159 (inverse (inverse ?3160))) =>= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2456 with 248 at 3 +Id : 120, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3 +Id : 124, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 120 with 3 at 3 +Id : 3170, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 124 with 13 at 3 +Id : 144, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3 +Id : 3378, {_}: multiply ?4138 (add (inverse ?4138) ?4139) =>= multiply ?4138 ?4139 [4139, 4138] by Demod 144 with 15 at 3 +Id : 3399, {_}: multiply ?4195 (inverse ?4195) =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Super 3378 with 2230 at 2,2 +Id : 3488, {_}: additive_identity =<= multiply ?4195 (inverse (inverse (inverse ?4195))) [4195] by Demod 3399 with 10 at 2 +Id : 3900, {_}: add (inverse (inverse ?4844)) additive_identity =?= add (inverse (inverse ?4844)) ?4844 [4844] by Super 3170 with 3488 at 2,2 +Id : 3924, {_}: add additive_identity (inverse (inverse ?4844)) =<= add (inverse (inverse ?4844)) ?4844 [4844] by Demod 3900 with 2 at 2 +Id : 3925, {_}: add additive_identity (inverse (inverse ?4844)) =?= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3924 with 2 at 3 +Id : 3926, {_}: inverse (inverse ?4844) =<= add ?4844 (inverse (inverse ?4844)) [4844] by Demod 3925 with 15 at 2 +Id : 3927, {_}: inverse (inverse ?4844) =>= ?4844 [4844] by Demod 3926 with 2230 at 3 +Id : 6845, {_}: add ?3160 (multiply ?3159 ?3160) =?= add (multiply additive_identity ?3159) ?3160 [3159, 3160] by Demod 2457 with 3927 at 2,2,2 +Id : 1130, {_}: add (multiply additive_identity ?1671) ?1672 =<= multiply ?1672 (add ?1671 ?1672) [1672, 1671] by Super 4 with 15 at 1,3 +Id : 1134, {_}: add (multiply additive_identity ?1683) (inverse ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Super 1130 with 8 at 2,3 +Id : 1186, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply (inverse ?1683) multiplicative_identity [1683] by Demod 1134 with 2 at 2 +Id : 1187, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= multiply multiplicative_identity (inverse ?1683) [1683] by Demod 1186 with 3 at 3 +Id : 1188, {_}: add (inverse ?1683) (multiply additive_identity ?1683) =>= inverse ?1683 [1683] by Demod 1187 with 13 at 3 +Id : 3360, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 144 with 15 at 3 +Id : 3364, {_}: add (inverse (add (inverse additive_identity) ?4095)) (multiply additive_identity ?4095) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Super 1188 with 3360 at 2,2 +Id : 3442, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add (inverse additive_identity) ?4095) [4095] by Demod 3364 with 2 at 2 +Id : 249, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2 +Id : 3443, {_}: add (multiply additive_identity ?4095) (inverse (add (inverse additive_identity) ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3442 with 249 at 1,1,3 +Id : 3444, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse (add multiplicative_identity ?4095) [4095] by Demod 3443 with 249 at 1,1,2,2 +Id : 2180, {_}: add ?2940 (inverse ?2940) =>= add ?2940 multiplicative_identity [2940] by Super 2169 with 12 at 2,2 +Id : 2231, {_}: multiplicative_identity =<= add ?2940 multiplicative_identity [2940] by Demod 2180 with 8 at 2 +Id : 2263, {_}: add multiplicative_identity ?3015 =>= multiplicative_identity [3015] by Super 2 with 2231 at 3 +Id : 3445, {_}: add (multiply additive_identity ?4095) (inverse (add multiplicative_identity ?4095)) =>= inverse multiplicative_identity [4095] by Demod 3444 with 2263 at 1,3 +Id : 3446, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4095] by Demod 3445 with 2263 at 1,2,2 +Id : 191, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2 +Id : 3447, {_}: add (multiply additive_identity ?4095) (inverse multiplicative_identity) =>= additive_identity [4095] by Demod 3446 with 191 at 3 +Id : 3448, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3447 with 2 at 2 +Id : 3449, {_}: add additive_identity (multiply additive_identity ?4095) =>= additive_identity [4095] by Demod 3448 with 191 at 1,2 +Id : 3450, {_}: multiply additive_identity ?4095 =>= additive_identity [4095] by Demod 3449 with 15 at 2 +Id : 6846, {_}: add ?3160 (multiply ?3159 ?3160) =>= add additive_identity ?3160 [3159, 3160] by Demod 6845 with 3450 at 1,3 +Id : 6847, {_}: add ?3160 (multiply ?3159 ?3160) =>= ?3160 [3159, 3160] by Demod 6846 with 15 at 3 +Id : 6852, {_}: add ?8316 (multiply ?8316 ?8317) =>= ?8316 [8317, 8316] by Super 58 with 6847 at 3 +Id : 7003, {_}: add (multiply ?8541 (multiply ?8542 ?8543)) (multiply ?8541 ?8543) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8543, 8542, 8541] by Super 65 with 6852 at 1,3 +Id : 7114, {_}: add (multiply ?8541 ?8543) (multiply ?8541 (multiply ?8542 ?8543)) =>= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7003 with 2 at 2 +Id : 7115, {_}: multiply ?8541 (add ?8543 (multiply ?8542 ?8543)) =?= multiply ?8541 (multiply (add ?8542 ?8541) ?8543) [8542, 8543, 8541] by Demod 7114 with 7 at 2 +Id : 21444, {_}: multiply ?30534 ?30535 =<= multiply ?30534 (multiply (add ?30536 ?30534) ?30535) [30536, 30535, 30534] by Demod 7115 with 6847 at 2,2 +Id : 21466, {_}: multiply (multiply ?30625 ?30626) ?30627 =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30626, 30625] by Super 21444 with 6847 at 1,2,3 +Id : 147, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3 +Id : 152, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 147 with 3 at 2 +Id : 4375, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 152 with 15 at 3 +Id : 532, {_}: add (multiply ?866 ?867) ?868 =<= multiply (add ?866 ?868) (add ?868 ?867) [868, 867, 866] by Super 31 with 2 at 2,3 +Id : 547, {_}: add (multiply ?925 ?926) (inverse ?925) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Super 532 with 8 at 1,3 +Id : 583, {_}: add (inverse ?925) (multiply ?925 ?926) =?= multiply multiplicative_identity (add (inverse ?925) ?926) [926, 925] by Demod 547 with 2 at 2 +Id : 584, {_}: add (inverse ?925) (multiply ?925 ?926) =>= add (inverse ?925) ?926 [926, 925] by Demod 583 with 13 at 3 +Id : 4646, {_}: multiply (inverse (inverse ?5719)) (add (inverse ?5719) ?5720) =>= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5720, 5719] by Super 4375 with 584 at 2,2 +Id : 4685, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (multiply ?5719 ?5720) (inverse (inverse ?5719)) [5719, 5720] by Demod 4646 with 4375 at 2 +Id : 4686, {_}: multiply ?5720 (inverse (inverse ?5719)) =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4685 with 3 at 3 +Id : 4687, {_}: multiply ?5720 ?5719 =<= multiply (inverse (inverse ?5719)) (multiply ?5719 ?5720) [5719, 5720] by Demod 4686 with 3927 at 2,2 +Id : 4688, {_}: multiply ?5720 ?5719 =<= multiply ?5719 (multiply ?5719 ?5720) [5719, 5720] by Demod 4687 with 3927 at 1,3 +Id : 21467, {_}: multiply (multiply ?30629 ?30630) ?30631 =<= multiply (multiply ?30629 ?30630) (multiply ?30629 ?30631) [30631, 30630, 30629] by Super 21444 with 6852 at 1,2,3 +Id : 36399, {_}: multiply (multiply ?58815 ?58816) (multiply ?58815 ?58817) =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Super 4688 with 21467 at 2,3 +Id : 36627, {_}: multiply (multiply ?58815 ?58816) ?58817 =<= multiply (multiply ?58815 ?58817) (multiply (multiply ?58815 ?58817) ?58816) [58817, 58816, 58815] by Demod 36399 with 21467 at 2 +Id : 36628, {_}: multiply (multiply ?58815 ?58816) ?58817 =>= multiply ?58816 (multiply ?58815 ?58817) [58817, 58816, 58815] by Demod 36627 with 4688 at 3 +Id : 36893, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply (multiply ?30625 ?30626) (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 21466 with 36628 at 2 +Id : 36894, {_}: multiply ?30626 (multiply ?30625 ?30627) =<= multiply ?30626 (multiply ?30625 (multiply ?30626 ?30627)) [30627, 30625, 30626] by Demod 36893 with 36628 at 3 +Id : 3522, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 248 with 3450 at 1,2 +Id : 3543, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3522 with 15 at 2 +Id : 7020, {_}: add (multiply ?8599 (multiply ?8600 ?8601)) ?8600 =>= multiply (add ?8599 ?8600) ?8600 [8601, 8600, 8599] by Super 32 with 6852 at 2,3 +Id : 7087, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply (add ?8599 ?8600) ?8600 [8601, 8599, 8600] by Demod 7020 with 2 at 2 +Id : 7088, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= multiply ?8600 (add ?8599 ?8600) [8601, 8599, 8600] by Demod 7087 with 3 at 3 +Id : 7089, {_}: add ?8600 (multiply ?8599 (multiply ?8600 ?8601)) =>= ?8600 [8601, 8599, 8600] by Demod 7088 with 3543 at 3 +Id : 20142, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply (multiply ?27776 (multiply ?27777 ?27778)) ?27777 [27778, 27777, 27776] by Super 3543 with 7089 at 2,3 +Id : 20329, {_}: multiply ?27776 (multiply ?27777 ?27778) =<= multiply ?27777 (multiply ?27776 (multiply ?27777 ?27778)) [27778, 27777, 27776] by Demod 20142 with 3 at 3 +Id : 36895, {_}: multiply ?30626 (multiply ?30625 ?30627) =?= multiply ?30625 (multiply ?30626 ?30627) [30627, 30625, 30626] by Demod 36894 with 20329 at 3 +Id : 34, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 31 with 2 at 1,3 +Id : 6868, {_}: add (multiply (multiply ?8366 ?8367) ?8368) ?8367 =>= multiply ?8367 (add ?8368 ?8367) [8368, 8367, 8366] by Super 34 with 6847 at 1,3 +Id : 6940, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= multiply ?8367 (add ?8368 ?8367) [8368, 8366, 8367] by Demod 6868 with 2 at 2 +Id : 6941, {_}: add ?8367 (multiply (multiply ?8366 ?8367) ?8368) =>= ?8367 [8368, 8366, 8367] by Demod 6940 with 3543 at 3 +Id : 19816, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply (multiply (multiply ?27180 ?27181) ?27182) ?27181 [27182, 27181, 27180] by Super 3543 with 6941 at 2,3 +Id : 19977, {_}: multiply (multiply ?27180 ?27181) ?27182 =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27181, 27180] by Demod 19816 with 3 at 3 +Id : 36891, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply (multiply ?27180 ?27181) ?27182) [27182, 27180, 27181] by Demod 19977 with 36628 at 2 +Id : 36892, {_}: multiply ?27181 (multiply ?27180 ?27182) =<= multiply ?27181 (multiply ?27181 (multiply ?27180 ?27182)) [27182, 27180, 27181] by Demod 36891 with 36628 at 2,3 +Id : 36900, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply (multiply ?27180 ?27182) ?27181 [27182, 27180, 27181] by Demod 36892 with 4688 at 3 +Id : 36901, {_}: multiply ?27181 (multiply ?27180 ?27182) =?= multiply ?27182 (multiply ?27180 ?27181) [27182, 27180, 27181] by Demod 36900 with 36628 at 3 +Id : 37364, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 37363 with 3 at 2,2 +Id : 37363, {_}: multiply c (multiply a b) =?= multiply c (multiply b a) [] by Demod 37362 with 3 at 2,3 +Id : 37362, {_}: multiply c (multiply a b) =?= multiply c (multiply a b) [] by Demod 37361 with 36901 at 2 +Id : 37361, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 37360 with 3 at 3 +Id : 37360, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 36895 at 2 +Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity +% SZS output end CNFRefutation for BOO007-2.p +22279: solved BOO007-2.p in 8.384524 using kbo +22279: status Unsatisfiable for BOO007-2.p +CLASH, statistics insufficient +22287: Facts: +22287: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +22287: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +22287: Id : 4, {_}: + add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +22287: Id : 5, {_}: + multiply ?12 (add ?13 ?14) + =<= + add (multiply ?12 ?13) (multiply ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +22287: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +22287: Id : 7, {_}: + multiply ?18 multiplicative_identity =>= ?18 + [18] by multiplicative_id1 ?18 +22287: Id : 8, {_}: + add ?20 (inverse ?20) =>= multiplicative_identity + [20] by additive_inverse1 ?20 +22287: Id : 9, {_}: + multiply ?22 (inverse ?22) =>= additive_identity + [22] by multiplicative_inverse1 ?22 +22287: Goal: +22287: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22287: Order: +22287: nrkbo +22287: Leaf order: +22287: additive_identity 2 0 0 +22287: multiplicative_identity 2 0 0 +22287: a 2 0 2 1,2 +22287: b 2 0 2 1,2,2 +22287: c 2 0 2 2,2,2 +22287: inverse 2 1 0 +22287: add 9 2 0 multiply +22287: multiply 13 2 4 0,2add +CLASH, statistics insufficient +22288: Facts: +22288: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +22288: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +22288: Id : 4, {_}: + add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +22288: Id : 5, {_}: + multiply ?12 (add ?13 ?14) + =<= + add (multiply ?12 ?13) (multiply ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +22288: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +22288: Id : 7, {_}: + multiply ?18 multiplicative_identity =>= ?18 + [18] by multiplicative_id1 ?18 +22288: Id : 8, {_}: + add ?20 (inverse ?20) =>= multiplicative_identity + [20] by additive_inverse1 ?20 +22288: Id : 9, {_}: + multiply ?22 (inverse ?22) =>= additive_identity + [22] by multiplicative_inverse1 ?22 +22288: Goal: +22288: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22288: Order: +22288: kbo +22288: Leaf order: +22288: additive_identity 2 0 0 +22288: multiplicative_identity 2 0 0 +22288: a 2 0 2 1,2 +22288: b 2 0 2 1,2,2 +22288: c 2 0 2 2,2,2 +22288: inverse 2 1 0 +22288: add 9 2 0 multiply +22288: multiply 13 2 4 0,2add +CLASH, statistics insufficient +22289: Facts: +22289: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +22289: Id : 3, {_}: + multiply ?5 ?6 =?= multiply ?6 ?5 + [6, 5] by commutativity_of_multiply ?5 ?6 +22289: Id : 4, {_}: + add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) + [10, 9, 8] by distributivity1 ?8 ?9 ?10 +22289: Id : 5, {_}: + multiply ?12 (add ?13 ?14) + =>= + add (multiply ?12 ?13) (multiply ?12 ?14) + [14, 13, 12] by distributivity2 ?12 ?13 ?14 +22289: Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +22289: Id : 7, {_}: + multiply ?18 multiplicative_identity =>= ?18 + [18] by multiplicative_id1 ?18 +22289: Id : 8, {_}: + add ?20 (inverse ?20) =>= multiplicative_identity + [20] by additive_inverse1 ?20 +22289: Id : 9, {_}: + multiply ?22 (inverse ?22) =>= additive_identity + [22] by multiplicative_inverse1 ?22 +22289: Goal: +22289: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22289: Order: +22289: lpo +22289: Leaf order: +22289: additive_identity 2 0 0 +22289: multiplicative_identity 2 0 0 +22289: a 2 0 2 1,2 +22289: b 2 0 2 1,2,2 +22289: c 2 0 2 2,2,2 +22289: inverse 2 1 0 +22289: add 9 2 0 multiply +22289: multiply 13 2 4 0,2add +Statistics : +Max weight : 25 +Found proof, 23.744275s +% SZS status Unsatisfiable for BOO007-4.p +% SZS output start CNFRefutation for BOO007-4.p +Id : 44, {_}: multiply ?112 (add ?113 ?114) =<= add (multiply ?112 ?113) (multiply ?112 ?114) [114, 113, 112] by distributivity2 ?112 ?113 ?114 +Id : 4, {_}: add ?8 (multiply ?9 ?10) =<= multiply (add ?8 ?9) (add ?8 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10 +Id : 9, {_}: multiply ?22 (inverse ?22) =>= additive_identity [22] by multiplicative_inverse1 ?22 +Id : 5, {_}: multiply ?12 (add ?13 ?14) =<= add (multiply ?12 ?13) (multiply ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14 +Id : 7, {_}: multiply ?18 multiplicative_identity =>= ?18 [18] by multiplicative_id1 ?18 +Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6 +Id : 8, {_}: add ?20 (inverse ?20) =>= multiplicative_identity [20] by additive_inverse1 ?20 +Id : 6, {_}: add ?16 additive_identity =>= ?16 [16] by additive_id1 ?16 +Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +Id : 25, {_}: add ?62 (multiply ?63 ?64) =<= multiply (add ?62 ?63) (add ?62 ?64) [64, 63, 62] by distributivity1 ?62 ?63 ?64 +Id : 516, {_}: add ?742 (multiply ?743 ?744) =<= multiply (add ?742 ?743) (add ?744 ?742) [744, 743, 742] by Super 25 with 2 at 2,3 +Id : 530, {_}: add ?796 (multiply additive_identity ?797) =<= multiply ?796 (add ?797 ?796) [797, 796] by Super 516 with 6 at 1,3 +Id : 1019, {_}: add ?1448 (multiply additive_identity ?1449) =<= multiply ?1448 (add ?1449 ?1448) [1449, 1448] by Super 516 with 6 at 1,3 +Id : 1024, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply (inverse ?1462) multiplicative_identity [1462] by Super 1019 with 8 at 2,3 +Id : 1064, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= multiply multiplicative_identity (inverse ?1462) [1462] by Demod 1024 with 3 at 3 +Id : 75, {_}: multiply multiplicative_identity ?178 =>= ?178 [178] by Super 3 with 7 at 3 +Id : 1065, {_}: add (inverse ?1462) (multiply additive_identity ?1462) =>= inverse ?1462 [1462] by Demod 1064 with 75 at 3 +Id : 97, {_}: multiply ?204 (add (inverse ?204) ?205) =>= add additive_identity (multiply ?204 ?205) [205, 204] by Super 5 with 9 at 1,3 +Id : 63, {_}: add additive_identity ?160 =>= ?160 [160] by Super 2 with 6 at 3 +Id : 2714, {_}: multiply ?204 (add (inverse ?204) ?205) =>= multiply ?204 ?205 [205, 204] by Demod 97 with 63 at 3 +Id : 2718, {_}: add (inverse (add (inverse additive_identity) ?3390)) (multiply additive_identity ?3390) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Super 1065 with 2714 at 2,2 +Id : 2791, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add (inverse additive_identity) ?3390) [3390] by Demod 2718 with 2 at 2 +Id : 184, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 63 at 2 +Id : 2792, {_}: add (multiply additive_identity ?3390) (inverse (add (inverse additive_identity) ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2791 with 184 at 1,1,3 +Id : 2793, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse (add multiplicative_identity ?3390) [3390] by Demod 2792 with 184 at 1,1,2,2 +Id : 86, {_}: add ?193 (multiply (inverse ?193) ?194) =>= multiply multiplicative_identity (add ?193 ?194) [194, 193] by Super 4 with 8 at 1,3 +Id : 1836, {_}: add ?2310 (multiply (inverse ?2310) ?2311) =>= add ?2310 ?2311 [2311, 2310] by Demod 86 with 75 at 3 +Id : 1846, {_}: add ?2338 (inverse ?2338) =>= add ?2338 multiplicative_identity [2338] by Super 1836 with 7 at 2,2 +Id : 1890, {_}: multiplicative_identity =<= add ?2338 multiplicative_identity [2338] by Demod 1846 with 8 at 2 +Id : 1917, {_}: add multiplicative_identity ?2407 =>= multiplicative_identity [2407] by Super 2 with 1890 at 3 +Id : 2794, {_}: add (multiply additive_identity ?3390) (inverse (add multiplicative_identity ?3390)) =>= inverse multiplicative_identity [3390] by Demod 2793 with 1917 at 1,3 +Id : 2795, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= inverse multiplicative_identity [3390] by Demod 2794 with 1917 at 1,2,2 +Id : 476, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 9 with 75 at 2 +Id : 2796, {_}: add (multiply additive_identity ?3390) (inverse multiplicative_identity) =>= additive_identity [3390] by Demod 2795 with 476 at 3 +Id : 2797, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2796 with 2 at 2 +Id : 2798, {_}: add additive_identity (multiply additive_identity ?3390) =>= additive_identity [3390] by Demod 2797 with 476 at 1,2 +Id : 2799, {_}: multiply additive_identity ?3390 =>= additive_identity [3390] by Demod 2798 with 63 at 2 +Id : 2854, {_}: add ?796 additive_identity =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 530 with 2799 at 2,2 +Id : 2870, {_}: ?796 =<= multiply ?796 (add ?797 ?796) [797, 796] by Demod 2854 with 6 at 2 +Id : 2113, {_}: add (multiply ?2595 ?2596) (multiply ?2597 (multiply ?2595 ?2598)) =<= multiply (add (multiply ?2595 ?2596) ?2597) (multiply ?2595 (add ?2596 ?2598)) [2598, 2597, 2596, 2595] by Super 4 with 5 at 2,3 +Id : 2126, {_}: add (multiply ?2655 multiplicative_identity) (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Super 2113 with 1917 at 2,2,3 +Id : 2201, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (add (multiply ?2655 multiplicative_identity) ?2656) (multiply ?2655 multiplicative_identity) [2657, 2656, 2655] by Demod 2126 with 7 at 1,2 +Id : 2202, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= multiply (multiply ?2655 multiplicative_identity) (add (multiply ?2655 multiplicative_identity) ?2656) [2657, 2656, 2655] by Demod 2201 with 3 at 3 +Id : 62, {_}: add ?157 (multiply additive_identity ?158) =<= multiply ?157 (add ?157 ?158) [158, 157] by Super 4 with 6 at 1,3 +Id : 2203, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =?= add (multiply ?2655 multiplicative_identity) (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2202 with 62 at 3 +Id : 2204, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 (multiply additive_identity ?2656) [2657, 2656, 2655] by Demod 2203 with 7 at 1,3 +Id : 12654, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= add ?2655 additive_identity [2657, 2656, 2655] by Demod 2204 with 2799 at 2,3 +Id : 12655, {_}: add ?2655 (multiply ?2656 (multiply ?2655 ?2657)) =>= ?2655 [2657, 2656, 2655] by Demod 12654 with 6 at 3 +Id : 12666, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply (multiply ?15534 (multiply ?15535 ?15536)) ?15535 [15536, 15535, 15534] by Super 2870 with 12655 at 2,3 +Id : 21339, {_}: multiply ?30912 (multiply ?30913 ?30914) =<= multiply ?30913 (multiply ?30912 (multiply ?30913 ?30914)) [30914, 30913, 30912] by Demod 12666 with 3 at 3 +Id : 21342, {_}: multiply ?30924 (multiply ?30925 ?30926) =<= multiply ?30925 (multiply ?30924 (multiply ?30926 ?30925)) [30926, 30925, 30924] by Super 21339 with 3 at 2,2,3 +Id : 28, {_}: add ?74 (multiply ?75 ?76) =<= multiply (add ?75 ?74) (add ?74 ?76) [76, 75, 74] by Super 25 with 2 at 1,3 +Id : 4808, {_}: multiply ?5796 (add ?5797 ?5798) =<= add (multiply ?5796 ?5797) (multiply ?5798 ?5796) [5798, 5797, 5796] by Super 44 with 3 at 2,3 +Id : 4837, {_}: multiply ?5913 (add multiplicative_identity ?5914) =?= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Super 4808 with 7 at 1,3 +Id : 4917, {_}: multiply ?5913 multiplicative_identity =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4837 with 1917 at 2,2 +Id : 4918, {_}: ?5913 =<= add ?5913 (multiply ?5914 ?5913) [5914, 5913] by Demod 4917 with 7 at 2 +Id : 5091, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply (add ?6287 ?6286) ?6286 [6288, 6287, 6286] by Super 28 with 4918 at 2,3 +Id : 5151, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= multiply ?6286 (add ?6287 ?6286) [6288, 6287, 6286] by Demod 5091 with 3 at 3 +Id : 5152, {_}: add ?6286 (multiply ?6287 (multiply ?6288 ?6286)) =>= ?6286 [6288, 6287, 6286] by Demod 5151 with 2870 at 3 +Id : 19536, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply (multiply ?27546 (multiply ?27547 ?27548)) ?27548 [27548, 27547, 27546] by Super 2870 with 5152 at 2,3 +Id : 19689, {_}: multiply ?27546 (multiply ?27547 ?27548) =<= multiply ?27548 (multiply ?27546 (multiply ?27547 ?27548)) [27548, 27547, 27546] by Demod 19536 with 3 at 3 +Id : 31289, {_}: multiply ?30924 (multiply ?30925 ?30926) =?= multiply ?30924 (multiply ?30926 ?30925) [30926, 30925, 30924] by Demod 21342 with 19689 at 3 +Id : 521, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply (add (inverse ?761) ?762) multiplicative_identity [762, 761] by Super 516 with 8 at 2,3 +Id : 550, {_}: add (inverse ?761) (multiply ?762 ?761) =?= multiply multiplicative_identity (add (inverse ?761) ?762) [762, 761] by Demod 521 with 3 at 3 +Id : 551, {_}: add (inverse ?761) (multiply ?762 ?761) =>= add (inverse ?761) ?762 [762, 761] by Demod 550 with 75 at 3 +Id : 3740, {_}: multiply ?4638 (add (inverse ?4638) ?4639) =>= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Super 2714 with 551 at 2,2 +Id : 3782, {_}: multiply ?4638 ?4639 =<= multiply ?4638 (multiply ?4639 ?4638) [4639, 4638] by Demod 3740 with 2714 at 2 +Id : 3863, {_}: multiply ?4768 (add ?4769 (multiply ?4770 ?4768)) =>= add (multiply ?4768 ?4769) (multiply ?4768 ?4770) [4770, 4769, 4768] by Super 5 with 3782 at 2,3 +Id : 15840, {_}: multiply ?20984 (add ?20985 (multiply ?20986 ?20984)) =>= multiply ?20984 (add ?20985 ?20986) [20986, 20985, 20984] by Demod 3863 with 5 at 3 +Id : 15903, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add (multiply ?21235 ?21236) ?21235) [21236, 21235, 21234] by Super 15840 with 5 at 2,2 +Id : 16059, {_}: multiply ?21234 (multiply ?21235 (add ?21236 ?21234)) =?= multiply ?21234 (add ?21235 (multiply ?21235 ?21236)) [21236, 21235, 21234] by Demod 15903 with 2 at 2,3 +Id : 4814, {_}: multiply ?5818 (add ?5819 multiplicative_identity) =?= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Super 4808 with 75 at 2,3 +Id : 4891, {_}: multiply ?5818 multiplicative_identity =<= add (multiply ?5818 ?5819) ?5818 [5819, 5818] by Demod 4814 with 1890 at 2,2 +Id : 4892, {_}: multiply ?5818 multiplicative_identity =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4891 with 2 at 3 +Id : 4893, {_}: ?5818 =<= add ?5818 (multiply ?5818 ?5819) [5819, 5818] by Demod 4892 with 7 at 2 +Id : 26804, {_}: multiply ?40743 (multiply ?40744 (add ?40745 ?40743)) =>= multiply ?40743 ?40744 [40745, 40744, 40743] by Demod 16059 with 4893 at 2,3 +Id : 26854, {_}: multiply (multiply ?40962 ?40963) (multiply ?40964 ?40962) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Super 26804 with 4893 at 2,2,2 +Id : 38294, {_}: multiply (multiply ?63621 ?63622) (multiply ?63621 ?63623) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Super 31289 with 26854 at 3 +Id : 26855, {_}: multiply (multiply ?40966 ?40967) (multiply ?40968 ?40967) =>= multiply (multiply ?40966 ?40967) ?40968 [40968, 40967, 40966] by Super 26804 with 4918 at 2,2,2 +Id : 38958, {_}: multiply (multiply ?65058 ?65059) (multiply ?65059 ?65060) =>= multiply (multiply ?65058 ?65059) ?65060 [65060, 65059, 65058] by Super 31289 with 26855 at 3 +Id : 38330, {_}: multiply (multiply ?63784 ?63785) (multiply ?63785 ?63786) =>= multiply (multiply ?63785 ?63786) ?63784 [63786, 63785, 63784] by Super 3 with 26854 at 3 +Id : 46713, {_}: multiply (multiply ?65059 ?65060) ?65058 =?= multiply (multiply ?65058 ?65059) ?65060 [65058, 65060, 65059] by Demod 38958 with 38330 at 2 +Id : 46797, {_}: multiply ?81775 (multiply ?81776 ?81777) =<= multiply (multiply ?81775 ?81776) ?81777 [81777, 81776, 81775] by Super 3 with 46713 at 3 +Id : 47389, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply (multiply ?63621 ?63622) ?63623 [63623, 63622, 63621] by Demod 38294 with 46797 at 2 +Id : 47390, {_}: multiply ?63621 (multiply ?63622 (multiply ?63621 ?63623)) =>= multiply ?63621 (multiply ?63622 ?63623) [63623, 63622, 63621] by Demod 47389 with 46797 at 3 +Id : 12809, {_}: multiply ?15534 (multiply ?15535 ?15536) =<= multiply ?15535 (multiply ?15534 (multiply ?15535 ?15536)) [15536, 15535, 15534] by Demod 12666 with 3 at 3 +Id : 47391, {_}: multiply ?63622 (multiply ?63621 ?63623) =?= multiply ?63621 (multiply ?63622 ?63623) [63623, 63621, 63622] by Demod 47390 with 12809 at 2 +Id : 47371, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply (multiply ?40962 ?40963) ?40964 [40964, 40963, 40962] by Demod 26854 with 46797 at 2 +Id : 47372, {_}: multiply ?40962 (multiply ?40963 (multiply ?40964 ?40962)) =>= multiply ?40962 (multiply ?40963 ?40964) [40964, 40963, 40962] by Demod 47371 with 46797 at 3 +Id : 47409, {_}: multiply ?40963 (multiply ?40964 ?40962) =?= multiply ?40962 (multiply ?40963 ?40964) [40962, 40964, 40963] by Demod 47372 with 19689 at 2 +Id : 47847, {_}: multiply c (multiply b a) =?= multiply c (multiply b a) [] by Demod 47846 with 3 at 2,3 +Id : 47846, {_}: multiply c (multiply b a) =?= multiply c (multiply a b) [] by Demod 47845 with 47409 at 2 +Id : 47845, {_}: multiply b (multiply a c) =>= multiply c (multiply a b) [] by Demod 47844 with 3 at 3 +Id : 47844, {_}: multiply b (multiply a c) =<= multiply (multiply a b) c [] by Demod 1 with 47391 at 2 +Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity +% SZS output end CNFRefutation for BOO007-4.p +22288: solved BOO007-4.p in 11.836739 using kbo +22288: status Unsatisfiable for BOO007-4.p +CLASH, statistics insufficient +22303: Facts: +22303: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =>= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +22303: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +22303: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +22303: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +22303: Id : 6, {_}: + multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 + [19, 18, 17] by l2 ?17 ?18 ?19 +22303: Id : 7, {_}: + multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 + [23, 22, 21] by l4 ?21 ?22 ?23 +22303: Id : 8, {_}: + add (multiply ?25 (inverse ?25)) ?26 =>= ?26 + [26, 25] by property3_dual ?25 ?26 +22303: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +22303: Id : 10, {_}: + multiply ?30 (inverse ?30) =>= n0 + [30] by multiplicative_inverse ?30 +22303: Id : 11, {_}: + add (add ?32 ?33) ?34 =?= add ?32 (add ?33 ?34) + [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +22303: Id : 12, {_}: + multiply (multiply ?36 ?37) ?38 =?= multiply ?36 (multiply ?37 ?38) + [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +22303: Goal: +22303: Id : 1, {_}: + multiply a (add b c) =<= add (multiply b a) (multiply c a) + [] by prove_multiply_add_property +22303: Order: +22303: nrkbo +22303: Leaf order: +22303: n1 1 0 0 +22303: n0 1 0 0 +22303: b 2 0 2 1,2,2 +22303: c 2 0 2 2,2,2 +22303: a 3 0 3 1,2 +22303: inverse 4 1 0 +22303: add 21 2 2 0,2,2multiply +22303: multiply 22 2 3 0,2add +CLASH, statistics insufficient +22304: Facts: +22304: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =>= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +22304: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +22304: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +22304: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +22304: Id : 6, {_}: + multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 + [19, 18, 17] by l2 ?17 ?18 ?19 +22304: Id : 7, {_}: + multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 + [23, 22, 21] by l4 ?21 ?22 ?23 +22304: Id : 8, {_}: + add (multiply ?25 (inverse ?25)) ?26 =>= ?26 + [26, 25] by property3_dual ?25 ?26 +22304: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +22304: Id : 10, {_}: + multiply ?30 (inverse ?30) =>= n0 + [30] by multiplicative_inverse ?30 +22304: Id : 11, {_}: + add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) + [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +22304: Id : 12, {_}: + multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) + [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +CLASH, statistics insufficient +22305: Facts: +22305: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =>= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +22305: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +22305: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +22305: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +22305: Id : 6, {_}: + multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 + [19, 18, 17] by l2 ?17 ?18 ?19 +22305: Id : 7, {_}: + multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 + [23, 22, 21] by l4 ?21 ?22 ?23 +22305: Id : 8, {_}: + add (multiply ?25 (inverse ?25)) ?26 =>= ?26 + [26, 25] by property3_dual ?25 ?26 +22305: Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +22305: Id : 10, {_}: + multiply ?30 (inverse ?30) =>= n0 + [30] by multiplicative_inverse ?30 +22305: Id : 11, {_}: + add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) + [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +22305: Id : 12, {_}: + multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) + [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +22305: Goal: +22305: Id : 1, {_}: + multiply a (add b c) =<= add (multiply b a) (multiply c a) + [] by prove_multiply_add_property +22305: Order: +22305: lpo +22305: Leaf order: +22305: n1 1 0 0 +22305: n0 1 0 0 +22305: b 2 0 2 1,2,2 +22305: c 2 0 2 2,2,2 +22305: a 3 0 3 1,2 +22305: inverse 4 1 0 +22305: add 21 2 2 0,2,2multiply +22305: multiply 22 2 3 0,2add +22304: Goal: +22304: Id : 1, {_}: + multiply a (add b c) =<= add (multiply b a) (multiply c a) + [] by prove_multiply_add_property +22304: Order: +22304: kbo +22304: Leaf order: +22304: n1 1 0 0 +22304: n0 1 0 0 +22304: b 2 0 2 1,2,2 +22304: c 2 0 2 2,2,2 +22304: a 3 0 3 1,2 +22304: inverse 4 1 0 +22304: add 21 2 2 0,2,2multiply +22304: multiply 22 2 3 0,2add +Statistics : +Max weight : 29 +Found proof, 45.037592s +% SZS status Unsatisfiable for BOO031-1.p +% SZS output start CNFRefutation for BOO031-1.p +Id : 7, {_}: multiply (multiply (add ?21 ?22) (add ?22 ?23)) ?22 =>= ?22 [23, 22, 21] by l4 ?21 ?22 ?23 +Id : 10, {_}: multiply ?30 (inverse ?30) =>= n0 [30] by multiplicative_inverse ?30 +Id : 8, {_}: add (multiply ?25 (inverse ?25)) ?26 =>= ?26 [26, 25] by property3_dual ?25 ?26 +Id : 12, {_}: multiply (multiply ?36 ?37) ?38 =>= multiply ?36 (multiply ?37 ?38) [38, 37, 36] by associativity_of_multiply ?36 ?37 ?38 +Id : 52, {_}: multiply (multiply (add ?189 ?190) (add ?190 ?191)) ?190 =>= ?190 [191, 190, 189] by l4 ?189 ?190 ?191 +Id : 9, {_}: add ?28 (inverse ?28) =>= n1 [28] by additive_inverse ?28 +Id : 5, {_}: multiply (add ?14 (inverse ?14)) ?15 =>= ?15 [15, 14] by property3 ?14 ?15 +Id : 2, {_}: add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) =>= multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) [4, 3, 2] by distributivity ?2 ?3 ?4 +Id : 18, {_}: add (add (multiply ?58 ?59) (multiply ?59 ?60)) ?59 =>= ?59 [60, 59, 58] by l3 ?58 ?59 ?60 +Id : 11, {_}: add (add ?32 ?33) ?34 =>= add ?32 (add ?33 ?34) [34, 33, 32] by associativity_of_add ?32 ?33 ?34 +Id : 4, {_}: add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 [12, 11, 10] by l3 ?10 ?11 ?12 +Id : 37, {_}: multiply ?128 (add ?129 (add ?128 ?130)) =>= ?128 [130, 129, 128] by l2 ?128 ?129 ?130 +Id : 6, {_}: multiply ?17 (add ?18 (add ?17 ?19)) =>= ?17 [19, 18, 17] by l2 ?17 ?18 ?19 +Id : 3, {_}: add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 [8, 7, 6] by l1 ?6 ?7 ?8 +Id : 35, {_}: add ?121 (multiply ?122 ?121) =>= ?121 [122, 121] by Super 3 with 6 at 2,2,2 +Id : 42, {_}: multiply ?149 (add ?149 ?150) =>= ?149 [150, 149] by Super 37 with 4 at 2,2 +Id : 1579, {_}: add (add ?2436 ?2437) ?2436 =>= add ?2436 ?2437 [2437, 2436] by Super 35 with 42 at 2,2 +Id : 1609, {_}: add ?2436 (add ?2437 ?2436) =>= add ?2436 ?2437 [2437, 2436] by Demod 1579 with 11 at 2 +Id : 19, {_}: add (multiply ?62 ?63) ?63 =>= ?63 [63, 62] by Super 18 with 3 at 1,2 +Id : 39, {_}: multiply ?137 (add ?138 ?137) =>= ?137 [138, 137] by Super 37 with 3 at 2,2,2 +Id : 1363, {_}: add ?2089 (add ?2090 ?2089) =>= add ?2090 ?2089 [2090, 2089] by Super 19 with 39 at 1,2 +Id : 2844, {_}: add ?2437 ?2436 =?= add ?2436 ?2437 [2436, 2437] by Demod 1609 with 1363 at 2 +Id : 32, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add (multiply ?109 ?107) ?107) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Super 2 with 6 at 2,2,2 +Id : 5786, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add (add ?106 (add ?107 ?108)) ?109) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 32 with 2844 at 2,2 +Id : 5787, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?107 (add ?106 (add ?107 ?108)))) [109, 108, 107, 106] by Demod 5786 with 11 at 1,3 +Id : 1088, {_}: add (multiply ?1721 ?1722) ?1722 =>= ?1722 [1722, 1721] by Super 18 with 3 at 1,2 +Id : 1091, {_}: add ?1730 (add ?1731 (add ?1730 ?1732)) =>= add ?1731 (add ?1730 ?1732) [1732, 1731, 1730] by Super 1088 with 6 at 1,2 +Id : 5788, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) (add ?107 (multiply ?109 ?107)) =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5787 with 1091 at 2,2,3 +Id : 5789, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add (add ?107 ?108) ?109)) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5788 with 35 at 2,2 +Id : 5790, {_}: add (multiply (add ?106 (add ?107 ?108)) ?109) ?107 =<= multiply (add ?106 (add ?107 (add ?108 ?109))) (multiply (add ?109 ?107) (add ?106 (add ?107 ?108))) [109, 108, 107, 106] by Demod 5789 with 11 at 2,1,3 +Id : 5814, {_}: add ?7785 (multiply (add ?7786 (add ?7785 ?7787)) ?7788) =<= multiply (add ?7786 (add ?7785 (add ?7787 ?7788))) (multiply (add ?7788 ?7785) (add ?7786 (add ?7785 ?7787))) [7788, 7787, 7786, 7785] by Demod 5790 with 2844 at 2 +Id : 79, {_}: multiply n1 ?15 =>= ?15 [15] by Demod 5 with 9 at 1,2 +Id : 1095, {_}: add ?1743 ?1743 =>= ?1743 [1743] by Super 1088 with 79 at 1,2 +Id : 5853, {_}: add ?7982 (multiply (add (add ?7982 ?7983) (add ?7982 ?7983)) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Super 5814 with 1095 at 2,2,3 +Id : 6183, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) (multiply (add ?7984 ?7982) (add ?7982 ?7983)) [7984, 7983, 7982] by Demod 5853 with 11 at 1,2,2 +Id : 1663, {_}: multiply (add ?2570 ?2571) ?2571 =>= ?2571 [2571, 2570] by Super 52 with 6 at 1,2 +Id : 1673, {_}: multiply ?2601 (multiply ?2602 ?2601) =>= multiply ?2602 ?2601 [2602, 2601] by Super 1663 with 35 at 1,2 +Id : 1365, {_}: multiply ?2095 (add ?2096 ?2095) =>= ?2095 [2096, 2095] by Super 37 with 3 at 2,2,2 +Id : 22, {_}: add ?71 (multiply ?71 ?72) =>= ?71 [72, 71] by Super 3 with 5 at 2,2 +Id : 1374, {_}: multiply (multiply ?2123 ?2124) ?2123 =>= multiply ?2123 ?2124 [2124, 2123] by Super 1365 with 22 at 2,2 +Id : 1408, {_}: multiply ?2123 (multiply ?2124 ?2123) =>= multiply ?2123 ?2124 [2124, 2123] by Demod 1374 with 12 at 2 +Id : 2987, {_}: multiply ?2601 ?2602 =?= multiply ?2602 ?2601 [2602, 2601] by Demod 1673 with 1408 at 2 +Id : 6184, {_}: add ?7982 (multiply (add ?7982 (add ?7983 (add ?7982 ?7983))) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6183 with 2987 at 3 +Id : 6185, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (multiply (add ?7984 ?7982) (add ?7982 ?7983)) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984))) [7984, 7983, 7982] by Demod 6184 with 1091 at 1,2,2 +Id : 6186, {_}: add ?7982 (multiply (add ?7983 (add ?7982 ?7983)) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6185 with 12 at 3 +Id : 6187, {_}: add ?7982 (multiply (add ?7982 ?7983) ?7984) =<= multiply (add ?7984 ?7982) (multiply (add ?7982 ?7983) (add (add ?7982 ?7983) (add ?7982 (add ?7983 ?7984)))) [7984, 7983, 7982] by Demod 6186 with 1363 at 1,2,2 +Id : 13074, {_}: add ?18195 (multiply (add ?18195 ?18196) ?18197) =>= multiply (add ?18197 ?18195) (add ?18195 ?18196) [18197, 18196, 18195] by Demod 6187 with 42 at 2,3 +Id : 16401, {_}: add ?22734 (multiply (add ?22735 ?22734) ?22736) =>= multiply (add ?22736 ?22734) (add ?22734 ?22735) [22736, 22735, 22734] by Super 13074 with 2844 at 1,2,2 +Id : 18162, {_}: add ?24925 (multiply ?24926 (add ?24927 ?24925)) =>= multiply (add ?24926 ?24925) (add ?24925 ?24927) [24927, 24926, 24925] by Super 16401 with 2987 at 2,2 +Id : 18171, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add (multiply ?24963 ?24964) ?24964) [24965, 24964, 24963] by Super 18162 with 35 at 2,2,2 +Id : 18379, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =<= multiply (add ?24965 (multiply ?24963 ?24964)) (add ?24964 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18171 with 2844 at 2,3 +Id : 18380, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply (add ?24965 (multiply ?24963 ?24964)) ?24964 [24965, 24964, 24963] by Demod 18379 with 35 at 2,3 +Id : 18381, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 (multiply ?24963 ?24964)) [24965, 24964, 24963] by Demod 18380 with 2987 at 3 +Id : 1575, {_}: multiply ?2421 ?2422 =<= multiply ?2421 (multiply (add ?2421 ?2423) ?2422) [2423, 2422, 2421] by Super 12 with 42 at 1,2 +Id : 16456, {_}: add ?22968 (multiply ?22969 (add ?22970 ?22968)) =>= multiply (add ?22969 ?22968) (add ?22968 ?22970) [22970, 22969, 22968] by Super 16401 with 2987 at 2,2 +Id : 1247, {_}: add ?1879 ?1880 =<= add ?1879 (add (multiply ?1879 ?1881) ?1880) [1881, 1880, 1879] by Super 11 with 22 at 1,2 +Id : 6619, {_}: multiply (multiply ?8607 ?8608) (add ?8607 ?8609) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Super 6 with 1247 at 2,2 +Id : 6763, {_}: multiply ?8607 (multiply ?8608 (add ?8607 ?8609)) =>= multiply ?8607 ?8608 [8609, 8608, 8607] by Demod 6619 with 12 at 2 +Id : 65, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =<= multiply (add ?237 ?238) (multiply (add ?238 (inverse ?238)) (add (inverse ?238) ?237)) [238, 237] by Super 2 with 8 at 2,2 +Id : 76, {_}: add (multiply ?237 ?238) (multiply (inverse ?238) ?237) =>= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 65 with 5 at 2,3 +Id : 18170, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add (multiply ?24959 ?24960) ?24959) [24961, 24960, 24959] by Super 18162 with 22 at 2,2,2 +Id : 18376, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =<= multiply (add ?24961 (multiply ?24959 ?24960)) (add ?24959 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18170 with 2844 at 2,3 +Id : 18377, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply (add ?24961 (multiply ?24959 ?24960)) ?24959 [24961, 24960, 24959] by Demod 18376 with 22 at 2,3 +Id : 18378, {_}: add (multiply ?24959 ?24960) (multiply ?24961 ?24959) =>= multiply ?24959 (add ?24961 (multiply ?24959 ?24960)) [24961, 24960, 24959] by Demod 18377 with 2987 at 3 +Id : 22657, {_}: multiply ?237 (add (inverse ?238) (multiply ?237 ?238)) =<= multiply (add ?237 ?238) (add (inverse ?238) ?237) [238, 237] by Demod 76 with 18378 at 2 +Id : 22699, {_}: multiply (inverse ?30910) (multiply ?30911 (add (inverse ?30910) (multiply ?30911 ?30910))) =>= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Super 6763 with 22657 at 2,2 +Id : 22814, {_}: multiply (inverse ?30910) ?30911 =<= multiply (inverse ?30910) (add ?30911 ?30910) [30911, 30910] by Demod 22699 with 6763 at 2 +Id : 23609, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add (inverse ?31619) ?31619) (add ?31619 ?31620) [31620, 31619] by Super 16456 with 22814 at 2,2 +Id : 23775, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =<= multiply (add ?31619 (inverse ?31619)) (add ?31619 ?31620) [31620, 31619] by Demod 23609 with 2844 at 1,3 +Id : 23776, {_}: add ?31619 (multiply (inverse ?31619) ?31620) =>= multiply n1 (add ?31619 ?31620) [31620, 31619] by Demod 23775 with 9 at 1,3 +Id : 24286, {_}: add ?32553 (multiply (inverse ?32553) ?32554) =>= add ?32553 ?32554 [32554, 32553] by Demod 23776 with 79 at 3 +Id : 13130, {_}: add ?18432 (multiply ?18433 (add ?18432 ?18434)) =>= multiply (add ?18433 ?18432) (add ?18432 ?18434) [18434, 18433, 18432] by Super 13074 with 2987 at 2,2 +Id : 22705, {_}: multiply ?30931 (add (inverse ?30932) (multiply ?30931 ?30932)) =<= multiply (add ?30931 ?30932) (add (inverse ?30932) ?30931) [30932, 30931] by Demod 76 with 18378 at 2 +Id : 22751, {_}: multiply ?31084 (add (inverse (inverse ?31084)) (multiply ?31084 (inverse ?31084))) =>= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Super 22705 with 9 at 1,3 +Id : 23065, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =?= multiply n1 (add (inverse (inverse ?31084)) ?31084) [31084] by Demod 22751 with 10 at 2,2,2 +Id : 23066, {_}: multiply ?31084 (add (inverse (inverse ?31084)) n0) =>= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23065 with 79 at 3 +Id : 130, {_}: multiply (add ?21 ?22) (multiply (add ?22 ?23) ?22) =>= ?22 [23, 22, 21] by Demod 7 with 12 at 2 +Id : 89, {_}: n0 =<= inverse n1 [] by Super 79 with 10 at 2 +Id : 360, {_}: add n1 n0 =>= n1 [] by Super 9 with 89 at 2,2 +Id : 382, {_}: multiply n1 (multiply (add n0 ?765) n0) =>= n0 [765] by Super 130 with 360 at 1,2 +Id : 422, {_}: multiply (add n0 ?765) n0 =>= n0 [765] by Demod 382 with 79 at 2 +Id : 88, {_}: add n0 ?26 =>= ?26 [26] by Demod 8 with 10 at 1,2 +Id : 423, {_}: multiply ?765 n0 =>= n0 [765] by Demod 422 with 88 at 1,2 +Id : 831, {_}: add ?1448 (multiply ?1449 n0) =>= ?1448 [1449, 1448] by Super 3 with 423 at 2,2,2 +Id : 867, {_}: add ?1448 n0 =>= ?1448 [1448] by Demod 831 with 423 at 2,2 +Id : 23067, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add (inverse (inverse ?31084)) ?31084 [31084] by Demod 23066 with 867 at 2,2 +Id : 23068, {_}: multiply ?31084 (inverse (inverse ?31084)) =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23067 with 2844 at 3 +Id : 23215, {_}: add ?31334 (multiply ?31335 (multiply ?31334 (inverse (inverse ?31334)))) =>= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Super 13130 with 23068 at 2,2,2 +Id : 23280, {_}: ?31334 =<= multiply (add ?31335 ?31334) (add ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23215 with 3 at 2 +Id : 23281, {_}: ?31334 =<= multiply (add ?31335 ?31334) (multiply ?31334 (inverse (inverse ?31334))) [31335, 31334] by Demod 23280 with 23068 at 2,3 +Id : 2547, {_}: multiply (multiply ?3698 ?3699) ?3700 =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Super 12 with 1408 at 1,2 +Id : 2578, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply (multiply ?3699 ?3698) ?3700) [3700, 3699, 3698] by Demod 2547 with 12 at 2 +Id : 2579, {_}: multiply ?3698 (multiply ?3699 ?3700) =<= multiply ?3698 (multiply ?3699 (multiply ?3698 ?3700)) [3700, 3699, 3698] by Demod 2578 with 12 at 2,3 +Id : 1667, {_}: multiply ?2583 (multiply ?2584 (multiply ?2583 ?2585)) =>= multiply ?2584 (multiply ?2583 ?2585) [2585, 2584, 2583] by Super 1663 with 3 at 1,2 +Id : 12236, {_}: multiply ?3698 (multiply ?3699 ?3700) =?= multiply ?3699 (multiply ?3698 ?3700) [3700, 3699, 3698] by Demod 2579 with 1667 at 3 +Id : 23282, {_}: ?31334 =<= multiply ?31334 (multiply (add ?31335 ?31334) (inverse (inverse ?31334))) [31335, 31334] by Demod 23281 with 12236 at 3 +Id : 1360, {_}: multiply ?2077 ?2078 =<= multiply ?2077 (multiply (add ?2079 ?2077) ?2078) [2079, 2078, 2077] by Super 12 with 39 at 1,2 +Id : 23283, {_}: ?31334 =<= multiply ?31334 (inverse (inverse ?31334)) [31334] by Demod 23282 with 1360 at 3 +Id : 23386, {_}: add (inverse (inverse ?31435)) ?31435 =>= inverse (inverse ?31435) [31435] by Super 35 with 23283 at 2,2 +Id : 23494, {_}: add ?31435 (inverse (inverse ?31435)) =>= inverse (inverse ?31435) [31435] by Demod 23386 with 2844 at 2 +Id : 23374, {_}: ?31084 =<= add ?31084 (inverse (inverse ?31084)) [31084] by Demod 23068 with 23283 at 2 +Id : 23495, {_}: ?31435 =<= inverse (inverse ?31435) [31435] by Demod 23494 with 23374 at 2 +Id : 24293, {_}: add (inverse ?32572) (multiply ?32572 ?32573) =>= add (inverse ?32572) ?32573 [32573, 32572] by Super 24286 with 23495 at 1,2,2 +Id : 23619, {_}: multiply (multiply (inverse ?31653) ?31654) ?31655 =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Super 12 with 22814 at 1,2 +Id : 23754, {_}: multiply (inverse ?31653) (multiply ?31654 ?31655) =<= multiply (inverse ?31653) (multiply (add ?31654 ?31653) ?31655) [31655, 31654, 31653] by Demod 23619 with 12 at 2 +Id : 77768, {_}: add (inverse (inverse ?103133)) (multiply (inverse ?103133) (multiply ?103134 ?103135)) =>= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Super 24293 with 23754 at 2,2 +Id : 78028, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =<= add (inverse (inverse ?103133)) (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 77768 with 24293 at 2 +Id : 78029, {_}: add (inverse (inverse ?103133)) (multiply ?103134 ?103135) =?= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78028 with 23495 at 1,3 +Id : 78030, {_}: add ?103133 (multiply ?103134 ?103135) =<= add ?103133 (multiply (add ?103134 ?103133) ?103135) [103135, 103134, 103133] by Demod 78029 with 23495 at 1,2 +Id : 13094, {_}: add ?18275 (multiply (add ?18276 ?18275) ?18277) =>= multiply (add ?18277 ?18275) (add ?18275 ?18276) [18277, 18276, 18275] by Super 13074 with 2844 at 1,2,2 +Id : 78031, {_}: add ?103133 (multiply ?103134 ?103135) =<= multiply (add ?103135 ?103133) (add ?103133 ?103134) [103135, 103134, 103133] by Demod 78030 with 13094 at 3 +Id : 78812, {_}: multiply ?104288 (add ?104289 ?104290) =<= multiply ?104288 (add ?104289 (multiply ?104290 ?104288)) [104290, 104289, 104288] by Super 1575 with 78031 at 2,3 +Id : 80954, {_}: add (multiply ?24963 ?24964) (multiply ?24965 ?24964) =>= multiply ?24964 (add ?24965 ?24963) [24965, 24964, 24963] by Demod 18381 with 78812 at 3 +Id : 81595, {_}: multiply a (add c b) =?= multiply a (add c b) [] by Demod 81594 with 2844 at 2,3 +Id : 81594, {_}: multiply a (add c b) =?= multiply a (add b c) [] by Demod 81593 with 80954 at 3 +Id : 81593, {_}: multiply a (add c b) =<= add (multiply c a) (multiply b a) [] by Demod 81592 with 2844 at 3 +Id : 81592, {_}: multiply a (add c b) =<= add (multiply b a) (multiply c a) [] by Demod 1 with 2844 at 2,2 +Id : 1, {_}: multiply a (add b c) =<= add (multiply b a) (multiply c a) [] by prove_multiply_add_property +% SZS output end CNFRefutation for BOO031-1.p +22304: solved BOO031-1.p in 22.545408 using kbo +22304: status Unsatisfiable for BOO031-1.p +NO CLASH, using fixed ground order +22316: Facts: +22316: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22316: Goal: +22316: Id : 1, {_}: add b a =<= add a b [] by huntinton_1 +22316: Order: +22316: nrkbo +22316: Leaf order: +22316: b 2 0 2 1,2 +22316: a 2 0 2 2,2 +22316: inverse 7 1 0 +22316: add 8 2 2 0,2 +NO CLASH, using fixed ground order +22317: Facts: +22317: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22317: Goal: +22317: Id : 1, {_}: add b a =<= add a b [] by huntinton_1 +22317: Order: +22317: kbo +22317: Leaf order: +22317: b 2 0 2 1,2 +22317: a 2 0 2 2,2 +22317: inverse 7 1 0 +22317: add 8 2 2 0,2 +NO CLASH, using fixed ground order +22318: Facts: +22318: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22318: Goal: +22318: Id : 1, {_}: add b a =<= add a b [] by huntinton_1 +22318: Order: +22318: lpo +22318: Leaf order: +22318: b 2 0 2 1,2 +22318: a 2 0 2 2,2 +22318: inverse 7 1 0 +22318: add 8 2 2 0,2 +Statistics : +Max weight : 70 +Found proof, 10.385052s +% SZS status Unsatisfiable for BOO072-1.p +% SZS output start CNFRefutation for BOO072-1.p +Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10 +Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2 +Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2 +Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2 +Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2 +Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2 +Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2 +Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2 +Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2 +Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2 +Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2 +Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2 +Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2 +Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2 +Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2 +Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2 +Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2 +Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2 +Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2 +Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2 +Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2 +Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2 +Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2 +Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3 +Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2 +Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2 +Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2 +Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2 +Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2 +Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3 +Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2 +Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3 +Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2 +Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2 +Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2 +Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2 +Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3 +Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2 +Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2 +Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2 +Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2 +Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2 +Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3 +Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3 +Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2 +Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2 +Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2 +Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2 +Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2 +Id : 12127, {_}: inverse (inverse (add ?22871 (inverse (inverse ?22872)))) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Super 1761 with 11260 at 1,2,3 +Id : 12312, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 (inverse (inverse ?22872)))))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12127 with 1733 at 2 +Id : 12313, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) (inverse (inverse ?22872)) [22872, 22871] by Demod 12312 with 1733 at 2,1,2,1,1,3 +Id : 12314, {_}: add ?22871 (inverse (inverse ?22872)) =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12313 with 1733 at 2,3 +Id : 12315, {_}: add ?22871 ?22872 =<= add (inverse (add ?22872 (inverse (add ?22871 ?22872)))) ?22872 [22872, 22871] by Demod 12314 with 1733 at 2,2 +Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2 +Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2 +Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2 +Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2 +Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2 +Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2 +Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2 +Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2 +Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2 +Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2 +Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2 +Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2 +Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2 +Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3 +Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2 +Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3 +Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3 +Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2 +Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3 +Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3 +Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3 +Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3 +Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3 +Id : 18514, {_}: add (add ?31834 ?31835) ?31834 =<= add (inverse (add ?31834 (inverse (add ?31834 ?31835)))) ?31834 [31835, 31834] by Super 12315 with 18257 at 1,2,1,1,3 +Id : 19938, {_}: add ?34185 ?34186 =<= add (inverse (add ?34185 (inverse (add ?34185 ?34186)))) ?34185 [34186, 34185] by Demod 18514 with 18257 at 2 +Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2 +Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2 +Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2 +Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3 +Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2 +Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3 +Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3 +Id : 20385, {_}: add ?34911 ?34912 =<= add (inverse (add (inverse (add ?34911 ?34912)) ?34911)) ?34911 [34912, 34911] by Super 19938 with 18480 at 1,1,3 +Id : 20390, {_}: add ?34925 (add ?34926 ?34925) =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34926, 34925] by Super 20385 with 8543 at 1,1,1,1,3 +Id : 20500, {_}: add ?34926 ?34925 =<= add (inverse (add (inverse (add ?34926 ?34925)) ?34925)) ?34925 [34925, 34926] by Demod 20390 with 8543 at 2 +Id : 5906, {_}: inverse (add (inverse (inverse ?12265)) (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Super 136 with 5602 at 1,1,1,2 +Id : 6067, {_}: inverse (add ?12265 (inverse (add (inverse ?12266) (inverse (add ?12266 ?12265))))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 5906 with 1733 at 1,1,2 +Id : 15857, {_}: add (inverse ?28730) (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Super 1785 with 15735 at 1,2,1,2,3 +Id : 16100, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add (inverse (inverse ?28730)) ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 15857 with 15735 at 2 +Id : 16101, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 (inverse (inverse ?28730)))) [28731, 28730] by Demod 16100 with 1733 at 1,1,2,1,3 +Id : 16102, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse (add ?28730 ?28730)) [28731, 28730] by Demod 16101 with 1733 at 2,1,2,3 +Id : 16103, {_}: inverse ?28730 =<= add (add (inverse ?28730) (inverse (add ?28730 ?28731))) (inverse ?28730) [28731, 28730] by Demod 16102 with 1724 at 1,2,3 +Id : 18477, {_}: inverse ?28730 =<= add (inverse ?28730) (inverse (add ?28730 ?28731)) [28731, 28730] by Demod 16103 with 18257 at 3 +Id : 21222, {_}: inverse (add ?12265 (inverse (inverse ?12266))) =>= inverse (add ?12266 ?12265) [12266, 12265] by Demod 6067 with 18477 at 1,2,1,2 +Id : 21223, {_}: inverse (add ?12265 ?12266) =?= inverse (add ?12266 ?12265) [12266, 12265] by Demod 21222 with 1733 at 2,1,2 +Id : 21386, {_}: add ?36951 ?36952 =<= add (inverse (add (inverse (add ?36952 ?36951)) ?36952)) ?36952 [36952, 36951] by Super 20500 with 21223 at 1,1,1,3 +Id : 19969, {_}: add ?34289 ?34290 =<= add (inverse (add (inverse (add ?34289 ?34290)) ?34289)) ?34289 [34290, 34289] by Super 19938 with 18480 at 1,1,3 +Id : 21454, {_}: add ?36951 ?36952 =?= add ?36952 ?36951 [36952, 36951] by Demod 21386 with 19969 at 3 +Id : 21981, {_}: add b a === add b a [] by Demod 1 with 21454 at 3 +Id : 1, {_}: add b a =<= add a b [] by huntinton_1 +% SZS output end CNFRefutation for BOO072-1.p +22316: solved BOO072-1.p in 10.380648 using nrkbo +22316: status Unsatisfiable for BOO072-1.p +NO CLASH, using fixed ground order +22328: Facts: +22328: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22328: Goal: +22328: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2 +22328: Order: +22328: nrkbo +22328: Leaf order: +22328: a 2 0 2 1,1,2 +22328: b 2 0 2 2,1,2 +22328: c 2 0 2 2,2 +22328: inverse 7 1 0 +22328: add 10 2 4 0,2 +NO CLASH, using fixed ground order +22329: Facts: +22329: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22329: Goal: +22329: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2 +22329: Order: +22329: kbo +22329: Leaf order: +22329: a 2 0 2 1,1,2 +22329: b 2 0 2 2,1,2 +22329: c 2 0 2 2,2 +22329: inverse 7 1 0 +22329: add 10 2 4 0,2 +NO CLASH, using fixed ground order +22330: Facts: +22330: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22330: Goal: +22330: Id : 1, {_}: add (add a b) c =>= add a (add b c) [] by huntinton_2 +22330: Order: +22330: lpo +22330: Leaf order: +22330: a 2 0 2 1,1,2 +22330: b 2 0 2 2,1,2 +22330: c 2 0 2 2,2 +22330: inverse 7 1 0 +22330: add 10 2 4 0,2 +% SZS status Timeout for BOO073-1.p +NO CLASH, using fixed ground order +22390: Facts: +22390: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22390: Goal: +22390: Id : 1, {_}: + add (inverse (add (inverse a) b)) + (inverse (add (inverse a) (inverse b))) + =>= + a + [] by huntinton_3 +22390: Order: +22390: nrkbo +22390: Leaf order: +22390: b 2 0 2 2,1,1,2 +22390: a 3 0 3 1,1,1,1,2 +22390: inverse 12 1 5 0,1,2 +22390: add 9 2 3 0,2 +NO CLASH, using fixed ground order +22391: Facts: +22391: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22391: Goal: +22391: Id : 1, {_}: + add (inverse (add (inverse a) b)) + (inverse (add (inverse a) (inverse b))) + =>= + a + [] by huntinton_3 +22391: Order: +22391: kbo +22391: Leaf order: +22391: b 2 0 2 2,1,1,2 +22391: a 3 0 3 1,1,1,1,2 +22391: inverse 12 1 5 0,1,2 +22391: add 9 2 3 0,2 +NO CLASH, using fixed ground order +22392: Facts: +22392: Id : 2, {_}: + inverse + (add (inverse (add (inverse (add ?2 ?3)) ?4)) + (inverse + (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) + =>= + ?4 + [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +22392: Goal: +22392: Id : 1, {_}: + add (inverse (add (inverse a) b)) + (inverse (add (inverse a) (inverse b))) + =>= + a + [] by huntinton_3 +22392: Order: +22392: lpo +22392: Leaf order: +22392: b 2 0 2 2,1,1,2 +22392: a 3 0 3 1,1,1,1,2 +22392: inverse 12 1 5 0,1,2 +22392: add 9 2 3 0,2 +Statistics : +Max weight : 70 +Found proof, 9.195802s +% SZS status Unsatisfiable for BOO074-1.p +% SZS output start CNFRefutation for BOO074-1.p +Id : 3, {_}: inverse (add (inverse (add (inverse (add ?7 ?8)) ?9)) (inverse (add ?7 (inverse (add (inverse ?9) (inverse (add ?9 ?10))))))) =>= ?9 [10, 9, 8, 7] by dn1 ?7 ?8 ?9 ?10 +Id : 2, {_}: inverse (add (inverse (add (inverse (add ?2 ?3)) ?4)) (inverse (add ?2 (inverse (add (inverse ?4) (inverse (add ?4 ?5))))))) =>= ?4 [5, 4, 3, 2] by dn1 ?2 ?3 ?4 ?5 +Id : 15, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?74)) ?75)) ?74)) ?76)) (inverse ?74))) ?74) =>= inverse ?74 [76, 75, 74] by Super 3 with 2 at 2,1,2 +Id : 20, {_}: inverse (add (inverse (add ?104 (inverse ?104))) ?104) =>= inverse ?104 [104] by Super 15 with 2 at 1,1,1,1,2 +Id : 99, {_}: inverse (add (inverse ?355) (inverse (add ?355 (inverse (add (inverse ?355) (inverse (add ?355 ?356))))))) =>= ?355 [356, 355] by Super 2 with 20 at 1,1,2 +Id : 136, {_}: inverse (add (inverse (add (inverse (add ?450 ?451)) ?452)) (inverse (add ?450 ?452))) =>= ?452 [452, 451, 450] by Super 2 with 99 at 2,1,2,1,2 +Id : 536, {_}: inverse (add (inverse (add (inverse (add ?1808 ?1809)) ?1810)) (inverse (add ?1808 ?1810))) =>= ?1810 [1810, 1809, 1808] by Super 2 with 99 at 2,1,2,1,2 +Id : 550, {_}: inverse (add (inverse (add ?1882 ?1883)) (inverse (add (inverse ?1882) ?1883))) =>= ?1883 [1883, 1882] by Super 536 with 99 at 1,1,1,1,2 +Id : 724, {_}: inverse (add ?2517 (inverse (add ?2518 (inverse (add (inverse ?2518) ?2517))))) =>= inverse (add (inverse ?2518) ?2517) [2518, 2517] by Super 136 with 550 at 1,1,2 +Id : 1584, {_}: inverse (add (inverse ?4978) (inverse (add ?4978 (inverse (add (inverse ?4978) (inverse ?4978)))))) =>= ?4978 [4978] by Super 99 with 724 at 2,1,2,1,2 +Id : 1652, {_}: inverse (add (inverse ?4978) (inverse ?4978)) =>= ?4978 [4978] by Demod 1584 with 724 at 2 +Id : 763, {_}: inverse (add (inverse (add ?2736 ?2737)) (inverse (add (inverse ?2736) ?2737))) =>= ?2737 [2737, 2736] by Super 536 with 99 at 1,1,1,1,2 +Id : 144, {_}: inverse (add (inverse ?482) (inverse (add ?482 (inverse (add (inverse ?482) (inverse (add ?482 ?483))))))) =>= ?482 [483, 482] by Super 2 with 20 at 1,1,2 +Id : 155, {_}: inverse (add (inverse ?528) (inverse (add ?528 ?528))) =>= ?528 [528] by Super 144 with 99 at 2,1,2,1,2 +Id : 782, {_}: inverse (add (inverse (add ?2830 (inverse (add ?2830 ?2830)))) ?2830) =>= inverse (add ?2830 ?2830) [2830] by Super 763 with 155 at 2,1,2 +Id : 871, {_}: inverse (add (inverse (add ?3076 ?3076)) (inverse (add ?3076 ?3076))) =>= ?3076 [3076] by Super 136 with 782 at 1,1,2 +Id : 1724, {_}: add ?3076 ?3076 =>= ?3076 [3076] by Demod 871 with 1652 at 2 +Id : 1754, {_}: inverse (inverse ?5284) =>= ?5284 [5284] by Demod 1652 with 1724 at 1,2 +Id : 1762, {_}: inverse (inverse (add (inverse ?5317) ?5318)) =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Super 1754 with 724 at 1,2 +Id : 1733, {_}: inverse (inverse ?4978) =>= ?4978 [4978] by Demod 1652 with 1724 at 1,2 +Id : 1785, {_}: add (inverse ?5317) ?5318 =<= add ?5318 (inverse (add ?5317 (inverse (add (inverse ?5317) ?5318)))) [5318, 5317] by Demod 1762 with 1733 at 2 +Id : 6, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse ?26)) ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Super 3 with 2 at 2,1,2 +Id : 1734, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add ?26 ?27)) ?26)) ?28)) (inverse ?26))) ?26) =>= inverse ?26 [28, 27, 26] by Demod 6 with 1733 at 1,1,1,1,1,1,1,1,1,1,2 +Id : 921, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse (add ?3102 ?3102))))) =>= inverse (add ?3102 ?3102) [3102] by Super 136 with 871 at 1,1,2 +Id : 1725, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse (add ?3102 ?3102) [3102] by Demod 921 with 1724 at 1,2,1,2,1,2 +Id : 1726, {_}: inverse (add ?3102 (inverse (add ?3102 (inverse ?3102)))) =>= inverse ?3102 [3102] by Demod 1725 with 1724 at 1,3 +Id : 1763, {_}: inverse (inverse ?5320) =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Super 1754 with 1726 at 1,2 +Id : 1786, {_}: ?5320 =<= add ?5320 (inverse (add ?5320 (inverse ?5320))) [5320] by Demod 1763 with 1733 at 2 +Id : 2715, {_}: inverse (add (inverse (add (inverse ?7389) (inverse (inverse ?7389)))) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Super 724 with 1786 at 1,2,1,2,1,2 +Id : 2755, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 (inverse (inverse ?7389))))) =>= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2715 with 1733 at 2,1,1,1,2 +Id : 2756, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =?= inverse (add (inverse ?7389) (inverse (add (inverse ?7389) (inverse (inverse ?7389))))) [7389] by Demod 2755 with 1733 at 2,1,2,1,2 +Id : 2757, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse (add ?7389 ?7389))) =>= inverse (inverse ?7389) [7389] by Demod 2756 with 1786 at 1,3 +Id : 2758, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= inverse (inverse ?7389) [7389] by Demod 2757 with 1724 at 1,2,1,2 +Id : 2759, {_}: inverse (add (inverse (add (inverse ?7389) ?7389)) (inverse ?7389)) =>= ?7389 [7389] by Demod 2758 with 1733 at 3 +Id : 2920, {_}: inverse ?7714 =<= add (inverse (add (inverse ?7714) ?7714)) (inverse ?7714) [7714] by Super 1733 with 2759 at 1,2 +Id : 3142, {_}: inverse (add (inverse (add (inverse (add (inverse (inverse ?8118)) ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Super 1734 with 2920 at 1,1,1,1,1,1,1,2 +Id : 3172, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) (inverse (inverse ?8118)))) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3142 with 1733 at 1,1,1,1,1,1,2 +Id : 3173, {_}: inverse (add (inverse (add (inverse (add ?8118 ?8119)) ?8118)) (inverse ?8118)) =>= inverse (inverse ?8118) [8119, 8118] by Demod 3172 with 1733 at 2,1,1,1,2 +Id : 8100, {_}: inverse (add (inverse (add (inverse (add ?15581 ?15582)) ?15581)) (inverse ?15581)) =>= ?15581 [15582, 15581] by Demod 3173 with 1733 at 3 +Id : 8144, {_}: inverse (add ?15759 (inverse (inverse (add ?15760 ?15759)))) =>= inverse (add ?15760 ?15759) [15760, 15759] by Super 8100 with 136 at 1,1,2 +Id : 8365, {_}: inverse (add ?15759 (add ?15760 ?15759)) =>= inverse (add ?15760 ?15759) [15760, 15759] by Demod 8144 with 1733 at 2,1,2 +Id : 8391, {_}: inverse (inverse (add ?15887 ?15888)) =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Super 1733 with 8365 at 1,2 +Id : 8543, {_}: add ?15887 ?15888 =<= add ?15888 (add ?15887 ?15888) [15888, 15887] by Demod 8391 with 1733 at 2 +Id : 12, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Super 2 with 6 at 2,1,2 +Id : 3710, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58))))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 12 with 1733 at 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2 +Id : 3711, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (inverse (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3710 with 1733 at 2,1,1,1,1,1,1,1,2 +Id : 3712, {_}: inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse (add (inverse ?57) (inverse (add ?57 ?58)))) ?59)) (inverse (add (inverse ?57) (inverse (add ?57 ?58)))))) ?60)) (add (inverse ?57) (inverse (add ?57 ?58))))) ?61)) ?57)) (add (inverse ?57) (inverse (add ?57 ?58)))) =>= ?57 [61, 60, 59, 58, 57] by Demod 3711 with 1733 at 2,1,2 +Id : 8459, {_}: inverse (add ?16264 (add ?16265 ?16264)) =>= inverse (add ?16265 ?16264) [16265, 16264] by Demod 8144 with 1733 at 2,1,2 +Id : 1749, {_}: inverse (add (inverse (add (inverse ?5262) ?5263)) (inverse (add ?5262 ?5263))) =>= ?5263 [5263, 5262] by Super 550 with 1733 at 1,1,2,1,2 +Id : 5602, {_}: inverse ?11750 =<= add (inverse (add (inverse ?11751) ?11750)) (inverse (add ?11751 ?11750)) [11751, 11750] by Super 1733 with 1749 at 1,2 +Id : 8468, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =<= inverse (add (inverse (add (inverse ?16285) ?16286)) (inverse (add ?16285 ?16286))) [16286, 16285] by Super 8459 with 5602 at 2,1,2 +Id : 8598, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= inverse (inverse ?16286) [16286, 16285] by Demod 8468 with 5602 at 1,3 +Id : 8599, {_}: inverse (add (inverse (add ?16285 ?16286)) (inverse ?16286)) =>= ?16286 [16286, 16285] by Demod 8598 with 1733 at 3 +Id : 8791, {_}: inverse ?16774 =<= add (inverse (add ?16775 ?16774)) (inverse ?16774) [16775, 16774] by Super 1733 with 8599 at 1,2 +Id : 10590, {_}: inverse (add (inverse (inverse ?20667)) (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Super 3712 with 8791 at 1,1,1,2 +Id : 10753, {_}: inverse (add ?20667 (add (inverse (inverse ?20667)) (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10590 with 1733 at 1,1,2 +Id : 10754, {_}: inverse (add ?20667 (add ?20667 (inverse (add (inverse ?20667) ?20668)))) =>= inverse ?20667 [20668, 20667] by Demod 10753 with 1733 at 1,2,1,2 +Id : 15430, {_}: inverse (inverse ?28103) =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Super 1733 with 10754 at 1,2 +Id : 15735, {_}: ?28103 =<= add ?28103 (add ?28103 (inverse (add (inverse ?28103) ?28104))) [28104, 28103] by Demod 15430 with 1733 at 2 +Id : 15853, {_}: add ?28715 (add ?28715 (inverse (add (inverse ?28715) ?28716))) =?= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Super 8543 with 15735 at 2,3 +Id : 16108, {_}: ?28715 =<= add (add ?28715 (inverse (add (inverse ?28715) ?28716))) ?28715 [28716, 28715] by Demod 15853 with 15735 at 2 +Id : 10568, {_}: inverse (add (inverse (inverse ?20566)) (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Super 136 with 8791 at 1,1,1,2 +Id : 10805, {_}: inverse (add ?20566 (inverse (add ?20567 (inverse ?20566)))) =>= inverse ?20566 [20567, 20566] by Demod 10568 with 1733 at 1,1,2 +Id : 11153, {_}: inverse (inverse ?21486) =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Super 1733 with 10805 at 1,2 +Id : 11260, {_}: ?21486 =<= add ?21486 (inverse (add ?21487 (inverse ?21486))) [21487, 21486] by Demod 11153 with 1733 at 2 +Id : 11176, {_}: inverse (add ?21600 (inverse (add ?21601 (inverse ?21600)))) =>= inverse ?21600 [21601, 21600] by Demod 10568 with 1733 at 1,1,2 +Id : 11183, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= inverse (inverse ?21642) [21643, 21642] by Super 11176 with 1733 at 2,1,2,1,2 +Id : 11564, {_}: inverse (add (inverse ?21642) (inverse (add ?21643 ?21642))) =>= ?21642 [21643, 21642] by Demod 11183 with 1733 at 3 +Id : 13294, {_}: inverse ?24726 =<= add (inverse ?24726) (inverse (add ?24727 ?24726)) [24727, 24726] by Super 1733 with 11564 at 1,2 +Id : 13313, {_}: inverse (add (inverse ?24792) (inverse (add ?24792 ?24793))) =<= add (inverse (add (inverse ?24792) (inverse (add ?24792 ?24793)))) ?24792 [24793, 24792] by Super 13294 with 3712 at 2,3 +Id : 16466, {_}: add (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) ?29660 =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Super 1785 with 13313 at 1,2,1,2,3 +Id : 16829, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (inverse (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))))))) [29661, 29660] by Demod 16466 with 13313 at 2 +Id : 16830, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (add (inverse ?29660) (inverse (add ?29660 ?29661))) (add (inverse ?29660) (inverse (add ?29660 ?29661))))) [29661, 29660] by Demod 16829 with 1733 at 2,1,2,3 +Id : 16831, {_}: inverse (add (inverse ?29660) (inverse (add ?29660 ?29661))) =<= add ?29660 (inverse (add (inverse ?29660) (inverse (add ?29660 ?29661)))) [29661, 29660] by Demod 16830 with 1724 at 1,2,3 +Id : 17624, {_}: ?31105 =<= add ?31105 (inverse (add (inverse ?31105) (inverse (add ?31105 ?31106)))) [31106, 31105] by Super 15735 with 16831 at 2,3 +Id : 17680, {_}: ?31105 =<= inverse (add (inverse ?31105) (inverse (add ?31105 ?31106))) [31106, 31105] by Demod 17624 with 16831 at 3 +Id : 18257, {_}: add ?31431 ?31432 =<= add (add ?31431 ?31432) ?31431 [31432, 31431] by Super 11260 with 17680 at 2,3 +Id : 18478, {_}: ?28715 =<= add ?28715 (inverse (add (inverse ?28715) ?28716)) [28716, 28715] by Demod 16108 with 18257 at 3 +Id : 18480, {_}: add (inverse ?5317) ?5318 =?= add ?5318 (inverse ?5317) [5318, 5317] by Demod 1785 with 18478 at 1,2,3 +Id : 1761, {_}: inverse ?5314 =<= add (inverse (add ?5315 ?5314)) (inverse (add (inverse ?5315) ?5314)) [5315, 5314] by Super 1754 with 550 at 1,2 +Id : 18617, {_}: a === a [] by Demod 18616 with 1733 at 2 +Id : 18616, {_}: inverse (inverse a) =>= a [] by Demod 18615 with 1761 at 2 +Id : 18615, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse b) (inverse a))) =>= a [] by Demod 18614 with 18480 at 1,2,2 +Id : 18614, {_}: add (inverse (add b (inverse a))) (inverse (add (inverse a) (inverse b))) =>= a [] by Demod 1 with 18480 at 1,1,2 +Id : 1, {_}: add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b))) =>= a [] by huntinton_3 +% SZS output end CNFRefutation for BOO074-1.p +22390: solved BOO074-1.p in 9.212575 using nrkbo +22390: status Unsatisfiable for BOO074-1.p +NO CLASH, using fixed ground order +22397: Facts: +22397: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22397: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22397: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)) + [] by strong_fixed_point +22397: Goal: +22397: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22397: Order: +22397: nrkbo +22397: Leaf order: +22397: strong_fixed_point 3 0 2 1,2 +22397: fixed_pt 3 0 3 2,2 +22397: w 4 0 0 +22397: b 6 0 0 +22397: apply 19 2 3 0,2 +NO CLASH, using fixed ground order +22398: Facts: +22398: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22398: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22398: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)) + [] by strong_fixed_point +22398: Goal: +22398: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22398: Order: +22398: kbo +22398: Leaf order: +22398: strong_fixed_point 3 0 2 1,2 +22398: fixed_pt 3 0 3 2,2 +22398: w 4 0 0 +22398: b 6 0 0 +22398: apply 19 2 3 0,2 +NO CLASH, using fixed ground order +22399: Facts: +22399: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22399: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22399: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)) + [] by strong_fixed_point +22399: Goal: +22399: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22399: Order: +22399: lpo +22399: Leaf order: +22399: strong_fixed_point 3 0 2 1,2 +22399: fixed_pt 3 0 3 2,2 +22399: w 4 0 0 +22399: b 6 0 0 +22399: apply 19 2 3 0,2 +% SZS status Timeout for COL003-12.p +NO CLASH, using fixed ground order +22420: Facts: +22420: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22420: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22420: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b + [] by strong_fixed_point +22420: Goal: +22420: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22420: Order: +22420: nrkbo +22420: Leaf order: +22420: strong_fixed_point 3 0 2 1,2 +22420: fixed_pt 3 0 3 2,2 +22420: w 4 0 0 +22420: b 7 0 0 +22420: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +22421: Facts: +22421: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22421: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22421: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b + [] by strong_fixed_point +22421: Goal: +22421: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22421: Order: +22421: kbo +22421: Leaf order: +22421: strong_fixed_point 3 0 2 1,2 +22421: fixed_pt 3 0 3 2,2 +22421: w 4 0 0 +22421: b 7 0 0 +22421: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +22422: Facts: +22422: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22422: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22422: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply (apply b (apply w w)) (apply b w))) b)) b + [] by strong_fixed_point +22422: Goal: +22422: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22422: Order: +22422: lpo +22422: Leaf order: +22422: strong_fixed_point 3 0 2 1,2 +22422: fixed_pt 3 0 3 2,2 +22422: w 4 0 0 +22422: b 7 0 0 +22422: apply 20 2 3 0,2 +% SZS status Timeout for COL003-17.p +NO CLASH, using fixed ground order +22445: Facts: +22445: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22445: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22445: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply (apply b (apply w w)) (apply b w))) + (apply (apply b b) b) + [] by strong_fixed_point +22445: Goal: +22445: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22445: Order: +22445: nrkbo +22445: Leaf order: +22445: strong_fixed_point 3 0 2 1,2 +22445: fixed_pt 3 0 3 2,2 +22445: w 4 0 0 +22445: b 7 0 0 +22445: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +22446: Facts: +22446: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22446: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22446: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply (apply b (apply w w)) (apply b w))) + (apply (apply b b) b) + [] by strong_fixed_point +22446: Goal: +22446: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22446: Order: +22446: kbo +22446: Leaf order: +22446: strong_fixed_point 3 0 2 1,2 +22446: fixed_pt 3 0 3 2,2 +22446: w 4 0 0 +22446: b 7 0 0 +22446: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +22447: Facts: +22447: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22447: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22447: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply (apply b (apply w w)) (apply b w))) + (apply (apply b b) b) + [] by strong_fixed_point +22447: Goal: +22447: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22447: Order: +22447: lpo +22447: Leaf order: +22447: strong_fixed_point 3 0 2 1,2 +22447: fixed_pt 3 0 3 2,2 +22447: w 4 0 0 +22447: b 7 0 0 +22447: apply 20 2 3 0,2 +% SZS status Timeout for COL003-18.p +NO CLASH, using fixed ground order +22471: Facts: +22471: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22471: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22471: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b + [] by strong_fixed_point +22471: Goal: +22471: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22471: Order: +22471: nrkbo +22471: Leaf order: +22471: strong_fixed_point 3 0 2 1,2 +22471: fixed_pt 3 0 3 2,2 +22471: w 4 0 0 +22471: b 7 0 0 +22471: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +22472: Facts: +22472: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22472: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22472: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b + [] by strong_fixed_point +22472: Goal: +22472: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22472: Order: +22472: kbo +22472: Leaf order: +22472: strong_fixed_point 3 0 2 1,2 +22472: fixed_pt 3 0 3 2,2 +22472: w 4 0 0 +22472: b 7 0 0 +22472: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +22473: Facts: +22473: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +22473: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +22473: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply (apply b (apply w w)) (apply (apply b (apply b w)) b))) b + [] by strong_fixed_point +22473: Goal: +22473: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +22473: Order: +22473: lpo +22473: Leaf order: +22473: strong_fixed_point 3 0 2 1,2 +22473: fixed_pt 3 0 3 2,2 +22473: w 4 0 0 +22473: b 7 0 0 +22473: apply 20 2 3 0,2 +% SZS status Timeout for COL003-19.p +CLASH, statistics insufficient +22495: Facts: +22495: Id : 2, {_}: + apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4) + [4, 3] by o_definition ?3 ?4 +22495: Id : 3, {_}: + apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7) + [8, 7, 6] by q1_definition ?6 ?7 ?8 +22495: Goal: +22495: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +22495: Order: +22495: nrkbo +22495: Leaf order: +22495: o 1 0 0 +22495: q1 1 0 0 +22495: combinator 1 0 1 1,3 +22495: apply 10 2 1 0,3 +CLASH, statistics insufficient +22496: Facts: +22496: Id : 2, {_}: + apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4) + [4, 3] by o_definition ?3 ?4 +22496: Id : 3, {_}: + apply (apply (apply q1 ?6) ?7) ?8 =>= apply ?6 (apply ?8 ?7) + [8, 7, 6] by q1_definition ?6 ?7 ?8 +22496: Goal: +22496: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +22496: Order: +22496: kbo +22496: Leaf order: +22496: o 1 0 0 +22496: q1 1 0 0 +22496: combinator 1 0 1 1,3 +22496: apply 10 2 1 0,3 +CLASH, statistics insufficient +22497: Facts: +22497: Id : 2, {_}: + apply (apply o ?3) ?4 =?= apply ?4 (apply ?3 ?4) + [4, 3] by o_definition ?3 ?4 +22497: Id : 3, {_}: + apply (apply (apply q1 ?6) ?7) ?8 =?= apply ?6 (apply ?8 ?7) + [8, 7, 6] by q1_definition ?6 ?7 ?8 +22497: Goal: +22497: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +22497: Order: +22497: lpo +22497: Leaf order: +22497: o 1 0 0 +22497: q1 1 0 0 +22497: combinator 1 0 1 1,3 +22497: apply 10 2 1 0,3 +% SZS status Timeout for COL011-1.p +CLASH, statistics insufficient +22518: Facts: +22518: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22518: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +22518: Id : 4, {_}: + apply (apply t ?9) ?10 =>= apply ?10 ?9 + [10, 9] by t_definition ?9 ?10 +22518: Goal: +22518: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22518: Order: +22518: nrkbo +22518: Leaf order: +22518: b 1 0 0 +22518: m 1 0 0 +22518: t 1 0 0 +22518: f 3 1 3 0,2,2 +22518: apply 13 2 3 0,2 +CLASH, statistics insufficient +22519: Facts: +22519: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22519: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +22519: Id : 4, {_}: + apply (apply t ?9) ?10 =>= apply ?10 ?9 + [10, 9] by t_definition ?9 ?10 +22519: Goal: +22519: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22519: Order: +22519: kbo +22519: Leaf order: +22519: b 1 0 0 +22519: m 1 0 0 +22519: t 1 0 0 +22519: f 3 1 3 0,2,2 +22519: apply 13 2 3 0,2 +CLASH, statistics insufficient +22520: Facts: +22520: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22520: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +22520: Id : 4, {_}: + apply (apply t ?9) ?10 =?= apply ?10 ?9 + [10, 9] by t_definition ?9 ?10 +22520: Goal: +22520: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22520: Order: +22520: lpo +22520: Leaf order: +22520: b 1 0 0 +22520: m 1 0 0 +22520: t 1 0 0 +22520: f 3 1 3 0,2,2 +22520: apply 13 2 3 0,2 +Goal subsumed +Statistics : +Max weight : 62 +Found proof, 0.520019s +% SZS status Unsatisfiable for COL034-1.p +% SZS output start CNFRefutation for COL034-1.p +Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +Id : 4, {_}: apply (apply t ?9) ?10 =>= apply ?10 ?9 [10, 9] by t_definition ?9 ?10 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 11, {_}: apply m (apply (apply b ?29) ?30) =<= apply ?29 (apply ?30 (apply (apply b ?29) ?30)) [30, 29] by Super 2 with 3 at 2 +Id : 2545, {_}: apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) === apply (f (apply (apply b m) (apply (apply b (apply t m)) b))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply b (apply t m)) b)))) m)) [] by Super 2544 with 11 at 2 +Id : 2544, {_}: apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1975, 1976, 1974] by Demod 2294 with 4 at 2,2 +Id : 2294, {_}: apply ?1974 (apply (apply t ?1975) (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))))) =<= apply (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976))) (apply ?1974 (apply (apply ?1976 (f (apply (apply b ?1974) (apply (apply b (apply t ?1975)) ?1976)))) ?1975)) [1976, 1975, 1974] by Super 53 with 4 at 2,2,3 +Id : 53, {_}: apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80))))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Demod 39 with 2 at 2,2 +Id : 39, {_}: apply ?78 (apply (apply (apply b ?79) ?80) (f (apply (apply b ?78) (apply (apply b ?79) ?80)))) =<= apply (f (apply (apply b ?78) (apply (apply b ?79) ?80))) (apply ?78 (apply ?79 (apply ?80 (f (apply (apply b ?78) (apply (apply b ?79) ?80)))))) [80, 79, 78] by Super 8 with 2 at 2,2,3 +Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL034-1.p +22518: solved COL034-1.p in 0.528032 using nrkbo +22518: status Unsatisfiable for COL034-1.p +CLASH, statistics insufficient +22525: Facts: +22525: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22525: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +22525: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +22525: Goal: +22525: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22525: Order: +22525: nrkbo +22525: Leaf order: +22525: s 1 0 0 +22525: b 1 0 0 +22525: c 1 0 0 +22525: f 3 1 3 0,2,2 +22525: apply 19 2 3 0,2 +CLASH, statistics insufficient +22526: Facts: +22526: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22526: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +22526: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +22526: Goal: +22526: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22526: Order: +22526: kbo +22526: Leaf order: +22526: s 1 0 0 +22526: b 1 0 0 +22526: c 1 0 0 +22526: f 3 1 3 0,2,2 +22526: apply 19 2 3 0,2 +CLASH, statistics insufficient +22527: Facts: +22527: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22527: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +22527: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +22527: Goal: +22527: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22527: Order: +22527: lpo +22527: Leaf order: +22527: s 1 0 0 +22527: b 1 0 0 +22527: c 1 0 0 +22527: f 3 1 3 0,2,2 +22527: apply 19 2 3 0,2 +% SZS status Timeout for COL037-1.p +CLASH, statistics insufficient +22551: Facts: +22551: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22551: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +22551: Id : 4, {_}: + apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 + [11, 10, 9] by c_definition ?9 ?10 ?11 +22551: Goal: +22551: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22551: Order: +22551: nrkbo +22551: Leaf order: +22551: b 1 0 0 +22551: m 1 0 0 +22551: c 1 0 0 +22551: f 3 1 3 0,2,2 +22551: apply 15 2 3 0,2 +CLASH, statistics insufficient +22552: Facts: +22552: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22552: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +22552: Id : 4, {_}: + apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 + [11, 10, 9] by c_definition ?9 ?10 ?11 +22552: Goal: +22552: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22552: Order: +22552: kbo +22552: Leaf order: +22552: b 1 0 0 +22552: m 1 0 0 +22552: c 1 0 0 +22552: f 3 1 3 0,2,2 +22552: apply 15 2 3 0,2 +CLASH, statistics insufficient +22553: Facts: +22553: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22553: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +22553: Id : 4, {_}: + apply (apply (apply c ?9) ?10) ?11 =?= apply (apply ?9 ?11) ?10 + [11, 10, 9] by c_definition ?9 ?10 ?11 +22553: Goal: +22553: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22553: Order: +22553: lpo +22553: Leaf order: +22553: b 1 0 0 +22553: m 1 0 0 +22553: c 1 0 0 +22553: f 3 1 3 0,2,2 +22553: apply 15 2 3 0,2 +Goal subsumed +Statistics : +Max weight : 54 +Found proof, 1.136025s +% SZS status Unsatisfiable for COL041-1.p +% SZS output start CNFRefutation for COL041-1.p +Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +Id : 4, {_}: apply (apply (apply c ?9) ?10) ?11 =>= apply (apply ?9 ?11) ?10 [11, 10, 9] by c_definition ?9 ?10 ?11 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2 +Id : 4380, {_}: apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) === apply (f (apply (apply b m) (apply (apply c b) m))) (apply m (apply (apply b (f (apply (apply b m) (apply (apply c b) m)))) m)) [] by Super 53 with 11 at 2 +Id : 53, {_}: apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Demod 39 with 4 at 2,2 +Id : 39, {_}: apply ?91 (apply (apply (apply c ?92) ?93) (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) =<= apply (f (apply (apply b ?91) (apply (apply c ?92) ?93))) (apply ?91 (apply (apply ?92 (f (apply (apply b ?91) (apply (apply c ?92) ?93)))) ?93)) [93, 92, 91] by Super 8 with 4 at 2,2,3 +Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL041-1.p +22551: solved COL041-1.p in 1.14407 using nrkbo +22551: status Unsatisfiable for COL041-1.p +CLASH, statistics insufficient +22558: Facts: +22558: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22558: Id : 3, {_}: + apply (apply (apply n ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?9) ?8) ?9 + [9, 8, 7] by n_definition ?7 ?8 ?9 +22558: Goal: +22558: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22558: Order: +22558: nrkbo +22558: Leaf order: +22558: b 1 0 0 +22558: n 1 0 0 +22558: f 3 1 3 0,2,2 +22558: apply 14 2 3 0,2 +CLASH, statistics insufficient +22559: Facts: +22559: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22559: Id : 3, {_}: + apply (apply (apply n ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?9) ?8) ?9 + [9, 8, 7] by n_definition ?7 ?8 ?9 +22559: Goal: +22559: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22559: Order: +22559: kbo +22559: Leaf order: +22559: b 1 0 0 +22559: n 1 0 0 +22559: f 3 1 3 0,2,2 +22559: apply 14 2 3 0,2 +CLASH, statistics insufficient +22560: Facts: +22560: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22560: Id : 3, {_}: + apply (apply (apply n ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?9) ?8) ?9 + [9, 8, 7] by n_definition ?7 ?8 ?9 +22560: Goal: +22560: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +22560: Order: +22560: lpo +22560: Leaf order: +22560: b 1 0 0 +22560: n 1 0 0 +22560: f 3 1 3 0,2,2 +22560: apply 14 2 3 0,2 +Goal subsumed +Statistics : +Max weight : 88 +Found proof, 25.425976s +% SZS status Unsatisfiable for COL044-1.p +% SZS output start CNFRefutation for COL044-1.p +Id : 4, {_}: apply (apply (apply b ?11) ?12) ?13 =>= apply ?11 (apply ?12 ?13) [13, 12, 11] by b_definition ?11 ?12 ?13 +Id : 3, {_}: apply (apply (apply n ?7) ?8) ?9 =?= apply (apply (apply ?7 ?9) ?8) ?9 [9, 8, 7] by n_definition ?7 ?8 ?9 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 8, {_}: apply (apply (apply n b) ?22) ?23 =?= apply ?23 (apply ?22 ?23) [23, 22] by Super 2 with 3 at 2 +Id : 5, {_}: apply ?15 (apply ?16 ?17) =?= apply ?15 (apply ?16 ?17) [17, 16, 15] by Super 4 with 2 at 2 +Id : 83, {_}: apply (apply (apply (apply n b) ?260) (apply b ?261)) ?262 =?= apply ?261 (apply (apply ?260 (apply b ?261)) ?262) [262, 261, 260] by Super 2 with 8 at 1,2 +Id : 24939, {_}: apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) =?= apply (apply (apply n b) (apply (apply (apply n (apply n b)) (apply b (apply n b))) (apply n (apply n b)))) (f (apply (apply (apply (apply n b) (apply n (apply n b))) (apply b (apply n b))) (apply n (apply n b)))) [] by Super 24245 with 83 at 1,2 +Id : 24245, {_}: apply (apply (apply (apply ?35313 ?35314) ?35315) ?35314) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) =?= apply (apply (apply n b) (apply (apply (apply n ?35313) ?35315) ?35314)) (f (apply (apply (apply ?35313 ?35314) ?35315) ?35314)) [35315, 35314, 35313] by Super 153 with 3 at 2,1,3 +Id : 153, {_}: apply (apply ?460 ?461) (f (apply ?460 ?461)) =<= apply (apply (apply n b) (apply ?460 ?461)) (f (apply ?460 ?461)) [461, 460] by Super 115 with 5 at 1,3 +Id : 115, {_}: apply ?375 (f ?375) =<= apply (apply (apply n b) ?375) (f ?375) [375] by Super 1 with 8 at 3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL044-1.p +22559: solved COL044-1.p in 12.720795 using kbo +22559: status Unsatisfiable for COL044-1.p +CLASH, statistics insufficient +22570: Facts: +22570: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +CLASH, statistics insufficient +22571: Facts: +22571: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22571: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +22571: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +22571: Goal: +22571: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +22571: Order: +22571: kbo +22571: Leaf order: +22571: b 1 0 0 +22571: w 1 0 0 +22571: m 1 0 0 +22571: f 3 1 3 0,2,2 +22571: apply 14 2 3 0,2 +CLASH, statistics insufficient +22572: Facts: +22572: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +22572: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +22572: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +22572: Goal: +22572: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +22572: Order: +22572: lpo +22572: Leaf order: +22572: b 1 0 0 +22572: w 1 0 0 +22572: m 1 0 0 +22572: f 3 1 3 0,2,2 +22572: apply 14 2 3 0,2 +22570: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +22570: Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +22570: Goal: +22570: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +22570: Order: +22570: nrkbo +22570: Leaf order: +22570: b 1 0 0 +22570: w 1 0 0 +22570: m 1 0 0 +22570: f 3 1 3 0,2,2 +22570: apply 14 2 3 0,2 +Goal subsumed +Statistics : +Max weight : 54 +Found proof, 12.496351s +% SZS status Unsatisfiable for COL049-1.p +% SZS output start CNFRefutation for COL049-1.p +Id : 3, {_}: apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 [8, 7] by w_definition ?7 ?8 +Id : 4, {_}: apply m ?10 =?= apply ?10 ?10 [10] by m_definition ?10 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 226, {_}: apply (apply w (apply b ?378)) ?379 =?= apply ?378 (apply ?379 ?379) [379, 378] by Super 2 with 3 at 2 +Id : 231, {_}: apply (apply w (apply b ?393)) ?394 =>= apply ?393 (apply m ?394) [394, 393] by Super 226 with 4 at 2,3 +Id : 289, {_}: apply m (apply w (apply b ?503)) =<= apply ?503 (apply m (apply w (apply b ?503))) [503] by Super 4 with 231 at 3 +Id : 15983, {_}: apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) === apply (f (apply (apply b m) (apply (apply b w) b))) (apply m (apply w (apply b (f (apply (apply b m) (apply (apply b w) b)))))) [] by Super 72 with 289 at 2 +Id : 72, {_}: apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125))))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Demod 59 with 2 at 2,2 +Id : 59, {_}: apply ?123 (apply (apply (apply b ?124) ?125) (f (apply (apply b ?123) (apply (apply b ?124) ?125)))) =<= apply (f (apply (apply b ?123) (apply (apply b ?124) ?125))) (apply ?123 (apply ?124 (apply ?125 (f (apply (apply b ?123) (apply (apply b ?124) ?125)))))) [125, 124, 123] by Super 8 with 2 at 2,2,3 +Id : 8, {_}: apply ?20 (apply ?21 (f (apply (apply b ?20) ?21))) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?20) ?21) (f (apply (apply b ?20) ?21)) =<= apply (f (apply (apply b ?20) ?21)) (apply ?20 (apply ?21 (f (apply (apply b ?20) ?21)))) [21, 20] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1 +% SZS output end CNFRefutation for COL049-1.p +22570: solved COL049-1.p in 6.296392 using nrkbo +22570: status Unsatisfiable for COL049-1.p +CLASH, statistics insufficient +22586: Facts: +22586: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22586: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +22586: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +22586: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +22586: Goal: +22586: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +22586: Order: +22586: nrkbo +22586: Leaf order: +22586: s 1 0 0 +22586: b 1 0 0 +22586: c 1 0 0 +22586: i 1 0 0 +22586: f 3 1 3 0,2,2 +22586: apply 20 2 3 0,2 +CLASH, statistics insufficient +22587: Facts: +22587: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22587: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +22587: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =>= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +22587: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +22587: Goal: +22587: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +22587: Order: +22587: kbo +22587: Leaf order: +22587: s 1 0 0 +22587: b 1 0 0 +22587: c 1 0 0 +22587: i 1 0 0 +22587: f 3 1 3 0,2,2 +22587: apply 20 2 3 0,2 +CLASH, statistics insufficient +22588: Facts: +22588: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +22588: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +22588: Id : 4, {_}: + apply (apply (apply c ?11) ?12) ?13 =?= apply (apply ?11 ?13) ?12 + [13, 12, 11] by c_definition ?11 ?12 ?13 +22588: Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +22588: Goal: +22588: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +22588: Order: +22588: lpo +22588: Leaf order: +22588: s 1 0 0 +22588: b 1 0 0 +22588: c 1 0 0 +22588: i 1 0 0 +22588: f 3 1 3 0,2,2 +22588: apply 20 2 3 0,2 +Goal subsumed +Statistics : +Max weight : 84 +Found proof, 2.121776s +% SZS status Unsatisfiable for COL057-1.p +% SZS output start CNFRefutation for COL057-1.p +Id : 3, {_}: apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) [9, 8, 7] by b_definition ?7 ?8 ?9 +Id : 5, {_}: apply i ?15 =>= ?15 [15] by i_definition ?15 +Id : 2, {_}: apply (apply (apply s ?3) ?4) ?5 =?= apply (apply ?3 ?5) (apply ?4 ?5) [5, 4, 3] by s_definition ?3 ?4 ?5 +Id : 37, {_}: apply (apply (apply s i) ?141) ?142 =?= apply ?142 (apply ?141 ?142) [142, 141] by Super 2 with 5 at 1,3 +Id : 16, {_}: apply (apply (apply s (apply b ?64)) ?65) ?66 =?= apply ?64 (apply ?66 (apply ?65 ?66)) [66, 65, 64] by Super 2 with 3 at 3 +Id : 9068, {_}: apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) === apply (apply (apply (apply s (apply b (apply s i))) i) (apply (apply s (apply b (apply s i))) i)) (f (apply (apply (apply s (apply b (apply s i))) i) (apply i (apply (apply s (apply b (apply s i))) i)))) [] by Super 9059 with 5 at 2,1,2 +Id : 9059, {_}: apply (apply ?16932 (apply ?16933 ?16932)) (f (apply ?16932 (apply ?16933 ?16932))) =?= apply (apply (apply (apply s (apply b (apply s i))) ?16933) ?16932) (f (apply ?16932 (apply ?16933 ?16932))) [16933, 16932] by Super 9058 with 16 at 1,3 +Id : 9058, {_}: apply ?16930 (f ?16930) =<= apply (apply (apply s i) ?16930) (f ?16930) [16930] by Super 1 with 37 at 3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_strong_fixed_point ?1 +% SZS output end CNFRefutation for COL057-1.p +22586: solved COL057-1.p in 2.124132 using nrkbo +22586: status Unsatisfiable for COL057-1.p +NO CLASH, using fixed ground order +22593: Facts: +22593: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +22593: Goal: +22593: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22593: Order: +22593: nrkbo +22593: Leaf order: +22593: a 2 0 2 1,2 +22593: b 2 0 2 1,2,2 +22593: c 2 0 2 2,2,2 +22593: inverse 5 1 0 +22593: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +22594: Facts: +22594: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +22594: Goal: +22594: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22594: Order: +22594: kbo +22594: Leaf order: +22594: a 2 0 2 1,2 +22594: b 2 0 2 1,2,2 +22594: c 2 0 2 2,2,2 +22594: inverse 5 1 0 +22594: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +22595: Facts: +22595: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +22595: Goal: +22595: Id : 1, {_}: + multiply a (multiply b c) =<= multiply (multiply a b) c + [] by prove_associativity +22595: Order: +22595: lpo +22595: Leaf order: +22595: a 2 0 2 1,2 +22595: b 2 0 2 1,2,2 +22595: c 2 0 2 2,2,2 +22595: inverse 5 1 0 +22595: multiply 10 2 4 0,2 +Statistics : +Max weight : 62 +Found proof, 23.394494s +% SZS status Unsatisfiable for GRP014-1.p +% SZS output start CNFRefutation for GRP014-1.p +Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by group_axiom ?2 ?3 ?4 ?5 +Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by group_axiom ?7 ?8 ?9 ?10 +Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2 +Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2 +Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2 +Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2 +Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2 +Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2 +Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3 +Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2 +Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2 +Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2 +Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2 +Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2 +Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2 +Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2 +Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2 +Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2 +Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2 +Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2 +Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3 +Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2 +Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2 +Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3 +Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2 +Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2 +Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2 +Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2 +Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2 +Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3 +Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2 +Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3 +Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2 +Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2 +Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2 +Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2 +Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2 +Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2 +Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2 +Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2 +Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3 +Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2 +Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2 +Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2 +Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2 +Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2 +Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2 +Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2 +Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2 +Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2 +Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2 +Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2 +Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2 +Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2 +Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2 +Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2 +Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2 +Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2 +Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2 +Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2 +Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2 +Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2 +Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2 +Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2 +Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2 +Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2 +Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2 +Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2 +Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2 +Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2 +Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2 +Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2 +Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2 +Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2 +Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2 +Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2 +Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2 +Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2 +Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2 +Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2 +Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2 +Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2 +Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2 +Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2 +Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3 +Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2 +Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2 +Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2 +Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2 +Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2 +Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2 +Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2 +Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2 +Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2 +Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2 +Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2 +Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2 +Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2 +Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3 +Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2 +Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2 +Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2 +Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2 +Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2 +Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2 +Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2 +Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2 +Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2 +Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3 +Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3 +Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2 +Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2 +Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3 +Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2 +Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2 +Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2 +Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2 +Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2 +Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2 +Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2 +Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2 +Id : 33337, {_}: multiply a (multiply b c) === multiply a (multiply b c) [] by Demod 1 with 32860 at 3 +Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity +% SZS output end CNFRefutation for GRP014-1.p +22593: solved GRP014-1.p in 11.760735 using nrkbo +22593: status Unsatisfiable for GRP014-1.p +CLASH, statistics insufficient +22602: Facts: +22602: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22602: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22602: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22602: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22602: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22602: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22602: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22602: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22602: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22602: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22602: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22602: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22602: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22602: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22602: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22602: Id : 17, {_}: + positive_part ?50 =<= least_upper_bound ?50 identity + [50] by lat4_1 ?50 +22602: Id : 18, {_}: + negative_part ?52 =<= greatest_lower_bound ?52 identity + [52] by lat4_2 ?52 +22602: Id : 19, {_}: + least_upper_bound ?54 (greatest_lower_bound ?55 ?56) + =<= + greatest_lower_bound (least_upper_bound ?54 ?55) + (least_upper_bound ?54 ?56) + [56, 55, 54] by lat4_3 ?54 ?55 ?56 +22602: Id : 20, {_}: + greatest_lower_bound ?58 (least_upper_bound ?59 ?60) + =<= + least_upper_bound (greatest_lower_bound ?58 ?59) + (greatest_lower_bound ?58 ?60) + [60, 59, 58] by lat4_4 ?58 ?59 ?60 +22602: Goal: +22602: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +22602: Order: +22602: nrkbo +22602: Leaf order: +22602: a 3 0 3 2 +22602: identity 4 0 0 +22602: inverse 1 1 0 +22602: positive_part 2 1 1 0,1,3 +22602: negative_part 2 1 1 0,2,3 +22602: greatest_lower_bound 19 2 0 +22602: least_upper_bound 19 2 0 +22602: multiply 19 2 1 0,3 +CLASH, statistics insufficient +22603: Facts: +22603: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22603: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22603: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22603: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22603: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22603: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22603: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22603: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22603: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22603: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22603: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22603: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22603: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22603: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22603: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22603: Id : 17, {_}: + positive_part ?50 =<= least_upper_bound ?50 identity + [50] by lat4_1 ?50 +22603: Id : 18, {_}: + negative_part ?52 =<= greatest_lower_bound ?52 identity + [52] by lat4_2 ?52 +22603: Id : 19, {_}: + least_upper_bound ?54 (greatest_lower_bound ?55 ?56) + =<= + greatest_lower_bound (least_upper_bound ?54 ?55) + (least_upper_bound ?54 ?56) + [56, 55, 54] by lat4_3 ?54 ?55 ?56 +22603: Id : 20, {_}: + greatest_lower_bound ?58 (least_upper_bound ?59 ?60) + =<= + least_upper_bound (greatest_lower_bound ?58 ?59) + (greatest_lower_bound ?58 ?60) + [60, 59, 58] by lat4_4 ?58 ?59 ?60 +22603: Goal: +22603: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +22603: Order: +22603: kbo +22603: Leaf order: +22603: a 3 0 3 2 +22603: identity 4 0 0 +22603: inverse 1 1 0 +22603: positive_part 2 1 1 0,1,3 +22603: negative_part 2 1 1 0,2,3 +22603: greatest_lower_bound 19 2 0 +22603: least_upper_bound 19 2 0 +22603: multiply 19 2 1 0,3 +CLASH, statistics insufficient +22604: Facts: +22604: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22604: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22604: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22604: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22604: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22604: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22604: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22604: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22604: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22604: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22604: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22604: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22604: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22604: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22604: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22604: Id : 17, {_}: + positive_part ?50 =>= least_upper_bound ?50 identity + [50] by lat4_1 ?50 +22604: Id : 18, {_}: + negative_part ?52 =>= greatest_lower_bound ?52 identity + [52] by lat4_2 ?52 +22604: Id : 19, {_}: + least_upper_bound ?54 (greatest_lower_bound ?55 ?56) + =<= + greatest_lower_bound (least_upper_bound ?54 ?55) + (least_upper_bound ?54 ?56) + [56, 55, 54] by lat4_3 ?54 ?55 ?56 +22604: Id : 20, {_}: + greatest_lower_bound ?58 (least_upper_bound ?59 ?60) + =>= + least_upper_bound (greatest_lower_bound ?58 ?59) + (greatest_lower_bound ?58 ?60) + [60, 59, 58] by lat4_4 ?58 ?59 ?60 +22604: Goal: +22604: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +22604: Order: +22604: lpo +22604: Leaf order: +22604: a 3 0 3 2 +22604: identity 4 0 0 +22604: inverse 1 1 0 +22604: positive_part 2 1 1 0,1,3 +22604: negative_part 2 1 1 0,2,3 +22604: greatest_lower_bound 19 2 0 +22604: least_upper_bound 19 2 0 +22604: multiply 19 2 1 0,3 +Statistics : +Max weight : 20 +Found proof, 10.348100s +% SZS status Unsatisfiable for GRP167-1.p +% SZS output start CNFRefutation for GRP167-1.p +Id : 185, {_}: multiply ?584 (greatest_lower_bound ?585 ?586) =<= greatest_lower_bound (multiply ?584 ?585) (multiply ?584 ?586) [586, 585, 584] by monotony_glb1 ?584 ?585 ?586 +Id : 218, {_}: multiply (least_upper_bound ?658 ?659) ?660 =<= least_upper_bound (multiply ?658 ?660) (multiply ?659 ?660) [660, 659, 658] by monotony_lub2 ?658 ?659 ?660 +Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32 +Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =?= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11 +Id : 250, {_}: multiply (greatest_lower_bound ?735 ?736) ?737 =<= greatest_lower_bound (multiply ?735 ?737) (multiply ?736 ?737) [737, 736, 735] by monotony_glb2 ?735 ?736 ?737 +Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =<= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +Id : 18, {_}: negative_part ?52 =<= greatest_lower_bound ?52 identity [52] by lat4_2 ?52 +Id : 364, {_}: greatest_lower_bound ?996 (least_upper_bound ?997 ?998) =<= least_upper_bound (greatest_lower_bound ?996 ?997) (greatest_lower_bound ?996 ?998) [998, 997, 996] by lat4_4 ?996 ?997 ?998 +Id : 17, {_}: positive_part ?50 =<= least_upper_bound ?50 identity [50] by lat4_1 ?50 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 155, {_}: multiply ?513 (least_upper_bound ?514 ?515) =<= least_upper_bound (multiply ?513 ?514) (multiply ?513 ?515) [515, 514, 513] by monotony_lub1 ?513 ?514 ?515 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 25, {_}: multiply (multiply ?69 ?70) ?71 =?= multiply ?69 (multiply ?70 ?71) [71, 70, 69] by associativity ?69 ?70 ?71 +Id : 27, {_}: multiply (multiply ?76 (inverse ?77)) ?77 =>= multiply ?76 identity [77, 76] by Super 25 with 3 at 2,3 +Id : 643, {_}: multiply (multiply ?1439 (inverse ?1440)) ?1440 =>= multiply ?1439 identity [1440, 1439] by Super 25 with 3 at 2,3 +Id : 645, {_}: multiply identity ?1444 =<= multiply (inverse (inverse ?1444)) identity [1444] by Super 643 with 3 at 1,2 +Id : 656, {_}: ?1444 =<= multiply (inverse (inverse ?1444)) identity [1444] by Demod 645 with 2 at 2 +Id : 26, {_}: multiply (multiply ?73 identity) ?74 =>= multiply ?73 ?74 [74, 73] by Super 25 with 2 at 2,3 +Id : 1111, {_}: multiply ?2369 ?2370 =<= multiply (inverse (inverse ?2369)) ?2370 [2370, 2369] by Super 26 with 656 at 1,2 +Id : 2348, {_}: ?1444 =<= multiply ?1444 identity [1444] by Demod 656 with 1111 at 3 +Id : 2350, {_}: multiply (multiply ?76 (inverse ?77)) ?77 =>= ?76 [77, 76] by Demod 27 with 2348 at 3 +Id : 2372, {_}: inverse (inverse ?4335) =<= multiply ?4335 identity [4335] by Super 2348 with 1111 at 3 +Id : 2377, {_}: inverse (inverse ?4335) =>= ?4335 [4335] by Demod 2372 with 2348 at 3 +Id : 25971, {_}: multiply (multiply ?35046 ?35047) (inverse ?35047) =>= ?35046 [35047, 35046] by Super 2350 with 2377 at 2,1,2 +Id : 161, {_}: multiply (inverse ?536) (least_upper_bound ?536 ?537) =>= least_upper_bound identity (multiply (inverse ?536) ?537) [537, 536] by Super 155 with 3 at 1,3 +Id : 279, {_}: least_upper_bound identity ?790 =>= positive_part ?790 [790] by Super 6 with 17 at 3 +Id : 4991, {_}: multiply (inverse ?8728) (least_upper_bound ?8728 ?8729) =>= positive_part (multiply (inverse ?8728) ?8729) [8729, 8728] by Demod 161 with 279 at 3 +Id : 5015, {_}: multiply (inverse ?8798) (positive_part ?8798) =?= positive_part (multiply (inverse ?8798) identity) [8798] by Super 4991 with 17 at 2,2 +Id : 5066, {_}: multiply (inverse ?8872) (positive_part ?8872) =>= positive_part (inverse ?8872) [8872] by Demod 5015 with 2348 at 1,3 +Id : 5077, {_}: multiply ?8900 (positive_part (inverse ?8900)) =>= positive_part (inverse (inverse ?8900)) [8900] by Super 5066 with 2377 at 1,2 +Id : 5091, {_}: multiply ?8900 (positive_part (inverse ?8900)) =>= positive_part ?8900 [8900] by Demod 5077 with 2377 at 1,3 +Id : 25993, {_}: multiply (positive_part ?35122) (inverse (positive_part (inverse ?35122))) =>= ?35122 [35122] by Super 25971 with 5091 at 1,2 +Id : 2406, {_}: multiply (multiply ?4349 ?4350) (inverse ?4350) =>= ?4349 [4350, 4349] by Super 2350 with 2377 at 2,1,2 +Id : 4974, {_}: multiply (inverse ?536) (least_upper_bound ?536 ?537) =>= positive_part (multiply (inverse ?536) ?537) [537, 536] by Demod 161 with 279 at 3 +Id : 373, {_}: greatest_lower_bound ?1035 (least_upper_bound ?1036 identity) =<= least_upper_bound (greatest_lower_bound ?1035 ?1036) (negative_part ?1035) [1036, 1035] by Super 364 with 18 at 2,3 +Id : 397, {_}: greatest_lower_bound ?1035 (positive_part ?1036) =<= least_upper_bound (greatest_lower_bound ?1035 ?1036) (negative_part ?1035) [1036, 1035] by Demod 373 with 17 at 2,2 +Id : 256, {_}: multiply (greatest_lower_bound (inverse ?758) ?759) ?758 =>= greatest_lower_bound identity (multiply ?759 ?758) [759, 758] by Super 250 with 3 at 1,3 +Id : 296, {_}: greatest_lower_bound identity ?821 =>= negative_part ?821 [821] by Super 5 with 18 at 3 +Id : 17350, {_}: multiply (greatest_lower_bound (inverse ?24308) ?24309) ?24308 =>= negative_part (multiply ?24309 ?24308) [24309, 24308] by Demod 256 with 296 at 3 +Id : 17377, {_}: multiply (negative_part (inverse ?24398)) ?24398 =>= negative_part (multiply identity ?24398) [24398] by Super 17350 with 18 at 1,2 +Id : 17420, {_}: multiply (negative_part (inverse ?24398)) ?24398 =>= negative_part ?24398 [24398] by Demod 17377 with 2 at 1,3 +Id : 17441, {_}: multiply (greatest_lower_bound (negative_part (inverse ?24443)) ?24444) ?24443 =>= greatest_lower_bound (negative_part ?24443) (multiply ?24444 ?24443) [24444, 24443] by Super 16 with 17420 at 1,3 +Id : 455, {_}: greatest_lower_bound identity (greatest_lower_bound ?1150 ?1151) =>= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Super 7 with 296 at 1,3 +Id : 465, {_}: negative_part (greatest_lower_bound ?1150 ?1151) =>= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Demod 455 with 296 at 2 +Id : 299, {_}: greatest_lower_bound ?828 (greatest_lower_bound ?829 identity) =>= negative_part (greatest_lower_bound ?828 ?829) [829, 828] by Super 7 with 18 at 3 +Id : 309, {_}: greatest_lower_bound ?828 (negative_part ?829) =<= negative_part (greatest_lower_bound ?828 ?829) [829, 828] by Demod 299 with 18 at 2,2 +Id : 831, {_}: greatest_lower_bound ?1150 (negative_part ?1151) =?= greatest_lower_bound (negative_part ?1150) ?1151 [1151, 1150] by Demod 465 with 309 at 2 +Id : 17491, {_}: multiply (greatest_lower_bound (inverse ?24443) (negative_part ?24444)) ?24443 =>= greatest_lower_bound (negative_part ?24443) (multiply ?24444 ?24443) [24444, 24443] by Demod 17441 with 831 at 1,2 +Id : 17492, {_}: multiply (greatest_lower_bound (inverse ?24443) (negative_part ?24444)) ?24443 =>= greatest_lower_bound (multiply ?24444 ?24443) (negative_part ?24443) [24444, 24443] by Demod 17491 with 5 at 3 +Id : 17323, {_}: multiply (greatest_lower_bound (inverse ?758) ?759) ?758 =>= negative_part (multiply ?759 ?758) [759, 758] by Demod 256 with 296 at 3 +Id : 17493, {_}: negative_part (multiply (negative_part ?24444) ?24443) =<= greatest_lower_bound (multiply ?24444 ?24443) (negative_part ?24443) [24443, 24444] by Demod 17492 with 17323 at 2 +Id : 5044, {_}: multiply (inverse ?8798) (positive_part ?8798) =>= positive_part (inverse ?8798) [8798] by Demod 5015 with 2348 at 1,3 +Id : 25992, {_}: multiply (positive_part (inverse ?35120)) (inverse (positive_part ?35120)) =>= inverse ?35120 [35120] by Super 25971 with 5044 at 1,2 +Id : 65949, {_}: negative_part (multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239))) =>= greatest_lower_bound (inverse ?78239) (negative_part (inverse (positive_part ?78239))) [78239] by Super 17493 with 25992 at 1,3 +Id : 285, {_}: greatest_lower_bound ?806 (positive_part ?806) =>= ?806 [806] by Super 12 with 17 at 2,2 +Id : 575, {_}: greatest_lower_bound (positive_part ?1304) ?1304 =>= ?1304 [1304] by Super 5 with 285 at 3 +Id : 424, {_}: least_upper_bound identity (least_upper_bound ?1119 ?1120) =>= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Super 8 with 279 at 1,3 +Id : 433, {_}: positive_part (least_upper_bound ?1119 ?1120) =>= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Demod 424 with 279 at 2 +Id : 282, {_}: least_upper_bound ?797 (least_upper_bound ?798 identity) =>= positive_part (least_upper_bound ?797 ?798) [798, 797] by Super 8 with 17 at 3 +Id : 292, {_}: least_upper_bound ?797 (positive_part ?798) =<= positive_part (least_upper_bound ?797 ?798) [798, 797] by Demod 282 with 17 at 2,2 +Id : 749, {_}: least_upper_bound ?1119 (positive_part ?1120) =?= least_upper_bound (positive_part ?1119) ?1120 [1120, 1119] by Demod 433 with 292 at 2 +Id : 758, {_}: least_upper_bound (positive_part (positive_part ?1606)) ?1606 =>= positive_part ?1606 [1606] by Super 9 with 749 at 2 +Id : 606, {_}: least_upper_bound ?1347 (positive_part ?1348) =<= positive_part (least_upper_bound ?1347 ?1348) [1348, 1347] by Demod 282 with 17 at 2,2 +Id : 616, {_}: least_upper_bound ?1379 (positive_part identity) =>= positive_part (positive_part ?1379) [1379] by Super 606 with 17 at 1,3 +Id : 278, {_}: positive_part identity =>= identity [] by Super 9 with 17 at 2 +Id : 628, {_}: least_upper_bound ?1379 identity =<= positive_part (positive_part ?1379) [1379] by Demod 616 with 278 at 2,2 +Id : 629, {_}: positive_part ?1379 =<= positive_part (positive_part ?1379) [1379] by Demod 628 with 17 at 2 +Id : 798, {_}: least_upper_bound (positive_part ?1606) ?1606 =>= positive_part ?1606 [1606] by Demod 758 with 629 at 1,2 +Id : 5005, {_}: multiply (inverse (positive_part ?8766)) (positive_part ?8766) =<= positive_part (multiply (inverse (positive_part ?8766)) ?8766) [8766] by Super 4991 with 798 at 2,2 +Id : 5040, {_}: identity =<= positive_part (multiply (inverse (positive_part ?8766)) ?8766) [8766] by Demod 5005 with 3 at 2 +Id : 5691, {_}: greatest_lower_bound identity (multiply (inverse (positive_part ?9483)) ?9483) =>= multiply (inverse (positive_part ?9483)) ?9483 [9483] by Super 575 with 5040 at 1,2 +Id : 5736, {_}: negative_part (multiply (inverse (positive_part ?9483)) ?9483) =>= multiply (inverse (positive_part ?9483)) ?9483 [9483] by Demod 5691 with 296 at 2 +Id : 770, {_}: least_upper_bound ?1642 (positive_part ?1643) =?= least_upper_bound (positive_part ?1642) ?1643 [1643, 1642] by Demod 433 with 292 at 2 +Id : 456, {_}: least_upper_bound identity (negative_part ?1153) =>= identity [1153] by Super 11 with 296 at 2,2 +Id : 464, {_}: positive_part (negative_part ?1153) =>= identity [1153] by Demod 456 with 279 at 2 +Id : 772, {_}: least_upper_bound (negative_part ?1647) (positive_part ?1648) =>= least_upper_bound identity ?1648 [1648, 1647] by Super 770 with 464 at 1,3 +Id : 812, {_}: least_upper_bound (negative_part ?1647) (positive_part ?1648) =>= positive_part ?1648 [1648, 1647] by Demod 772 with 279 at 3 +Id : 5068, {_}: multiply (inverse (negative_part ?8875)) identity =>= positive_part (inverse (negative_part ?8875)) [8875] by Super 5066 with 464 at 2,2 +Id : 5087, {_}: inverse (negative_part ?8875) =<= positive_part (inverse (negative_part ?8875)) [8875] by Demod 5068 with 2348 at 2 +Id : 5099, {_}: least_upper_bound (negative_part ?8914) (inverse (negative_part ?8915)) =>= positive_part (inverse (negative_part ?8915)) [8915, 8914] by Super 812 with 5087 at 2,2 +Id : 5137, {_}: least_upper_bound (inverse (negative_part ?8915)) (negative_part ?8914) =>= positive_part (inverse (negative_part ?8915)) [8914, 8915] by Demod 5099 with 6 at 2 +Id : 5138, {_}: least_upper_bound (inverse (negative_part ?8915)) (negative_part ?8914) =>= inverse (negative_part ?8915) [8914, 8915] by Demod 5137 with 5087 at 3 +Id : 7238, {_}: multiply (inverse (inverse (negative_part ?11513))) (inverse (negative_part ?11513)) =?= positive_part (multiply (inverse (inverse (negative_part ?11513))) (negative_part ?11514)) [11514, 11513] by Super 4974 with 5138 at 2,2 +Id : 7311, {_}: identity =<= positive_part (multiply (inverse (inverse (negative_part ?11513))) (negative_part ?11514)) [11514, 11513] by Demod 7238 with 3 at 2 +Id : 7312, {_}: identity =<= positive_part (multiply (negative_part ?11513) (negative_part ?11514)) [11514, 11513] by Demod 7311 with 2377 at 1,1,3 +Id : 11865, {_}: negative_part (multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876))) =<= multiply (inverse (positive_part (multiply (negative_part ?16875) (negative_part ?16876)))) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Super 5736 with 7312 at 1,1,1,2 +Id : 2405, {_}: multiply ?4347 (inverse ?4347) =>= identity [4347] by Super 3 with 2377 at 1,2 +Id : 2415, {_}: identity =<= inverse identity [] by Super 2 with 2405 at 2 +Id : 11917, {_}: negative_part (multiply identity (multiply (negative_part ?16875) (negative_part ?16876))) =<= multiply (inverse (positive_part (multiply (negative_part ?16875) (negative_part ?16876)))) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11865 with 2415 at 1,1,2 +Id : 11918, {_}: negative_part (multiply identity (multiply (negative_part ?16875) (negative_part ?16876))) =>= multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11917 with 7312 at 1,1,3 +Id : 11919, {_}: negative_part (multiply (negative_part ?16875) (negative_part ?16876)) =<= multiply (inverse identity) (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11918 with 2 at 1,2 +Id : 11920, {_}: negative_part (multiply (negative_part ?16875) (negative_part ?16876)) =<= multiply identity (multiply (negative_part ?16875) (negative_part ?16876)) [16876, 16875] by Demod 11919 with 2415 at 1,3 +Id : 13421, {_}: negative_part (multiply (negative_part ?18780) (negative_part ?18781)) =>= multiply (negative_part ?18780) (negative_part ?18781) [18781, 18780] by Demod 11920 with 2 at 3 +Id : 5075, {_}: multiply (inverse (positive_part ?8895)) (positive_part ?8895) =>= positive_part (inverse (positive_part ?8895)) [8895] by Super 5066 with 629 at 2,2 +Id : 5090, {_}: identity =<= positive_part (inverse (positive_part ?8895)) [8895] by Demod 5075 with 3 at 2 +Id : 5175, {_}: greatest_lower_bound identity (inverse (positive_part ?9005)) =>= inverse (positive_part ?9005) [9005] by Super 575 with 5090 at 1,2 +Id : 5216, {_}: negative_part (inverse (positive_part ?9005)) =>= inverse (positive_part ?9005) [9005] by Demod 5175 with 296 at 2 +Id : 13433, {_}: negative_part (multiply (negative_part ?18822) (inverse (positive_part ?18823))) =>= multiply (negative_part ?18822) (negative_part (inverse (positive_part ?18823))) [18823, 18822] by Super 13421 with 5216 at 2,1,2 +Id : 13543, {_}: negative_part (multiply (negative_part ?18822) (inverse (positive_part ?18823))) =>= multiply (negative_part ?18822) (inverse (positive_part ?18823)) [18823, 18822] by Demod 13433 with 5216 at 2,3 +Id : 66057, {_}: multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239)) =>= greatest_lower_bound (inverse ?78239) (negative_part (inverse (positive_part ?78239))) [78239] by Demod 65949 with 13543 at 2 +Id : 66058, {_}: multiply (negative_part (positive_part (inverse ?78239))) (inverse (positive_part ?78239)) =>= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66057 with 5216 at 2,3 +Id : 451, {_}: negative_part (least_upper_bound identity ?1143) =>= identity [1143] by Super 12 with 296 at 2 +Id : 469, {_}: negative_part (positive_part ?1143) =>= identity [1143] by Demod 451 with 279 at 1,2 +Id : 66059, {_}: multiply identity (inverse (positive_part ?78239)) =<= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66058 with 469 at 1,2 +Id : 66060, {_}: inverse (positive_part ?78239) =<= greatest_lower_bound (inverse ?78239) (inverse (positive_part ?78239)) [78239] by Demod 66059 with 2 at 2 +Id : 66290, {_}: greatest_lower_bound (inverse ?78524) (positive_part (inverse (positive_part ?78524))) =>= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Super 397 with 66060 at 1,3 +Id : 66456, {_}: greatest_lower_bound (inverse ?78524) identity =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66290 with 5090 at 2,2 +Id : 66457, {_}: greatest_lower_bound identity (inverse ?78524) =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66456 with 5 at 2 +Id : 66458, {_}: negative_part (inverse ?78524) =<= least_upper_bound (inverse (positive_part ?78524)) (negative_part (inverse ?78524)) [78524] by Demod 66457 with 296 at 2 +Id : 80743, {_}: multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706)) =<= positive_part (multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706))) [90706] by Super 4974 with 66458 at 2,2 +Id : 80871, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply (inverse (inverse (positive_part ?90706))) (negative_part (inverse ?90706))) [90706] by Demod 80743 with 2377 at 1,2 +Id : 80872, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply (positive_part ?90706) (negative_part (inverse ?90706))) [90706] by Demod 80871 with 2377 at 1,1,3 +Id : 224, {_}: multiply (least_upper_bound (inverse ?681) ?682) ?681 =>= least_upper_bound identity (multiply ?682 ?681) [682, 681] by Super 218 with 3 at 1,3 +Id : 15127, {_}: multiply (least_upper_bound (inverse ?21966) ?21967) ?21966 =>= positive_part (multiply ?21967 ?21966) [21967, 21966] by Demod 224 with 279 at 3 +Id : 5107, {_}: least_upper_bound (inverse (negative_part ?8933)) (positive_part ?8934) =>= least_upper_bound (inverse (negative_part ?8933)) ?8934 [8934, 8933] by Super 749 with 5087 at 1,3 +Id : 15147, {_}: multiply (least_upper_bound (inverse (negative_part ?22031)) ?22032) (negative_part ?22031) =>= positive_part (multiply (positive_part ?22032) (negative_part ?22031)) [22032, 22031] by Super 15127 with 5107 at 1,2 +Id : 15100, {_}: multiply (least_upper_bound (inverse ?681) ?682) ?681 =>= positive_part (multiply ?682 ?681) [682, 681] by Demod 224 with 279 at 3 +Id : 15182, {_}: positive_part (multiply ?22032 (negative_part ?22031)) =<= positive_part (multiply (positive_part ?22032) (negative_part ?22031)) [22031, 22032] by Demod 15147 with 15100 at 2 +Id : 80873, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =<= positive_part (multiply ?90706 (negative_part (inverse ?90706))) [90706] by Demod 80872 with 15182 at 3 +Id : 191, {_}: multiply (inverse ?607) (greatest_lower_bound ?607 ?608) =>= greatest_lower_bound identity (multiply (inverse ?607) ?608) [608, 607] by Super 185 with 3 at 1,3 +Id : 14063, {_}: multiply (inverse ?19549) (greatest_lower_bound ?19549 ?19550) =>= negative_part (multiply (inverse ?19549) ?19550) [19550, 19549] by Demod 191 with 296 at 3 +Id : 14093, {_}: multiply (inverse ?19640) (negative_part ?19640) =?= negative_part (multiply (inverse ?19640) identity) [19640] by Super 14063 with 18 at 2,2 +Id : 14179, {_}: multiply (inverse ?19758) (negative_part ?19758) =>= negative_part (inverse ?19758) [19758] by Demod 14093 with 2348 at 1,3 +Id : 14205, {_}: multiply ?19826 (negative_part (inverse ?19826)) =>= negative_part (inverse (inverse ?19826)) [19826] by Super 14179 with 2377 at 1,2 +Id : 14261, {_}: multiply ?19826 (negative_part (inverse ?19826)) =>= negative_part ?19826 [19826] by Demod 14205 with 2377 at 1,3 +Id : 80874, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =>= positive_part (negative_part ?90706) [90706] by Demod 80873 with 14261 at 1,3 +Id : 80875, {_}: multiply (positive_part ?90706) (negative_part (inverse ?90706)) =>= identity [90706] by Demod 80874 with 464 at 3 +Id : 81247, {_}: multiply identity (inverse (negative_part (inverse ?91006))) =>= positive_part ?91006 [91006] by Super 2406 with 80875 at 1,2 +Id : 81627, {_}: inverse (negative_part (inverse ?91433)) =>= positive_part ?91433 [91433] by Demod 81247 with 2 at 2 +Id : 81628, {_}: inverse (negative_part ?91435) =<= positive_part (inverse ?91435) [91435] by Super 81627 with 2377 at 1,1,2 +Id : 82425, {_}: multiply (positive_part ?35122) (inverse (inverse (negative_part ?35122))) =>= ?35122 [35122] by Demod 25993 with 81628 at 1,2,2 +Id : 82501, {_}: multiply (positive_part ?35122) (negative_part ?35122) =>= ?35122 [35122] by Demod 82425 with 2377 at 2,2 +Id : 82875, {_}: a === a [] by Demod 1 with 82501 at 3 +Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4 +% SZS output end CNFRefutation for GRP167-1.p +22602: solved GRP167-1.p in 10.376648 using nrkbo +22602: status Unsatisfiable for GRP167-1.p +CLASH, statistics insufficient +22609: Facts: +22609: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22609: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22609: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22609: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22609: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22609: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22609: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22609: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22609: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22609: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22609: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22609: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22609: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22609: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22609: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22609: Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +22609: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +22609: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by lat4_3 ?53 ?54 +22609: Id : 20, {_}: + positive_part ?56 =<= least_upper_bound ?56 identity + [56] by lat4_4 ?56 +22609: Id : 21, {_}: + negative_part ?58 =<= greatest_lower_bound ?58 identity + [58] by lat4_5 ?58 +22609: Id : 22, {_}: + least_upper_bound ?60 (greatest_lower_bound ?61 ?62) + =<= + greatest_lower_bound (least_upper_bound ?60 ?61) + (least_upper_bound ?60 ?62) + [62, 61, 60] by lat4_6 ?60 ?61 ?62 +22609: Id : 23, {_}: + greatest_lower_bound ?64 (least_upper_bound ?65 ?66) + =<= + least_upper_bound (greatest_lower_bound ?64 ?65) + (greatest_lower_bound ?64 ?66) + [66, 65, 64] by lat4_7 ?64 ?65 ?66 +22609: Goal: +22609: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +22609: Order: +22609: nrkbo +22609: Leaf order: +22609: a 3 0 3 2 +22609: identity 6 0 0 +22609: positive_part 2 1 1 0,1,3 +22609: negative_part 2 1 1 0,2,3 +22609: inverse 7 1 0 +22609: greatest_lower_bound 19 2 0 +22609: least_upper_bound 19 2 0 +22609: multiply 21 2 1 0,3 +CLASH, statistics insufficient +22610: Facts: +22610: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22610: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22610: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22610: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22610: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +CLASH, statistics insufficient +22611: Facts: +22611: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22611: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22611: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22611: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22610: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22610: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22610: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22610: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22610: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22610: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22610: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22610: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22610: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22610: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22610: Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +22610: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +22610: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by lat4_3 ?53 ?54 +22610: Id : 20, {_}: + positive_part ?56 =<= least_upper_bound ?56 identity + [56] by lat4_4 ?56 +22610: Id : 21, {_}: + negative_part ?58 =<= greatest_lower_bound ?58 identity + [58] by lat4_5 ?58 +22610: Id : 22, {_}: + least_upper_bound ?60 (greatest_lower_bound ?61 ?62) + =<= + greatest_lower_bound (least_upper_bound ?60 ?61) + (least_upper_bound ?60 ?62) + [62, 61, 60] by lat4_6 ?60 ?61 ?62 +22610: Id : 23, {_}: + greatest_lower_bound ?64 (least_upper_bound ?65 ?66) + =<= + least_upper_bound (greatest_lower_bound ?64 ?65) + (greatest_lower_bound ?64 ?66) + [66, 65, 64] by lat4_7 ?64 ?65 ?66 +22610: Goal: +22610: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +22610: Order: +22610: kbo +22610: Leaf order: +22610: a 3 0 3 2 +22610: identity 6 0 0 +22610: positive_part 2 1 1 0,1,3 +22610: negative_part 2 1 1 0,2,3 +22610: inverse 7 1 0 +22610: greatest_lower_bound 19 2 0 +22610: least_upper_bound 19 2 0 +22610: multiply 21 2 1 0,3 +22611: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22611: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22611: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22611: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22611: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22611: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22611: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22611: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22611: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22611: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22611: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22611: Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +22611: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +22611: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by lat4_3 ?53 ?54 +22611: Id : 20, {_}: + positive_part ?56 =>= least_upper_bound ?56 identity + [56] by lat4_4 ?56 +22611: Id : 21, {_}: + negative_part ?58 =>= greatest_lower_bound ?58 identity + [58] by lat4_5 ?58 +22611: Id : 22, {_}: + least_upper_bound ?60 (greatest_lower_bound ?61 ?62) + =<= + greatest_lower_bound (least_upper_bound ?60 ?61) + (least_upper_bound ?60 ?62) + [62, 61, 60] by lat4_6 ?60 ?61 ?62 +22611: Id : 23, {_}: + greatest_lower_bound ?64 (least_upper_bound ?65 ?66) + =>= + least_upper_bound (greatest_lower_bound ?64 ?65) + (greatest_lower_bound ?64 ?66) + [66, 65, 64] by lat4_7 ?64 ?65 ?66 +22611: Goal: +22611: Id : 1, {_}: + a =<= multiply (positive_part a) (negative_part a) + [] by prove_lat4 +22611: Order: +22611: lpo +22611: Leaf order: +22611: a 3 0 3 2 +22611: identity 6 0 0 +22611: positive_part 2 1 1 0,1,3 +22611: negative_part 2 1 1 0,2,3 +22611: inverse 7 1 0 +22611: greatest_lower_bound 19 2 0 +22611: least_upper_bound 19 2 0 +22611: multiply 21 2 1 0,3 +Statistics : +Max weight : 16 +Found proof, 6.082892s +% SZS status Unsatisfiable for GRP167-2.p +% SZS output start CNFRefutation for GRP167-2.p +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11 +Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =?= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 22, {_}: least_upper_bound ?60 (greatest_lower_bound ?61 ?62) =<= greatest_lower_bound (least_upper_bound ?60 ?61) (least_upper_bound ?60 ?62) [62, 61, 60] by lat4_6 ?60 ?61 ?62 +Id : 221, {_}: multiply (least_upper_bound ?664 ?665) ?666 =<= least_upper_bound (multiply ?664 ?666) (multiply ?665 ?666) [666, 665, 664] by monotony_lub2 ?664 ?665 ?666 +Id : 21, {_}: negative_part ?58 =<= greatest_lower_bound ?58 identity [58] by lat4_5 ?58 +Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 20, {_}: positive_part ?56 =<= least_upper_bound ?56 identity [56] by lat4_4 ?56 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by lat4_3 ?53 ?54 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 17, {_}: inverse identity =>= identity [] by lat4_1 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 28, {_}: multiply (multiply ?75 ?76) ?77 =?= multiply ?75 (multiply ?76 ?77) [77, 76, 75] by associativity ?75 ?76 ?77 +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by lat4_2 ?51 +Id : 302, {_}: inverse (multiply ?849 ?850) =<= multiply (inverse ?850) (inverse ?849) [850, 849] by lat4_3 ?849 ?850 +Id : 1638, {_}: inverse (multiply ?3326 (inverse ?3327)) =>= multiply ?3327 (inverse ?3326) [3327, 3326] by Super 302 with 18 at 1,3 +Id : 30, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= multiply ?82 identity [83, 82] by Super 28 with 3 at 2,3 +Id : 303, {_}: inverse (multiply identity ?852) =<= multiply (inverse ?852) identity [852] by Super 302 with 17 at 2,3 +Id : 587, {_}: inverse ?1361 =<= multiply (inverse ?1361) identity [1361] by Demod 303 with 2 at 1,2 +Id : 589, {_}: inverse (inverse ?1364) =<= multiply ?1364 identity [1364] by Super 587 with 18 at 1,3 +Id : 603, {_}: ?1364 =<= multiply ?1364 identity [1364] by Demod 589 with 18 at 2 +Id : 645, {_}: multiply (multiply ?82 (inverse ?83)) ?83 =>= ?82 [83, 82] by Demod 30 with 603 at 3 +Id : 1648, {_}: inverse ?3357 =<= multiply ?3358 (inverse (multiply ?3357 (inverse (inverse ?3358)))) [3358, 3357] by Super 1638 with 645 at 1,2 +Id : 306, {_}: inverse (multiply ?859 (inverse ?860)) =>= multiply ?860 (inverse ?859) [860, 859] by Super 302 with 18 at 1,3 +Id : 1667, {_}: inverse ?3357 =<= multiply ?3358 (multiply (inverse ?3358) (inverse ?3357)) [3358, 3357] by Demod 1648 with 306 at 2,3 +Id : 48018, {_}: inverse ?56639 =<= multiply ?56640 (inverse (multiply ?56639 ?56640)) [56640, 56639] by Demod 1667 with 19 at 2,3 +Id : 657, {_}: multiply ?1476 (least_upper_bound ?1477 identity) =?= least_upper_bound (multiply ?1476 ?1477) ?1476 [1477, 1476] by Super 13 with 603 at 2,3 +Id : 4078, {_}: multiply ?7362 (positive_part ?7363) =<= least_upper_bound (multiply ?7362 ?7363) ?7362 [7363, 7362] by Demod 657 with 20 at 2,2 +Id : 4080, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= least_upper_bound identity (inverse ?7367) [7367] by Super 4078 with 3 at 1,3 +Id : 320, {_}: least_upper_bound identity ?881 =>= positive_part ?881 [881] by Super 6 with 20 at 3 +Id : 4115, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= positive_part (inverse ?7367) [7367] by Demod 4080 with 320 at 3 +Id : 618, {_}: multiply (multiply ?1420 (inverse ?1421)) ?1421 =>= multiply ?1420 identity [1421, 1420] by Super 28 with 3 at 2,3 +Id : 620, {_}: multiply (multiply ?1425 ?1426) (inverse ?1426) =>= multiply ?1425 identity [1426, 1425] by Super 618 with 18 at 2,1,2 +Id : 34073, {_}: multiply (multiply ?41189 ?41190) (inverse ?41190) =>= ?41189 [41190, 41189] by Demod 620 with 603 at 3 +Id : 651, {_}: multiply ?1462 (greatest_lower_bound ?1463 identity) =?= greatest_lower_bound (multiply ?1462 ?1463) ?1462 [1463, 1462] by Super 14 with 603 at 2,3 +Id : 676, {_}: multiply ?1462 (negative_part ?1463) =<= greatest_lower_bound (multiply ?1462 ?1463) ?1462 [1463, 1462] by Demod 651 with 21 at 2,2 +Id : 227, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= least_upper_bound identity (multiply ?688 ?687) [688, 687] by Super 221 with 3 at 1,3 +Id : 14335, {_}: multiply (least_upper_bound (inverse ?21902) ?21903) ?21902 =>= positive_part (multiply ?21903 ?21902) [21903, 21902] by Demod 227 with 320 at 3 +Id : 14360, {_}: multiply (positive_part (inverse ?21984)) ?21984 =>= positive_part (multiply identity ?21984) [21984] by Super 14335 with 20 at 1,2 +Id : 14399, {_}: multiply (positive_part (inverse ?21984)) ?21984 =>= positive_part ?21984 [21984] by Demod 14360 with 2 at 1,3 +Id : 14409, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= greatest_lower_bound (positive_part ?22003) (positive_part (inverse ?22003)) [22003] by Super 676 with 14399 at 1,3 +Id : 504, {_}: least_upper_bound identity (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (least_upper_bound identity ?1268) (positive_part ?1269) [1269, 1268] by Super 22 with 320 at 2,3 +Id : 513, {_}: positive_part (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (least_upper_bound identity ?1268) (positive_part ?1269) [1269, 1268] by Demod 504 with 320 at 2 +Id : 514, {_}: positive_part (greatest_lower_bound ?1268 ?1269) =<= greatest_lower_bound (positive_part ?1268) (positive_part ?1269) [1269, 1268] by Demod 513 with 320 at 1,3 +Id : 14487, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= positive_part (greatest_lower_bound ?22003 (inverse ?22003)) [22003] by Demod 14409 with 514 at 3 +Id : 501, {_}: least_upper_bound identity (least_upper_bound ?1262 ?1263) =>= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Super 8 with 320 at 1,3 +Id : 518, {_}: positive_part (least_upper_bound ?1262 ?1263) =>= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Demod 501 with 320 at 2 +Id : 317, {_}: least_upper_bound ?872 (least_upper_bound ?873 identity) =>= positive_part (least_upper_bound ?872 ?873) [873, 872] by Super 8 with 20 at 3 +Id : 329, {_}: least_upper_bound ?872 (positive_part ?873) =<= positive_part (least_upper_bound ?872 ?873) [873, 872] by Demod 317 with 20 at 2,2 +Id : 975, {_}: least_upper_bound ?1262 (positive_part ?1263) =?= least_upper_bound (positive_part ?1262) ?1263 [1263, 1262] by Demod 518 with 329 at 2 +Id : 4147, {_}: multiply (inverse ?7493) (positive_part ?7493) =>= positive_part (inverse ?7493) [7493] by Demod 4080 with 320 at 3 +Id : 337, {_}: greatest_lower_bound identity ?912 =>= negative_part ?912 [912] by Super 5 with 21 at 3 +Id : 533, {_}: least_upper_bound identity (negative_part ?1296) =>= identity [1296] by Super 11 with 337 at 2,2 +Id : 549, {_}: positive_part (negative_part ?1296) =>= identity [1296] by Demod 533 with 320 at 2 +Id : 4149, {_}: multiply (inverse (negative_part ?7496)) identity =>= positive_part (inverse (negative_part ?7496)) [7496] by Super 4147 with 549 at 2,2 +Id : 4174, {_}: inverse (negative_part ?7496) =<= positive_part (inverse (negative_part ?7496)) [7496] by Demod 4149 with 603 at 2 +Id : 4193, {_}: least_upper_bound (inverse (negative_part ?7552)) (positive_part ?7553) =>= least_upper_bound (inverse (negative_part ?7552)) ?7553 [7553, 7552] by Super 975 with 4174 at 1,3 +Id : 14357, {_}: multiply (least_upper_bound (inverse (negative_part ?21975)) ?21976) (negative_part ?21975) =>= positive_part (multiply (positive_part ?21976) (negative_part ?21975)) [21976, 21975] by Super 14335 with 4193 at 1,2 +Id : 14303, {_}: multiply (least_upper_bound (inverse ?687) ?688) ?687 =>= positive_part (multiply ?688 ?687) [688, 687] by Demod 227 with 320 at 3 +Id : 14396, {_}: positive_part (multiply ?21976 (negative_part ?21975)) =<= positive_part (multiply (positive_part ?21976) (negative_part ?21975)) [21975, 21976] by Demod 14357 with 14303 at 2 +Id : 15618, {_}: positive_part (multiply (inverse ?23238) (negative_part ?23238)) =<= positive_part (positive_part (greatest_lower_bound ?23238 (inverse ?23238))) [23238] by Super 14396 with 14487 at 1,3 +Id : 4791, {_}: multiply ?8267 (negative_part ?8268) =<= greatest_lower_bound (multiply ?8267 ?8268) ?8267 [8268, 8267] by Demod 651 with 21 at 2,2 +Id : 4793, {_}: multiply (inverse ?8272) (negative_part ?8272) =>= greatest_lower_bound identity (inverse ?8272) [8272] by Super 4791 with 3 at 1,3 +Id : 4834, {_}: multiply (inverse ?8272) (negative_part ?8272) =>= negative_part (inverse ?8272) [8272] by Demod 4793 with 337 at 3 +Id : 15709, {_}: positive_part (negative_part (inverse ?23238)) =<= positive_part (positive_part (greatest_lower_bound ?23238 (inverse ?23238))) [23238] by Demod 15618 with 4834 at 1,2 +Id : 774, {_}: least_upper_bound ?1603 (positive_part ?1604) =<= positive_part (least_upper_bound ?1603 ?1604) [1604, 1603] by Demod 317 with 20 at 2,2 +Id : 784, {_}: least_upper_bound ?1635 (positive_part identity) =>= positive_part (positive_part ?1635) [1635] by Super 774 with 20 at 1,3 +Id : 322, {_}: positive_part identity =>= identity [] by Super 9 with 20 at 2 +Id : 796, {_}: least_upper_bound ?1635 identity =<= positive_part (positive_part ?1635) [1635] by Demod 784 with 322 at 2,2 +Id : 797, {_}: positive_part ?1635 =<= positive_part (positive_part ?1635) [1635] by Demod 796 with 20 at 2 +Id : 15710, {_}: positive_part (negative_part (inverse ?23238)) =<= positive_part (greatest_lower_bound ?23238 (inverse ?23238)) [23238] by Demod 15709 with 797 at 3 +Id : 15711, {_}: identity =<= positive_part (greatest_lower_bound ?23238 (inverse ?23238)) [23238] by Demod 15710 with 549 at 2 +Id : 15820, {_}: multiply (positive_part (inverse ?22003)) (negative_part ?22003) =>= identity [22003] by Demod 14487 with 15711 at 3 +Id : 34109, {_}: multiply identity (inverse (negative_part ?41304)) =>= positive_part (inverse ?41304) [41304] by Super 34073 with 15820 at 1,2 +Id : 34155, {_}: inverse (negative_part ?41304) =<= positive_part (inverse ?41304) [41304] by Demod 34109 with 2 at 2 +Id : 34195, {_}: multiply (inverse ?7367) (positive_part ?7367) =>= inverse (negative_part ?7367) [7367] by Demod 4115 with 34155 at 3 +Id : 48045, {_}: inverse (inverse ?56723) =<= multiply (positive_part ?56723) (inverse (inverse (negative_part ?56723))) [56723] by Super 48018 with 34195 at 1,2,3 +Id : 48126, {_}: ?56723 =<= multiply (positive_part ?56723) (inverse (inverse (negative_part ?56723))) [56723] by Demod 48045 with 18 at 2 +Id : 48127, {_}: ?56723 =<= multiply (positive_part ?56723) (negative_part ?56723) [56723] by Demod 48126 with 18 at 2,3 +Id : 48357, {_}: a === a [] by Demod 1 with 48127 at 3 +Id : 1, {_}: a =<= multiply (positive_part a) (negative_part a) [] by prove_lat4 +% SZS output end CNFRefutation for GRP167-2.p +22609: solved GRP167-2.p in 6.08038 using nrkbo +22609: status Unsatisfiable for GRP167-2.p +NO CLASH, using fixed ground order +22621: Facts: +NO CLASH, using fixed ground order +22622: Facts: +22622: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22622: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22622: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22622: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22622: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22622: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22622: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22622: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22622: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22622: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22622: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22622: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22622: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22622: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22622: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22622: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1 +22622: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2 +22622: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3 +22622: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4 +22622: Goal: +22622: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09a +22622: Order: +22622: kbo +22622: Leaf order: +22622: b 4 0 1 1,2,2 +22622: c 4 0 2 2,2,2 +22622: a 5 0 2 1,2 +22622: identity 6 0 0 +22622: inverse 1 1 0 +22622: least_upper_bound 16 2 0 +22622: greatest_lower_bound 16 2 2 0,2 +22622: multiply 19 2 1 0,2,2 +NO CLASH, using fixed ground order +22623: Facts: +22623: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22623: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22623: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22623: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22623: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22623: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22623: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22623: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22623: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22623: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22623: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22623: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22623: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22623: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22623: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22623: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1 +22623: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2 +22623: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3 +22623: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4 +22623: Goal: +22623: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09a +22623: Order: +22623: lpo +22623: Leaf order: +22623: b 4 0 1 1,2,2 +22623: c 4 0 2 2,2,2 +22623: a 5 0 2 1,2 +22623: identity 6 0 0 +22623: inverse 1 1 0 +22623: least_upper_bound 16 2 0 +22623: greatest_lower_bound 16 2 2 0,2 +22623: multiply 19 2 1 0,2,2 +22621: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22621: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22621: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22621: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22621: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22621: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22621: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22621: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22621: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22621: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22621: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22621: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22621: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22621: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22621: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22621: Id : 17, {_}: least_upper_bound identity a =>= a [] by p09a_1 +22621: Id : 18, {_}: least_upper_bound identity b =>= b [] by p09a_2 +22621: Id : 19, {_}: least_upper_bound identity c =>= c [] by p09a_3 +22621: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09a_4 +22621: Goal: +22621: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09a +22621: Order: +22621: nrkbo +22621: Leaf order: +22621: b 4 0 1 1,2,2 +22621: c 4 0 2 2,2,2 +22621: a 5 0 2 1,2 +22621: identity 6 0 0 +22621: inverse 1 1 0 +22621: least_upper_bound 16 2 0 +22621: greatest_lower_bound 16 2 2 0,2 +22621: multiply 19 2 1 0,2,2 +% SZS status Timeout for GRP178-1.p +NO CLASH, using fixed ground order +22657: Facts: +22657: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22657: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22657: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22657: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22657: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22657: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22657: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22657: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22657: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22657: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22657: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22657: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22657: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22657: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22657: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22657: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1 +22657: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2 +22657: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3 +22657: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4 +22657: Goal: +22657: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09b +22657: Order: +22657: nrkbo +22657: Leaf order: +22657: b 3 0 1 1,2,2 +22657: c 3 0 2 2,2,2 +22657: a 4 0 2 1,2 +22657: identity 9 0 0 +22657: inverse 1 1 0 +22657: least_upper_bound 13 2 0 +22657: multiply 19 2 1 0,2,2 +22657: greatest_lower_bound 19 2 2 0,2 +NO CLASH, using fixed ground order +22658: Facts: +22658: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22658: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22658: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22658: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22658: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22658: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22658: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22658: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22658: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22658: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22658: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22658: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22658: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22658: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22658: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22658: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1 +22658: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2 +22658: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3 +22658: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4 +22658: Goal: +22658: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09b +22658: Order: +22658: kbo +22658: Leaf order: +22658: b 3 0 1 1,2,2 +22658: c 3 0 2 2,2,2 +22658: a 4 0 2 1,2 +22658: identity 9 0 0 +22658: inverse 1 1 0 +22658: least_upper_bound 13 2 0 +22658: multiply 19 2 1 0,2,2 +22658: greatest_lower_bound 19 2 2 0,2 +NO CLASH, using fixed ground order +22659: Facts: +22659: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22659: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22659: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22659: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22659: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22659: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22659: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22659: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22659: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22659: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22659: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22659: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22659: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22659: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22659: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22659: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1 +22659: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2 +22659: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3 +22659: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4 +22659: Goal: +22659: Id : 1, {_}: + greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c + [] by prove_p09b +22659: Order: +22659: lpo +22659: Leaf order: +22659: b 3 0 1 1,2,2 +22659: c 3 0 2 2,2,2 +22659: a 4 0 2 1,2 +22659: identity 9 0 0 +22659: inverse 1 1 0 +22659: least_upper_bound 13 2 0 +22659: multiply 19 2 1 0,2,2 +22659: greatest_lower_bound 19 2 2 0,2 +% SZS status Timeout for GRP178-2.p +CLASH, statistics insufficient +22685: Facts: +22685: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22685: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22685: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22685: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22685: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22685: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22685: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22685: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22685: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22685: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22685: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22685: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22685: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22685: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22685: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22685: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_1 +22685: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2 +22685: Id : 19, {_}: + inverse (greatest_lower_bound ?52 ?53) + =<= + least_upper_bound (inverse ?52) (inverse ?53) + [53, 52] by p12x_3 ?52 ?53 +22685: Id : 20, {_}: + inverse (least_upper_bound ?55 ?56) + =<= + greatest_lower_bound (inverse ?55) (inverse ?56) + [56, 55] by p12x_4 ?55 ?56 +22685: Goal: +22685: Id : 1, {_}: a =>= b [] by prove_p12x +22685: Order: +22685: nrkbo +22685: Leaf order: +22685: identity 2 0 0 +22685: a 3 0 1 2 +22685: b 3 0 1 3 +22685: c 4 0 0 +22685: inverse 7 1 0 +22685: greatest_lower_bound 17 2 0 +22685: least_upper_bound 17 2 0 +22685: multiply 18 2 0 +CLASH, statistics insufficient +22686: Facts: +22686: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22686: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22686: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22686: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22686: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +CLASH, statistics insufficient +22687: Facts: +22687: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22687: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22687: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22687: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22687: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22687: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22686: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22686: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22686: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22686: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22686: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22686: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22686: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22686: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22686: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22686: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22686: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_1 +22686: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2 +22686: Id : 19, {_}: + inverse (greatest_lower_bound ?52 ?53) + =<= + least_upper_bound (inverse ?52) (inverse ?53) + [53, 52] by p12x_3 ?52 ?53 +22686: Id : 20, {_}: + inverse (least_upper_bound ?55 ?56) + =<= + greatest_lower_bound (inverse ?55) (inverse ?56) + [56, 55] by p12x_4 ?55 ?56 +22686: Goal: +22686: Id : 1, {_}: a =>= b [] by prove_p12x +22686: Order: +22686: kbo +22686: Leaf order: +22686: identity 2 0 0 +22686: a 3 0 1 2 +22686: b 3 0 1 3 +22686: c 4 0 0 +22686: inverse 7 1 0 +22686: greatest_lower_bound 17 2 0 +22686: least_upper_bound 17 2 0 +22686: multiply 18 2 0 +22687: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22687: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22687: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22687: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22687: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22687: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22687: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22687: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22687: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22687: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_1 +22687: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_2 +22687: Id : 19, {_}: + inverse (greatest_lower_bound ?52 ?53) + =>= + least_upper_bound (inverse ?52) (inverse ?53) + [53, 52] by p12x_3 ?52 ?53 +22687: Id : 20, {_}: + inverse (least_upper_bound ?55 ?56) + =>= + greatest_lower_bound (inverse ?55) (inverse ?56) + [56, 55] by p12x_4 ?55 ?56 +22687: Goal: +22687: Id : 1, {_}: a =>= b [] by prove_p12x +22687: Order: +22687: lpo +22687: Leaf order: +22687: identity 2 0 0 +22687: a 3 0 1 2 +22687: b 3 0 1 3 +22687: c 4 0 0 +22687: inverse 7 1 0 +22687: greatest_lower_bound 17 2 0 +22687: least_upper_bound 17 2 0 +22687: multiply 18 2 0 +% SZS status Timeout for GRP181-3.p +NO CLASH, using fixed ground order +22714: Facts: +22714: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22714: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22714: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22714: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22714: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22714: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22714: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22714: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22714: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22714: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22714: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22714: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22714: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22714: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22714: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22714: Id : 17, {_}: inverse identity =>= identity [] by p21_1 +22714: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51 +22714: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p21_3 ?53 ?54 +22714: Goal: +22714: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +22714: Order: +22714: nrkbo +22714: Leaf order: +22714: a 4 0 4 1,1,2 +22714: identity 8 0 4 2,1,2 +22714: inverse 9 1 2 0,2,2 +22714: least_upper_bound 15 2 2 0,1,2 +22714: greatest_lower_bound 15 2 2 0,1,2,2 +22714: multiply 22 2 2 0,2 +NO CLASH, using fixed ground order +22715: Facts: +22715: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22715: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22715: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22715: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22715: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22715: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22715: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22715: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22715: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22715: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22715: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22715: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22715: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22715: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22715: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22715: Id : 17, {_}: inverse identity =>= identity [] by p21_1 +22715: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51 +22715: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p21_3 ?53 ?54 +22715: Goal: +22715: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +22715: Order: +22715: kbo +22715: Leaf order: +22715: a 4 0 4 1,1,2 +22715: identity 8 0 4 2,1,2 +22715: inverse 9 1 2 0,2,2 +22715: least_upper_bound 15 2 2 0,1,2 +22715: greatest_lower_bound 15 2 2 0,1,2,2 +22715: multiply 22 2 2 0,2 +NO CLASH, using fixed ground order +22716: Facts: +22716: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22716: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22716: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22716: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22716: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22716: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22716: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22716: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22716: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22716: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22716: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22716: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22716: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22716: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22716: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22716: Id : 17, {_}: inverse identity =>= identity [] by p21_1 +22716: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21_2 ?51 +22716: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p21_3 ?53 ?54 +22716: Goal: +22716: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +22716: Order: +22716: lpo +22716: Leaf order: +22716: a 4 0 4 1,1,2 +22716: identity 8 0 4 2,1,2 +22716: inverse 9 1 2 0,2,2 +22716: least_upper_bound 15 2 2 0,1,2 +22716: greatest_lower_bound 15 2 2 0,1,2,2 +22716: multiply 22 2 2 0,2 +% SZS status Timeout for GRP184-2.p +NO CLASH, using fixed ground order +22807: Facts: +22807: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22807: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22807: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22807: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22807: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22807: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22807: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22807: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22807: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22807: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22807: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22807: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22807: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22807: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22807: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22807: Goal: +22807: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +22807: Order: +22807: nrkbo +22807: Leaf order: +22807: a 3 0 3 1,1,1,2 +22807: b 3 0 3 2,1,1,2 +22807: identity 7 0 5 2,1,2 +22807: inverse 1 1 0 +22807: greatest_lower_bound 13 2 0 +22807: least_upper_bound 19 2 6 0,2 +22807: multiply 21 2 3 0,1,1,2 +NO CLASH, using fixed ground order +22808: Facts: +22808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22808: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22808: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22808: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22808: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22808: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22808: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22808: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22808: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22808: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22808: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22808: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22808: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22808: Goal: +22808: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +22808: Order: +22808: kbo +22808: Leaf order: +22808: a 3 0 3 1,1,1,2 +22808: b 3 0 3 2,1,1,2 +22808: identity 7 0 5 2,1,2 +22808: inverse 1 1 0 +22808: greatest_lower_bound 13 2 0 +22808: least_upper_bound 19 2 6 0,2 +22808: multiply 21 2 3 0,1,1,2 +NO CLASH, using fixed ground order +22809: Facts: +22809: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22809: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22809: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22809: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22809: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22809: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22809: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22809: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22809: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22809: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22809: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22809: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22809: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22809: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22809: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22809: Goal: +22809: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +22809: Order: +22809: lpo +22809: Leaf order: +22809: a 3 0 3 1,1,1,2 +22809: b 3 0 3 2,1,1,2 +22809: identity 7 0 5 2,1,2 +22809: inverse 1 1 0 +22809: greatest_lower_bound 13 2 0 +22809: least_upper_bound 19 2 6 0,2 +22809: multiply 21 2 3 0,1,1,2 +Statistics : +Max weight : 21 +Found proof, 1.740382s +% SZS status Unsatisfiable for GRP185-1.p +% SZS output start CNFRefutation for GRP185-1.p +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2 +Id : 482, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2 +Id : 484, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 482 with 3 at 2,3 +Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2 +Id : 490, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 482 with 27 at 2,3 +Id : 725, {_}: ?599 =<= multiply ?599 identity [599] by Demod 484 with 490 at 3 +Id : 73, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3 +Id : 57, {_}: least_upper_bound ?143 (least_upper_bound ?144 ?145) =?= least_upper_bound ?144 (least_upper_bound ?145 ?143) [145, 144, 143] by Super 6 with 8 at 3 +Id : 3011, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) === least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3010 with 73 at 2,2,2 +Id : 3010, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (least_upper_bound identity (multiply a b)))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3009 with 8 at 2,2 +Id : 3009, {_}: least_upper_bound b (least_upper_bound (least_upper_bound a identity) (least_upper_bound identity (multiply a b))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3008 with 8 at 2 +Id : 3008, {_}: least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (least_upper_bound identity (multiply a b)) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 3007 with 8 at 2,3 +Id : 3007, {_}: least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (least_upper_bound identity (multiply a b)) =>= least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b)) [] by Demod 3006 with 57 at 2 +Id : 3006, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b)) [] by Demod 3005 with 8 at 3 +Id : 3005, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3004 with 2 at 2,2,2,2,2 +Id : 3004, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3003 with 725 at 1,2,2,2,2 +Id : 3003, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3002 with 2 at 1,2,2,2 +Id : 3002, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b) [] by Demod 3001 with 6 at 3 +Id : 3001, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity)) [] by Demod 3000 with 73 at 2,2 +Id : 3000, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity)) [] by Demod 2999 with 2 at 2,2,2,3 +Id : 2999, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity))) [] by Demod 2998 with 725 at 1,2,2,3 +Id : 2998, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2997 with 2 at 1,2,3 +Id : 2997, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2996 with 8 at 2,2,2 +Id : 2996, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 2995 with 8 at 3 +Id : 2995, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2994 with 15 at 2,2,2,2 +Id : 2994, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2993 with 15 at 1,2,2,2 +Id : 2993, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 2992 with 15 at 2,3 +Id : 2992, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity) [] by Demod 2991 with 15 at 1,3 +Id : 2991, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 2990 with 13 at 2,2,2 +Id : 2990, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 2989 with 13 at 3 +Id : 2989, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 56 with 8 at 2 +Id : 56, {_}: least_upper_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 6 at 1,2 +Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a +% SZS output end CNFRefutation for GRP185-1.p +22809: solved GRP185-1.p in 0.852052 using lpo +22809: status Unsatisfiable for GRP185-1.p +NO CLASH, using fixed ground order +22814: Facts: +NO CLASH, using fixed ground order +22815: Facts: +22815: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22815: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22815: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22815: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22815: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22815: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22815: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +NO CLASH, using fixed ground order +22816: Facts: +22816: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22816: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22816: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22816: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22816: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22816: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22816: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22816: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22814: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22815: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22814: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +22815: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22815: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22815: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22814: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +22814: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +22814: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +22815: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22814: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +22815: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22814: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +22814: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +22814: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22814: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22814: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22814: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22814: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22814: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22814: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22814: Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +22814: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +22814: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22a_3 ?53 ?54 +22814: Goal: +22814: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +22814: Order: +22814: nrkbo +22814: Leaf order: +22814: a 3 0 3 1,1,1,2 +22814: b 3 0 3 2,1,1,2 +22814: identity 9 0 5 2,1,2 +22814: inverse 7 1 0 +22814: greatest_lower_bound 13 2 0 +22814: least_upper_bound 19 2 6 0,2 +22814: multiply 23 2 3 0,1,1,2 +22816: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +22815: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22815: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22815: Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +22815: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +22815: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22a_3 ?53 ?54 +22815: Goal: +22815: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +22815: Order: +22815: kbo +22815: Leaf order: +22815: a 3 0 3 1,1,1,2 +22815: b 3 0 3 2,1,1,2 +22815: identity 9 0 5 2,1,2 +22815: inverse 7 1 0 +22815: greatest_lower_bound 13 2 0 +22815: least_upper_bound 19 2 6 0,2 +22815: multiply 23 2 3 0,1,1,2 +22816: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +22816: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +22816: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +22816: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +22816: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +22816: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +22816: Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +22816: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +22816: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22a_3 ?53 ?54 +22816: Goal: +22816: Id : 1, {_}: + least_upper_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + multiply (least_upper_bound a identity) + (least_upper_bound b identity) + [] by prove_p22a +22816: Order: +22816: lpo +22816: Leaf order: +22816: a 3 0 3 1,1,1,2 +22816: b 3 0 3 2,1,1,2 +22816: identity 9 0 5 2,1,2 +22816: inverse 7 1 0 +22816: greatest_lower_bound 13 2 0 +22816: least_upper_bound 19 2 6 0,2 +22816: multiply 23 2 3 0,1,1,2 +Statistics : +Max weight : 21 +Found proof, 4.698116s +% SZS status Unsatisfiable for GRP185-2.p +% SZS output start CNFRefutation for GRP185-2.p +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22a_2 ?51 +Id : 17, {_}: inverse identity =>= identity [] by p22a_1 +Id : 426, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22a_3 ?520 ?521 +Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +Id : 62, {_}: least_upper_bound ?157 (least_upper_bound ?158 ?159) =<= least_upper_bound (least_upper_bound ?157 ?158) ?159 [159, 158, 157] by associativity_of_lub ?157 ?158 ?159 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 63, {_}: least_upper_bound ?161 (least_upper_bound ?162 ?163) =<= least_upper_bound (least_upper_bound ?162 ?161) ?163 [163, 162, 161] by Super 62 with 6 at 1,3 +Id : 69, {_}: least_upper_bound ?161 (least_upper_bound ?162 ?163) =?= least_upper_bound ?162 (least_upper_bound ?161 ?163) [163, 162, 161] by Demod 63 with 8 at 3 +Id : 76, {_}: least_upper_bound ?186 (least_upper_bound ?186 ?187) =>= least_upper_bound ?186 ?187 [187, 186] by Super 8 with 9 at 1,3 +Id : 427, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 426 with 17 at 2,3 +Id : 481, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 427 with 2 at 1,2 +Id : 483, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 481 with 18 at 1,3 +Id : 491, {_}: ?572 =<= multiply ?572 identity [572] by Demod 483 with 18 at 2 +Id : 60, {_}: least_upper_bound ?149 (least_upper_bound ?150 ?151) =?= least_upper_bound ?150 (least_upper_bound ?151 ?149) [151, 150, 149] by Super 6 with 8 at 3 +Id : 706, {_}: least_upper_bound ?667 (least_upper_bound ?667 ?668) =>= least_upper_bound ?667 ?668 [668, 667] by Super 8 with 9 at 1,3 +Id : 707, {_}: least_upper_bound ?670 (least_upper_bound ?671 ?670) =>= least_upper_bound ?670 ?671 [671, 670] by Super 706 with 6 at 2,2 +Id : 1184, {_}: least_upper_bound ?916 (least_upper_bound (least_upper_bound ?917 ?916) ?918) =?= least_upper_bound (least_upper_bound ?916 ?917) ?918 [918, 917, 916] by Super 8 with 707 at 1,3 +Id : 1214, {_}: least_upper_bound ?916 (least_upper_bound ?917 (least_upper_bound ?916 ?918)) =<= least_upper_bound (least_upper_bound ?916 ?917) ?918 [918, 917, 916] by Demod 1184 with 8 at 2,2 +Id : 1215, {_}: least_upper_bound ?916 (least_upper_bound ?917 (least_upper_bound ?916 ?918)) =>= least_upper_bound ?916 (least_upper_bound ?917 ?918) [918, 917, 916] by Demod 1214 with 8 at 3 +Id : 7862, {_}: least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) === least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7861 with 69 at 2 +Id : 7861, {_}: least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7860 with 60 at 2,2 +Id : 7860, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7859 with 491 at 2,2,2,2 +Id : 7859, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) =>= least_upper_bound a (least_upper_bound b (least_upper_bound identity (multiply a b))) [] by Demod 7858 with 69 at 3 +Id : 7858, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 7857 with 1215 at 2,2 +Id : 7857, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b))) [] by Demod 7856 with 60 at 2,3 +Id : 7856, {_}: least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) [] by Demod 7855 with 69 at 2 +Id : 7855, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) a)) [] by Demod 7854 with 491 at 2,2,2,3 +Id : 7854, {_}: least_upper_bound identity (least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) [] by Demod 7853 with 69 at 2,2 +Id : 7853, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound identity (least_upper_bound (multiply a b) (multiply a identity))) [] by Demod 7852 with 69 at 2,3 +Id : 7852, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity)))) =>= least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity))) [] by Demod 7851 with 76 at 2,2 +Id : 7851, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound b (least_upper_bound (multiply a b) (least_upper_bound identity (multiply a identity))) [] by Demod 7850 with 69 at 3 +Id : 7850, {_}: least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 509 with 69 at 2 +Id : 509, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 508 with 6 at 2,2,2,2,2 +Id : 508, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound identity (multiply a identity))) [] by Demod 507 with 6 at 2,2,3 +Id : 507, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 506 with 2 at 2,2,2,2,2,2 +Id : 506, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 505 with 2 at 1,2,2,2,2 +Id : 505, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) identity)) [] by Demod 504 with 2 at 2,2,2,3 +Id : 504, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 503 with 2 at 1,2,3 +Id : 503, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 502 with 8 at 2,2,2 +Id : 502, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity))) [] by Demod 501 with 8 at 3 +Id : 501, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 500 with 15 at 2,2,2,2 +Id : 500, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 499 with 15 at 1,2,2,2 +Id : 499, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity)) [] by Demod 498 with 15 at 2,3 +Id : 498, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity) [] by Demod 497 with 15 at 1,3 +Id : 497, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 496 with 13 at 2,2,2 +Id : 496, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity) [] by Demod 495 with 13 at 3 +Id : 495, {_}: least_upper_bound (multiply a b) (least_upper_bound identity (multiply (least_upper_bound a identity) (least_upper_bound b identity))) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by Demod 1 with 8 at 2 +Id : 1, {_}: least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= multiply (least_upper_bound a identity) (least_upper_bound b identity) [] by prove_p22a +% SZS output end CNFRefutation for GRP185-2.p +22816: solved GRP185-2.p in 2.292143 using lpo +22816: status Unsatisfiable for GRP185-2.p +CLASH, statistics insufficient +22828: Facts: +22828: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22828: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22828: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22828: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22828: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22828: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22828: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22828: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22828: Id : 10, {_}: + multiply (multiply ?22 (multiply ?23 ?24)) ?22 + =?= + multiply (multiply ?22 ?23) (multiply ?24 ?22) + [24, 23, 22] by moufang1 ?22 ?23 ?24 +22828: Goal: +22828: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +22828: Order: +22828: nrkbo +22828: Leaf order: +22828: a 2 0 2 1,1,1,2 +22828: c 2 0 2 2,1,2 +22828: identity 4 0 0 +22828: b 4 0 4 2,1,1,2 +22828: right_inverse 1 1 0 +22828: left_inverse 1 1 0 +22828: left_division 2 2 0 +22828: right_division 2 2 0 +22828: multiply 20 2 6 0,2 +CLASH, statistics insufficient +22829: Facts: +22829: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22829: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22829: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22829: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22829: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22829: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22829: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22829: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22829: Id : 10, {_}: + multiply (multiply ?22 (multiply ?23 ?24)) ?22 + =>= + multiply (multiply ?22 ?23) (multiply ?24 ?22) + [24, 23, 22] by moufang1 ?22 ?23 ?24 +22829: Goal: +22829: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +22829: Order: +22829: kbo +22829: Leaf order: +22829: a 2 0 2 1,1,1,2 +22829: c 2 0 2 2,1,2 +22829: identity 4 0 0 +22829: b 4 0 4 2,1,1,2 +22829: right_inverse 1 1 0 +22829: left_inverse 1 1 0 +22829: left_division 2 2 0 +22829: right_division 2 2 0 +22829: multiply 20 2 6 0,2 +CLASH, statistics insufficient +22830: Facts: +22830: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22830: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22830: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22830: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22830: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22830: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22830: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22830: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22830: Id : 10, {_}: + multiply (multiply ?22 (multiply ?23 ?24)) ?22 + =>= + multiply (multiply ?22 ?23) (multiply ?24 ?22) + [24, 23, 22] by moufang1 ?22 ?23 ?24 +22830: Goal: +22830: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +22830: Order: +22830: lpo +22830: Leaf order: +22830: a 2 0 2 1,1,1,2 +22830: c 2 0 2 2,1,2 +22830: identity 4 0 0 +22830: b 4 0 4 2,1,1,2 +22830: right_inverse 1 1 0 +22830: left_inverse 1 1 0 +22830: left_division 2 2 0 +22830: right_division 2 2 0 +22830: multiply 20 2 6 0,2 +% SZS status Timeout for GRP200-1.p +CLASH, statistics insufficient +22867: Facts: +22867: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22867: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22867: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22867: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22867: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22867: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22867: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22867: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22867: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?24) ?23 + =?= + multiply ?22 (multiply ?23 (multiply ?24 ?23)) + [24, 23, 22] by moufang2 ?22 ?23 ?24 +22867: Goal: +22867: Id : 1, {_}: + multiply (multiply (multiply a b) a) c + =>= + multiply a (multiply b (multiply a c)) + [] by prove_moufang3 +22867: Order: +22867: nrkbo +22867: Leaf order: +22867: b 2 0 2 2,1,1,2 +22867: c 2 0 2 2,2 +22867: identity 4 0 0 +22867: a 4 0 4 1,1,1,2 +22867: right_inverse 1 1 0 +22867: left_inverse 1 1 0 +22867: left_division 2 2 0 +22867: right_division 2 2 0 +22867: multiply 20 2 6 0,2 +CLASH, statistics insufficient +22868: Facts: +22868: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22868: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22868: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22868: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22868: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22868: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22868: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22868: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22868: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?24) ?23 + =>= + multiply ?22 (multiply ?23 (multiply ?24 ?23)) + [24, 23, 22] by moufang2 ?22 ?23 ?24 +22868: Goal: +22868: Id : 1, {_}: + multiply (multiply (multiply a b) a) c + =>= + multiply a (multiply b (multiply a c)) + [] by prove_moufang3 +22868: Order: +22868: kbo +22868: Leaf order: +22868: b 2 0 2 2,1,1,2 +22868: c 2 0 2 2,2 +22868: identity 4 0 0 +22868: a 4 0 4 1,1,1,2 +22868: right_inverse 1 1 0 +22868: left_inverse 1 1 0 +22868: left_division 2 2 0 +22868: right_division 2 2 0 +22868: multiply 20 2 6 0,2 +CLASH, statistics insufficient +22869: Facts: +22869: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22869: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22869: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22869: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22869: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22869: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22869: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22869: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22869: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?24) ?23 + =>= + multiply ?22 (multiply ?23 (multiply ?24 ?23)) + [24, 23, 22] by moufang2 ?22 ?23 ?24 +22869: Goal: +22869: Id : 1, {_}: + multiply (multiply (multiply a b) a) c + =>= + multiply a (multiply b (multiply a c)) + [] by prove_moufang3 +22869: Order: +22869: lpo +22869: Leaf order: +22869: b 2 0 2 2,1,1,2 +22869: c 2 0 2 2,2 +22869: identity 4 0 0 +22869: a 4 0 4 1,1,1,2 +22869: right_inverse 1 1 0 +22869: left_inverse 1 1 0 +22869: left_division 2 2 0 +22869: right_division 2 2 0 +22869: multiply 20 2 6 0,2 +Statistics : +Max weight : 15 +Found proof, 24.434685s +% SZS status Unsatisfiable for GRP201-1.p +% SZS output start CNFRefutation for GRP201-1.p +Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49 +Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18 +Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13 +Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7 +Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20 +Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?24) ?23 =>= multiply ?22 (multiply ?23 (multiply ?24 ?23)) [24, 23, 22] by moufang2 ?22 ?23 ?24 +Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16 +Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 54, {_}: multiply (multiply (multiply ?119 ?120) ?121) ?120 =>= multiply ?119 (multiply ?120 (multiply ?121 ?120)) [121, 120, 119] by moufang2 ?119 ?120 ?121 +Id : 55, {_}: multiply (multiply ?123 ?124) ?123 =<= multiply identity (multiply ?123 (multiply ?124 ?123)) [124, 123] by Super 54 with 2 at 1,1,2 +Id : 71, {_}: multiply (multiply ?123 ?124) ?123 =>= multiply ?123 (multiply ?124 ?123) [124, 123] by Demod 55 with 2 at 3 +Id : 897, {_}: right_division (multiply ?1221 (multiply ?1222 (multiply ?1223 ?1222))) ?1222 =>= multiply (multiply ?1221 ?1222) ?1223 [1223, 1222, 1221] by Super 7 with 10 at 1,2 +Id : 904, {_}: right_division (multiply ?1247 (multiply ?1248 identity)) ?1248 =>= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Super 897 with 9 at 2,2,1,2 +Id : 944, {_}: right_division (multiply ?1247 ?1248) ?1248 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 904 with 3 at 2,1,2 +Id : 945, {_}: ?1247 =<= multiply (multiply ?1247 ?1248) (left_inverse ?1248) [1248, 1247] by Demod 944 with 7 at 2 +Id : 1320, {_}: left_division (multiply ?1774 ?1775) ?1774 =>= left_inverse ?1775 [1775, 1774] by Super 5 with 945 at 2,2 +Id : 1325, {_}: left_division ?1787 ?1788 =<= left_inverse (left_division ?1788 ?1787) [1788, 1787] by Super 1320 with 4 at 1,2 +Id : 1124, {_}: ?1512 =<= multiply (multiply ?1512 ?1513) (left_inverse ?1513) [1513, 1512] by Demod 944 with 7 at 2 +Id : 1136, {_}: right_division ?1545 ?1546 =<= multiply ?1545 (left_inverse ?1546) [1546, 1545] by Super 1124 with 6 at 1,3 +Id : 1239, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (multiply ?1665 (left_inverse ?1664)) [1665, 1664] by Super 71 with 1136 at 2 +Id : 1291, {_}: right_division (multiply (left_inverse ?1664) ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1239 with 1136 at 2,3 +Id : 621, {_}: right_division (multiply ?874 (multiply ?875 ?874)) ?874 =>= multiply ?874 ?875 [875, 874] by Super 7 with 71 at 1,2 +Id : 2721, {_}: right_division (multiply (left_inverse ?3427) (multiply ?3427 (multiply ?3428 ?3427))) ?3427 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Super 1291 with 621 at 2,3 +Id : 53, {_}: right_division (multiply ?115 (multiply ?116 (multiply ?117 ?116))) ?116 =>= multiply (multiply ?115 ?116) ?117 [117, 116, 115] by Super 7 with 10 at 1,2 +Id : 2757, {_}: multiply (multiply (left_inverse ?3427) ?3427) ?3428 =>= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3428, 3427] by Demod 2721 with 53 at 2 +Id : 2758, {_}: multiply identity ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2757 with 9 at 1,2 +Id : 2759, {_}: ?3428 =<= multiply (left_inverse ?3427) (multiply ?3427 ?3428) [3427, 3428] by Demod 2758 with 2 at 2 +Id : 3344, {_}: left_division (left_inverse ?4254) ?4255 =>= multiply ?4254 ?4255 [4255, 4254] by Super 5 with 2759 at 2,2 +Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2 +Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2 +Id : 425, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2 +Id : 626, {_}: multiply (multiply ?892 ?893) ?892 =>= multiply ?892 (multiply ?893 ?892) [893, 892] by Demod 55 with 2 at 3 +Id : 633, {_}: multiply identity ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Super 626 with 8 at 1,2 +Id : 654, {_}: ?911 =<= multiply ?911 (multiply (right_inverse ?911) ?911) [911] by Demod 633 with 2 at 2 +Id : 727, {_}: left_division ?1053 ?1053 =<= multiply (right_inverse ?1053) ?1053 [1053] by Super 5 with 654 at 2,2 +Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2 +Id : 754, {_}: identity =<= multiply (right_inverse ?1053) ?1053 [1053] by Demod 727 with 24 at 2 +Id : 784, {_}: right_division identity ?1115 =>= right_inverse ?1115 [1115] by Super 7 with 754 at 1,2 +Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2 +Id : 808, {_}: left_inverse ?1115 =<= right_inverse ?1115 [1115] by Demod 784 with 45 at 2 +Id : 829, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 425 with 808 at 2 +Id : 3348, {_}: left_division ?4266 ?4267 =<= multiply (left_inverse ?4266) ?4267 [4267, 4266] by Super 3344 with 829 at 1,2 +Id : 3417, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =<= multiply (left_inverse ?4342) (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Super 10 with 3348 at 1,1,2 +Id : 3495, {_}: multiply (multiply (left_division ?4342 ?4343) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4343, 4342] by Demod 3417 with 3348 at 3 +Id : 3351, {_}: left_division (left_division ?4274 ?4275) ?4276 =<= multiply (left_division ?4275 ?4274) ?4276 [4276, 4275, 4274] by Super 3344 with 1325 at 1,2 +Id : 9541, {_}: multiply (left_division (left_division ?4343 ?4342) ?4344) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4344, 4342, 4343] by Demod 3495 with 3351 at 1,2 +Id : 9542, {_}: left_division (left_division ?4344 (left_division ?4343 ?4342)) ?4343 =>= left_division ?4342 (multiply ?4343 (multiply ?4344 ?4343)) [4342, 4343, 4344] by Demod 9541 with 3351 at 2 +Id : 9554, {_}: left_division ?10951 (left_division ?10952 (left_division ?10951 ?10953)) =<= left_inverse (left_division ?10953 (multiply ?10951 (multiply ?10952 ?10951))) [10953, 10952, 10951] by Super 1325 with 9542 at 1,3 +Id : 27037, {_}: left_division ?28025 (left_division ?28026 (left_division ?28025 ?28027)) =<= left_division (multiply ?28025 (multiply ?28026 ?28025)) ?28027 [28027, 28026, 28025] by Demod 9554 with 1325 at 3 +Id : 27055, {_}: left_division (left_inverse ?28099) (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Super 27037 with 1136 at 2,1,3 +Id : 3143, {_}: left_division (left_inverse ?4011) ?4012 =>= multiply ?4011 ?4012 [4012, 4011] by Super 5 with 2759 at 2,2 +Id : 27191, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (multiply (left_inverse ?28099) (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27055 with 3143 at 2 +Id : 27192, {_}: multiply ?28099 (left_division ?28100 (left_division (left_inverse ?28099) ?28101)) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28101, 28100, 28099] by Demod 27191 with 3348 at 1,3 +Id : 1117, {_}: right_division ?1491 (left_inverse ?1492) =>= multiply ?1491 ?1492 [1492, 1491] by Super 7 with 945 at 1,2 +Id : 1524, {_}: right_division ?2086 (left_division ?2087 ?2088) =<= multiply ?2086 (left_division ?2088 ?2087) [2088, 2087, 2086] by Super 1117 with 1325 at 2,2 +Id : 27193, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (left_division ?28099 (right_division ?28100 ?28099)) ?28101 [28100, 28101, 28099] by Demod 27192 with 1524 at 2 +Id : 3400, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= multiply (left_inverse ?1664) (right_division ?1665 ?1664) [1665, 1664] by Demod 1291 with 3348 at 1,2 +Id : 3401, {_}: right_division (left_division ?1664 ?1665) ?1664 =<= left_division ?1664 (right_division ?1665 ?1664) [1665, 1664] by Demod 3400 with 3348 at 3 +Id : 27194, {_}: right_division ?28099 (left_division (left_division (left_inverse ?28099) ?28101) ?28100) =>= left_division (right_division (left_division ?28099 ?28100) ?28099) ?28101 [28100, 28101, 28099] by Demod 27193 with 3401 at 1,3 +Id : 40132, {_}: right_division ?42719 (left_division (multiply ?42719 ?42720) ?42721) =<= left_division (right_division (left_division ?42719 ?42721) ?42719) ?42720 [42721, 42720, 42719] by Demod 27194 with 3143 at 1,2,2 +Id : 1118, {_}: left_division (multiply ?1494 ?1495) ?1494 =>= left_inverse ?1495 [1495, 1494] by Super 5 with 945 at 2,2 +Id : 3133, {_}: left_division ?3978 (left_inverse ?3979) =>= left_inverse (multiply ?3979 ?3978) [3979, 3978] by Super 1118 with 2759 at 1,2 +Id : 40144, {_}: right_division ?42768 (left_division (multiply ?42768 ?42769) (left_inverse ?42770)) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42770, 42769, 42768] by Super 40132 with 3133 at 1,1,3 +Id : 40468, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (right_division (left_inverse (multiply ?42770 ?42768)) ?42768) ?42769 [42769, 42770, 42768] by Demod 40144 with 3133 at 2,2 +Id : 3414, {_}: right_division (left_inverse ?4334) ?4335 =<= left_division ?4334 (left_inverse ?4335) [4335, 4334] by Super 1136 with 3348 at 3 +Id : 3502, {_}: right_division (left_inverse ?4334) ?4335 =>= left_inverse (multiply ?4335 ?4334) [4335, 4334] by Demod 3414 with 3133 at 3 +Id : 40469, {_}: right_division ?42768 (left_inverse (multiply ?42770 (multiply ?42768 ?42769))) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40468 with 3502 at 1,3 +Id : 40470, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= left_division (left_inverse (multiply ?42768 (multiply ?42770 ?42768))) ?42769 [42769, 42770, 42768] by Demod 40469 with 1117 at 2 +Id : 40471, {_}: multiply ?42768 (multiply ?42770 (multiply ?42768 ?42769)) =<= multiply (multiply ?42768 (multiply ?42770 ?42768)) ?42769 [42769, 42770, 42768] by Demod 40470 with 3143 at 3 +Id : 50862, {_}: multiply a (multiply b (multiply a c)) =?= multiply a (multiply b (multiply a c)) [] by Demod 50861 with 40471 at 2 +Id : 50861, {_}: multiply (multiply a (multiply b a)) c =>= multiply a (multiply b (multiply a c)) [] by Demod 1 with 71 at 1,2 +Id : 1, {_}: multiply (multiply (multiply a b) a) c =>= multiply a (multiply b (multiply a c)) [] by prove_moufang3 +% SZS output end CNFRefutation for GRP201-1.p +22868: solved GRP201-1.p in 12.232764 using kbo +22868: status Unsatisfiable for GRP201-1.p +CLASH, statistics insufficient +22882: Facts: +CLASH, statistics insufficient +22883: Facts: +22883: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22883: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22883: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22883: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22883: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22883: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22883: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22883: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22883: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +22883: Goal: +22883: Id : 1, {_}: + multiply (multiply a (multiply b c)) a + =>= + multiply (multiply a b) (multiply c a) + [] by prove_moufang1 +22883: Order: +22883: kbo +22883: Leaf order: +22883: b 2 0 2 1,2,1,2 +22883: c 2 0 2 2,2,1,2 +22883: identity 4 0 0 +22883: a 4 0 4 1,1,2 +22883: right_inverse 1 1 0 +22883: left_inverse 1 1 0 +22883: left_division 2 2 0 +22883: right_division 2 2 0 +22883: multiply 20 2 6 0,2 +22882: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22882: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22882: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22882: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22882: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22882: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22882: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22882: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22882: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =?= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +22882: Goal: +22882: Id : 1, {_}: + multiply (multiply a (multiply b c)) a + =>= + multiply (multiply a b) (multiply c a) + [] by prove_moufang1 +22882: Order: +22882: nrkbo +22882: Leaf order: +22882: b 2 0 2 1,2,1,2 +22882: c 2 0 2 2,2,1,2 +22882: identity 4 0 0 +22882: a 4 0 4 1,1,2 +22882: right_inverse 1 1 0 +22882: left_inverse 1 1 0 +22882: left_division 2 2 0 +22882: right_division 2 2 0 +22882: multiply 20 2 6 0,2 +CLASH, statistics insufficient +22884: Facts: +22884: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +22884: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +22884: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +22884: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +22884: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +22884: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +22884: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +22884: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +22884: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +22884: Goal: +22884: Id : 1, {_}: + multiply (multiply a (multiply b c)) a + =>= + multiply (multiply a b) (multiply c a) + [] by prove_moufang1 +22884: Order: +22884: lpo +22884: Leaf order: +22884: b 2 0 2 1,2,1,2 +22884: c 2 0 2 2,2,1,2 +22884: identity 4 0 0 +22884: a 4 0 4 1,1,2 +22884: right_inverse 1 1 0 +22884: left_inverse 1 1 0 +22884: left_division 2 2 0 +22884: right_division 2 2 0 +22884: multiply 20 2 6 0,2 +Statistics : +Max weight : 20 +Found proof, 29.906330s +% SZS status Unsatisfiable for GRP202-1.p +% SZS output start CNFRefutation for GRP202-1.p +Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128 +Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7 +Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20 +Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10 +Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18 +Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13 +Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16 +Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24 +Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2 +Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2 +Id : 894, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2 +Id : 900, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 894 with 6 at 2,1,2 +Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2 +Id : 2577, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3 +Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2 +Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3 +Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3 +Id : 765, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2 +Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2 +Id : 791, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 765 with 24 at 2 +Id : 819, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 791 at 1,2 +Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2 +Id : 846, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 819 with 45 at 2 +Id : 861, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 846 at 2,2 +Id : 2586, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2577 with 861 at 2,2,1,2 +Id : 2645, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2586 with 3 at 2,1,2 +Id : 2833, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 900 with 2645 at 2,3 +Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2 +Id : 969, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2 +Id : 976, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 969 with 9 at 2,1,2,2,2,2 +Id : 1036, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 976 with 3 at 1,2,2,2,2 +Id : 1037, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1036 with 4 at 2,2,2 +Id : 1172, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1037 at 2,2 +Id : 2879, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2833 with 1172 at 1,2 +Id : 2880, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2879 with 1172 at 3 +Id : 2881, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2880 with 5 at 1,2 +Id : 2882, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2881 with 5 at 3 +Id : 1389, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1172 at 1,2 +Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2 +Id : 1395, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1389 with 28 at 1,2 +Id : 3679, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2 +Id : 3684, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3679 with 4 at 2,2,3 +Id : 2950, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1395 with 2882 at 1,3 +Id : 3037, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2882 with 2950 at 2 +Id : 3056, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3037 with 1172 at 1,2 +Id : 3057, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3056 with 1172 at 3 +Id : 3222, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2882 with 3057 at 2,2 +Id : 8079, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3684 with 3222 at 2 +Id : 3218, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1172 with 3057 at 1,3 +Id : 8080, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8079 with 3218 at 2,3 +Id : 8081, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8080 with 3222 at 3 +Id : 8094, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1395 with 8081 at 1,3 +Id : 8159, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8094 with 1395 at 3 +Id : 23778, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2882 with 8159 at 2 +Id : 2960, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2881 with 5 at 3 +Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2 +Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2 +Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2 +Id : 864, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 846 at 2 +Id : 2964, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2960 with 864 at 2,2 +Id : 3107, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1172 with 2964 at 3 +Id : 3145, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3107 with 2950 at 3 +Id : 23925, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23778 with 3145 at 1,2 +Id : 23926, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23925 with 2964 at 2,2 +Id : 23927, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23926 with 3218 at 3 +Id : 23928, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23927 with 2950 at 2 +Id : 23929, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23928 with 3145 at 1,1,3 +Id : 1175, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1036 with 4 at 2,2,2 +Id : 1185, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1175 with 4 at 2,2 +Id : 1426, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1185 with 1395 at 1,3 +Id : 23930, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23929 with 1426 at 1,2 +Id : 23931, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23930 with 1185 at 1,3 +Id : 37380, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23931 with 3057 at 2 +Id : 37397, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37380 with 2964 at 1,1,3 +Id : 37604, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37397 with 2882 at 2,2 +Id : 37605, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37604 with 1426 at 1,3 +Id : 8101, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8080 with 3222 at 3 +Id : 8114, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8101 with 3145 at 2,2 +Id : 8186, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8114 with 2882 at 2 +Id : 8187, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8186 with 2950 at 3 +Id : 8188, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8187 with 2964 at 1,2 +Id : 8189, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8188 with 3218 at 1,3 +Id : 8190, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8189 with 1426 at 2 +Id : 8191, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8190 with 3057 at 3 +Id : 8192, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8191 with 3145 at 1,2,3 +Id : 24138, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8192 with 1185 at 2,3 +Id : 24175, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24138 with 2882 at 1,2 +Id : 24394, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24175 with 2964 at 1,2,3 +Id : 24395, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24394 with 1426 at 2,3 +Id : 47972, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37605 with 24395 at 2 +Id : 1255, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1172 at 1,3 +Id : 1319, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1255 with 1172 at 2 +Id : 3086, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1319 with 2964 at 2,2 +Id : 3087, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3086 with 2964 at 3 +Id : 48040, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47972 with 3087 at 1,3 +Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2 +Id : 3668, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2 +Id : 7892, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3668 with 3218 at 3 +Id : 7900, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3057 with 7892 at 1,2 +Id : 7969, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7900 with 3057 at 2 +Id : 22647, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3145 with 7969 at 2 +Id : 22730, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22647 with 1172 at 1,2 +Id : 22731, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22730 with 3145 at 2,2 +Id : 22732, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22731 with 2964 at 1,2,1,3 +Id : 22733, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22732 with 3145 at 2 +Id : 22734, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22733 with 1426 at 2,1,3 +Id : 22735, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22734 with 3222 at 1,2 +Id : 22736, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22735 with 3222 at 1,3 +Id : 22737, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22736 with 1395 at 2 +Id : 33406, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22737 with 1395 at 3 +Id : 33487, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33406 with 1185 at 1,3 +Id : 33773, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33487 with 1185 at 1,2 +Id : 2967, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2960 with 1395 at 2,2 +Id : 33774, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33773 with 2967 at 1,3 +Id : 48410, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 48040 with 33774 at 1,2,2 +Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2 +Id : 1260, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1172 at 2,1,2 +Id : 1315, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1260 with 1172 at 2,3 +Id : 5054, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1315 with 3222 at 1,2 +Id : 5055, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5054 with 3222 at 3 +Id : 5056, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5055 with 1426 at 2 +Id : 48411, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48410 with 5056 at 3 +Id : 3100, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2964 at 2,1,2 +Id : 3156, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3100 with 1172 at 1,2 +Id : 3157, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3156 with 1172 at 3 +Id : 3158, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3157 with 3087 at 1,2 +Id : 3159, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3158 with 1172 at 2,2,3 +Id : 3160, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3159 with 1426 at 2 +Id : 7103, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3160 with 3222 at 2,3 +Id : 7119, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3145 with 7103 at 2 +Id : 7221, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7119 with 1185 at 2,2,2 +Id : 7222, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7221 with 2967 at 1,3 +Id : 7223, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7222 with 1395 at 3 +Id : 21525, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3057 with 7223 at 1,2 +Id : 21646, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21525 with 1395 at 2 +Id : 48412, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48411 with 21646 at 2,2 +Id : 48413, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48412 with 1426 at 1,2,3 +Id : 3103, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2964 at 2,2 +Id : 48414, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48413 with 3103 at 2 +Id : 48415, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48414 with 28 at 1,2,3 +Id : 48416, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48415 with 1395 at 2 +Id : 52586, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1395 with 48416 at 1,3 +Id : 52816, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52586 with 1395 at 3 +Id : 55129, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2882 with 52816 at 2 +Id : 55322, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55129 with 1185 at 1,2 +Id : 55323, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55322 with 2950 at 2,2 +Id : 55324, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55323 with 3218 at 3 +Id : 55325, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55324 with 2882 at 2 +Id : 55326, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55325 with 3145 at 1,3 +Id : 55327, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55326 with 1185 at 3 +Id : 55328, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55327 with 70 at 3 +Id : 57081, {_}: multiply a (multiply (multiply b c) a) =?= multiply a (multiply (multiply b c) a) [] by Demod 57080 with 55328 at 3 +Id : 57080, {_}: multiply a (multiply (multiply b c) a) =<= multiply (multiply a b) (multiply c a) [] by Demod 1 with 70 at 2 +Id : 1, {_}: multiply (multiply a (multiply b c)) a =>= multiply (multiply a b) (multiply c a) [] by prove_moufang1 +% SZS output end CNFRefutation for GRP202-1.p +22883: solved GRP202-1.p in 14.88493 using kbo +22883: status Unsatisfiable for GRP202-1.p +NO CLASH, using fixed ground order +22932: Facts: +22932: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +22932: Goal: +22932: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +22932: Order: +22932: nrkbo +22932: Leaf order: +22932: b2 2 0 2 1,1,1,2 +22932: a2 2 0 2 2,2 +22932: inverse 6 1 1 0,1,1,2 +22932: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +22933: Facts: +22933: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +22933: Goal: +22933: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +22933: Order: +22933: kbo +22933: Leaf order: +22933: b2 2 0 2 1,1,1,2 +22933: a2 2 0 2 2,2 +22933: inverse 6 1 1 0,1,1,2 +22933: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +22934: Facts: +22934: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +22934: Goal: +22934: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +22934: Order: +22934: lpo +22934: Leaf order: +22934: b2 2 0 2 1,1,1,2 +22934: a2 2 0 2 2,2 +22934: inverse 6 1 1 0,1,1,2 +22934: multiply 8 2 2 0,2 +% SZS status Timeout for GRP404-1.p +NO CLASH, using fixed ground order +23295: Facts: +23295: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23295: Goal: +23295: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23295: Order: +23295: nrkbo +23295: Leaf order: +23295: a3 2 0 2 1,1,2 +23295: b3 2 0 2 2,1,2 +23295: c3 2 0 2 2,2 +23295: inverse 5 1 0 +23295: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23296: Facts: +23296: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23296: Goal: +23296: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23296: Order: +23296: kbo +23296: Leaf order: +23296: a3 2 0 2 1,1,2 +23296: b3 2 0 2 2,1,2 +23296: c3 2 0 2 2,2 +23296: inverse 5 1 0 +23296: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23297: Facts: +23297: Id : 2, {_}: + multiply ?2 + (inverse + (multiply (inverse (multiply (inverse (multiply ?2 ?3)) ?4)) + (inverse (multiply ?3 (multiply (inverse ?3) ?3))))) + =>= + ?4 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23297: Goal: +23297: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23297: Order: +23297: lpo +23297: Leaf order: +23297: a3 2 0 2 1,1,2 +23297: b3 2 0 2 2,1,2 +23297: c3 2 0 2 2,2 +23297: inverse 5 1 0 +23297: multiply 10 2 4 0,2 +% SZS status Timeout for GRP405-1.p +NO CLASH, using fixed ground order +23512: Facts: +NO CLASH, using fixed ground order +23513: Facts: +23513: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23513: Goal: +23513: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23513: Order: +23513: kbo +23513: Leaf order: +23513: b2 2 0 2 1,1,1,2 +23513: a2 2 0 2 2,2 +23513: inverse 6 1 1 0,1,1,2 +23513: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +23514: Facts: +23514: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23514: Goal: +23514: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23514: Order: +23514: lpo +23514: Leaf order: +23514: b2 2 0 2 1,1,1,2 +23514: a2 2 0 2 2,2 +23514: inverse 6 1 1 0,1,1,2 +23514: multiply 8 2 2 0,2 +23512: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23512: Goal: +23512: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23512: Order: +23512: nrkbo +23512: Leaf order: +23512: b2 2 0 2 1,1,1,2 +23512: a2 2 0 2 2,2 +23512: inverse 6 1 1 0,1,1,2 +23512: multiply 8 2 2 0,2 +Statistics : +Max weight : 71 +Found proof, 51.580663s +% SZS status Unsatisfiable for GRP410-1.p +% SZS output start CNFRefutation for GRP410-1.p +Id : 3, {_}: multiply (multiply (inverse (multiply ?6 (inverse (multiply ?7 ?8)))) (multiply ?6 (inverse ?8))) (inverse (multiply (inverse ?8) ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8 +Id : 2, {_}: multiply (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 5, {_}: multiply (multiply (inverse (multiply ?15 (inverse ?16))) (multiply ?15 (inverse (inverse (multiply (inverse ?17) ?17))))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16, 15] by Super 3 with 2 at 1,2,1,1,1,2 +Id : 104, {_}: multiply (inverse (multiply ?498 (inverse (multiply (multiply ?499 (inverse (multiply (inverse ?500) ?500))) ?500)))) (multiply ?498 (inverse ?500)) =>= ?499 [500, 499, 498] by Super 2 with 5 at 2 +Id : 161, {_}: multiply (multiply (inverse (multiply ?829 (inverse ?830))) (multiply ?829 (inverse (multiply ?831 (inverse ?832))))) (inverse (multiply (inverse (multiply ?831 (inverse ?832))) (multiply ?831 (inverse ?832)))) =>= inverse (multiply ?831 (inverse (multiply (multiply ?830 (inverse (multiply (inverse ?832) ?832))) ?832))) [832, 831, 830, 829] by Super 2 with 104 at 1,2,1,1,1,2 +Id : 218, {_}: multiply (inverse (multiply ?1090 (inverse (multiply (inverse (multiply ?1091 (inverse (multiply (multiply ?1092 (inverse (multiply (inverse ?1093) ?1093))) ?1093)))) (multiply ?1091 (inverse ?1093)))))) (multiply ?1090 (inverse (multiply ?1091 (inverse ?1093)))) =?= multiply (inverse (multiply ?1094 (inverse ?1092))) (multiply ?1094 (inverse (multiply ?1091 (inverse ?1093)))) [1094, 1093, 1092, 1091, 1090] by Super 104 with 161 at 1,1,2,1,1,2 +Id : 846, {_}: multiply (inverse (multiply ?3342 (inverse ?3343))) (multiply ?3342 (inverse (multiply ?3344 (inverse ?3345)))) =?= multiply (inverse (multiply ?3346 (inverse ?3343))) (multiply ?3346 (inverse (multiply ?3344 (inverse ?3345)))) [3346, 3345, 3344, 3343, 3342] by Demod 218 with 104 at 1,2,1,1,2 +Id : 210, {_}: inverse (multiply ?1043 (inverse (multiply (multiply (multiply ?1044 (multiply ?1043 (inverse ?1045))) (inverse (multiply (inverse ?1045) ?1045))) ?1045))) =>= ?1044 [1045, 1044, 1043] by Super 2 with 161 at 2 +Id : 856, {_}: multiply (inverse (multiply ?3416 (inverse ?3417))) (multiply ?3416 (inverse (multiply ?3418 (inverse (multiply (multiply (multiply ?3419 (multiply ?3418 (inverse ?3420))) (inverse (multiply (inverse ?3420) ?3420))) ?3420))))) =?= multiply (inverse (multiply ?3421 (inverse ?3417))) (multiply ?3421 ?3419) [3421, 3420, 3419, 3418, 3417, 3416] by Super 846 with 210 at 2,2,3 +Id : 1213, {_}: multiply (inverse (multiply ?5198 (inverse ?5199))) (multiply ?5198 ?5200) =?= multiply (inverse (multiply ?5201 (inverse ?5199))) (multiply ?5201 ?5200) [5201, 5200, 5199, 5198] by Demod 856 with 210 at 2,2,2 +Id : 1228, {_}: multiply (inverse (multiply ?5296 (inverse (multiply ?5297 (inverse (multiply (multiply (multiply ?5298 (multiply ?5297 (inverse ?5299))) (inverse (multiply (inverse ?5299) ?5299))) ?5299)))))) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5299, 5298, 5297, 5296] by Super 1213 with 210 at 2,1,1,3 +Id : 1288, {_}: multiply (inverse (multiply ?5296 ?5298)) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5298, 5296] by Demod 1228 with 210 at 2,1,1,2 +Id : 1314, {_}: multiply (inverse (multiply ?5709 (inverse (multiply (multiply ?5710 (inverse (multiply (inverse (multiply ?5711 ?5712)) (multiply ?5711 ?5712)))) (multiply ?5713 ?5712))))) (multiply ?5709 (inverse (multiply ?5713 ?5712))) =>= ?5710 [5713, 5712, 5711, 5710, 5709] by Super 104 with 1288 at 1,2,1,1,2,1,1,2 +Id : 2743, {_}: multiply ?12126 (inverse (multiply (inverse (multiply ?12127 ?12128)) (multiply ?12127 ?12128))) =?= multiply ?12126 (inverse (multiply (inverse (multiply ?12129 ?12128)) (multiply ?12129 ?12128))) [12129, 12128, 12127, 12126] by Super 2 with 1314 at 1,2 +Id : 6, {_}: multiply (multiply (inverse ?20) (multiply (multiply (inverse (multiply ?21 (inverse (multiply ?20 ?22)))) (multiply ?21 (inverse ?22))) (inverse ?22))) (inverse (multiply (inverse ?22) ?22)) =>= inverse ?22 [22, 21, 20] by Super 3 with 2 at 1,1,1,2 +Id : 2747, {_}: multiply ?12151 (inverse (multiply (inverse (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153)))) (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153))))) =?= multiply ?12151 (inverse (multiply (inverse (multiply (multiply (inverse ?12154) (multiply (multiply (inverse (multiply ?12155 (inverse (multiply ?12154 ?12153)))) (multiply ?12155 (inverse ?12153))) (inverse ?12153))) (inverse (multiply (inverse ?12153) ?12153)))) (inverse ?12153))) [12155, 12154, 12153, 12152, 12151] by Super 2743 with 6 at 2,1,2,3 +Id : 3023, {_}: multiply ?13436 (inverse (multiply (inverse (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438)))) (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438))))) =>= multiply ?13436 (inverse (multiply (inverse (inverse ?13438)) (inverse ?13438))) [13438, 13437, 13436] by Demod 2747 with 6 at 1,1,1,2,3 +Id : 3033, {_}: multiply ?13495 (inverse (multiply (inverse (multiply (multiply (inverse (multiply ?13496 (inverse (multiply ?13497 ?13498)))) (multiply ?13496 (inverse ?13498))) (inverse (multiply (inverse ?13498) ?13498)))) ?13497)) =>= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13496, 13495] by Super 3023 with 2 at 2,1,2,2 +Id : 3493, {_}: multiply ?14948 (inverse (multiply (inverse ?14949) ?14949)) =?= multiply ?14948 (inverse (multiply (inverse (inverse ?14950)) (inverse ?14950))) [14950, 14949, 14948] by Demod 3033 with 2 at 1,1,1,2,2 +Id : 3250, {_}: multiply ?13495 (inverse (multiply (inverse ?13497) ?13497)) =?= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13495] by Demod 3033 with 2 at 1,1,1,2,2 +Id : 3510, {_}: multiply ?15042 (inverse (multiply (inverse ?15043) ?15043)) =?= multiply ?15042 (inverse (multiply (inverse ?15044) ?15044)) [15044, 15043, 15042] by Super 3493 with 3250 at 3 +Id : 3957, {_}: multiply (inverse (multiply ?16893 (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896)))) (multiply ?16893 (inverse ?16896)) =>= ?16894 [16896, 16895, 16894, 16893] by Super 104 with 3510 at 1,1,2,1,1,2 +Id : 4003, {_}: multiply (multiply (inverse (multiply ?17133 (inverse (multiply ?17134 ?17135)))) (multiply ?17133 (inverse ?17135))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134, 17133] by Super 2 with 3510 at 2 +Id : 4810, {_}: multiply (multiply (inverse ?21607) ?21607) (inverse (multiply (inverse (multiply (inverse ?21608) ?21608)) (multiply (inverse ?21608) ?21608))) =>= inverse (multiply (inverse ?21608) ?21608) [21608, 21607] by Super 6 with 4003 at 2,1,2 +Id : 1364, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (multiply ?5999 (inverse ?5998))) (multiply ?5999 (inverse ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5999, 5998, 5997, 5996, 5995] by Super 161 with 1288 at 1,2,2 +Id : 4844, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (multiply (inverse (inverse ?21769)) (inverse ?21769)) [21769, 21768] by Super 4810 with 1364 at 2 +Id : 21277, {_}: multiply (inverse (multiply (inverse (inverse ?53833)) (inverse ?53833))) (multiply ?53834 (inverse ?53833)) =>= multiply ?53834 (inverse ?53833) [53834, 53833] by Super 3957 with 4844 at 1,2 +Id : 21278, {_}: multiply (inverse (multiply (inverse (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838))))) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53837, 53836] by Super 21277 with 210 at 2,2,2 +Id : 21547, {_}: multiply (inverse (multiply (inverse ?53837) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53836, 53837] by Demod 21278 with 210 at 1,1,1,1,2 +Id : 21548, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =?= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53838, 53836, 53839, 53837] by Demod 21547 with 210 at 2,1,1,2 +Id : 21549, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =>= multiply ?53839 ?53837 [53839, 53837] by Demod 21548 with 210 at 2,3 +Id : 22063, {_}: multiply (inverse (multiply ?55325 ?55326)) (multiply ?55325 ?55326) =>= multiply (inverse ?55326) ?55326 [55326, 55325] by Super 1288 with 21549 at 3 +Id : 22073, {_}: multiply (inverse (multiply (inverse (multiply ?55370 (inverse (multiply (multiply ?55371 (inverse (multiply (inverse ?55372) ?55372))) ?55373)))) (multiply ?55370 (inverse ?55373)))) ?55371 =>= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55372, 55371, 55370] by Super 22063 with 3957 at 2,2 +Id : 22230, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55370, 55371] by Demod 22073 with 3957 at 1,1,2 +Id : 21784, {_}: multiply (inverse (multiply ?54500 ?54501)) (multiply ?54500 ?54501) =>= multiply (inverse ?54501) ?54501 [54501, 54500] by Super 1288 with 21549 at 3 +Id : 22543, {_}: multiply (inverse ?56820) ?56820 =?= multiply (inverse (inverse ?56821)) (inverse ?56821) [56821, 56820] by Demod 22230 with 21784 at 3 +Id : 22231, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (inverse ?55373)) (inverse ?55373) [55373, 55371] by Demod 22230 with 21784 at 3 +Id : 22585, {_}: multiply (inverse ?57023) ?57023 =?= multiply (inverse ?57024) ?57024 [57024, 57023] by Super 22543 with 22231 at 3 +Id : 22724, {_}: multiply (inverse (multiply (inverse ?57285) ?57285)) (multiply ?57286 ?57287) =>= multiply ?57286 ?57287 [57287, 57286, 57285] by Super 21549 with 22585 at 1,1,2 +Id : 23108, {_}: multiply (inverse (multiply ?58913 ?58914)) (multiply ?58913 ?58915) =>= multiply (inverse ?58914) ?58915 [58915, 58914, 58913] by Super 1288 with 22724 at 3 +Id : 23378, {_}: multiply (multiply (inverse (inverse (multiply ?17134 ?17135))) (inverse ?17135)) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 4003 with 23108 at 1,2 +Id : 1370, {_}: inverse (multiply ?6029 (inverse (multiply (multiply (multiply (inverse (multiply ?6030 ?6031)) (multiply ?6030 (inverse ?6032))) (inverse (multiply (inverse ?6032) ?6032))) ?6032))) =>= inverse (multiply ?6029 ?6031) [6032, 6031, 6030, 6029] by Super 210 with 1288 at 1,1,1,2,1,2 +Id : 4845, {_}: multiply (multiply (inverse ?21771) ?21771) (inverse (multiply (inverse ?21772) ?21772)) =?= inverse (multiply (inverse ?21773) ?21773) [21773, 21772, 21771] by Super 4810 with 3510 at 2 +Id : 7295, {_}: inverse (multiply ?28092 (inverse (multiply (inverse (multiply (inverse ?28093) ?28093)) ?28094))) =>= inverse (multiply ?28092 (inverse ?28094)) [28094, 28093, 28092] by Super 1370 with 4845 at 1,1,2,1,2 +Id : 22930, {_}: inverse (multiply (inverse ?58245) ?58245) =?= inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?58246) ?58246)) ?58247))) (inverse ?58247)) [58247, 58246, 58245] by Super 7295 with 22585 at 1,2 +Id : 8, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?26) (multiply (multiply (inverse (multiply ?27 (inverse (multiply ?26 ?28)))) (multiply ?27 (inverse ?28))) (inverse ?28))) (inverse (multiply ?29 (multiply (inverse ?28) ?28))))) (inverse ?28)) (inverse (multiply (inverse (multiply (inverse ?28) ?28)) (multiply (inverse ?28) ?28))) =>= ?29 [29, 28, 27, 26] by Super 2 with 6 at 2,1,2 +Id : 7694, {_}: inverse (multiply ?30248 (inverse (multiply (inverse (multiply (inverse ?30249) ?30249)) ?30250))) =>= inverse (multiply ?30248 (inverse ?30250)) [30250, 30249, 30248] by Super 1370 with 4845 at 1,1,2,1,2 +Id : 9751, {_}: inverse (multiply ?34833 (inverse (multiply (inverse (multiply ?34834 ?34835)) (multiply ?34834 ?34836)))) =>= inverse (multiply ?34833 (inverse (multiply (inverse ?34835) ?34836))) [34836, 34835, 34834, 34833] by Super 7694 with 1288 at 1,2,1,2 +Id : 9799, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (multiply ?35158 (inverse ?35159))) (multiply ?35158 ?35160)))) =?= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35158, 35157] by Super 9751 with 7295 at 1,1,2,1,2 +Id : 7715, {_}: inverse (multiply ?30362 (inverse (multiply (inverse (multiply ?30363 ?30364)) (multiply ?30363 ?30365)))) =>= inverse (multiply ?30362 (inverse (multiply (inverse ?30364) ?30365))) [30365, 30364, 30363, 30362] by Super 7694 with 1288 at 1,2,1,2 +Id : 10327, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (inverse ?35159)) ?35160))) =<= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35157] by Demod 9799 with 7715 at 2 +Id : 14061, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?43109) (multiply (multiply (inverse (multiply ?43110 (inverse (multiply ?43109 ?43111)))) (multiply ?43110 (inverse ?43111))) (inverse ?43111))) (inverse (multiply (inverse (inverse ?43112)) (multiply (inverse ?43111) ?43111))))) (inverse ?43111)) (inverse (multiply (inverse (multiply (inverse ?43111) ?43111)) (multiply (inverse ?43111) ?43111))) =?= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112, 43111, 43110, 43109] by Super 8 with 10327 at 1,1,2 +Id : 14495, {_}: inverse (inverse ?43112) =<= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112] by Demod 14061 with 8 at 2 +Id : 23770, {_}: inverse (multiply (inverse ?60796) ?60796) =?= inverse (multiply (inverse (inverse ?60797)) (inverse ?60797)) [60797, 60796] by Demod 22930 with 14495 at 1,1,3 +Id : 23801, {_}: inverse (multiply (inverse ?60931) ?60931) =?= inverse (multiply (inverse ?60932) ?60932) [60932, 60931] by Super 23770 with 22585 at 1,3 +Id : 25761, {_}: multiply (multiply (inverse (inverse (multiply (inverse ?63084) ?63084))) (inverse ?63085)) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085, 63084] by Super 23378 with 23801 at 1,1,1,2 +Id : 27867, {_}: multiply (inverse (multiply (inverse ?66211) ?66211)) (inverse ?66212) =?= multiply (multiply (inverse (inverse (multiply (inverse ?66213) ?66213))) (inverse ?66212)) (inverse (multiply (inverse ?66214) ?66214)) [66214, 66213, 66212, 66211] by Super 22724 with 25761 at 2,2 +Id : 28152, {_}: multiply (inverse (multiply (inverse ?66849) ?66849)) (inverse ?66850) =>= inverse ?66850 [66850, 66849] by Demod 27867 with 25761 at 3 +Id : 28153, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =?= inverse (multiply ?66854 (inverse (multiply (multiply (multiply ?66853 (multiply ?66854 (inverse ?66855))) (inverse (multiply (inverse ?66855) ?66855))) ?66855))) [66855, 66854, 66853, 66852] by Super 28152 with 210 at 2,2 +Id : 28218, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =>= ?66853 [66853, 66852] by Demod 28153 with 210 at 3 +Id : 23366, {_}: multiply (inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896))) (inverse ?16896) =>= ?16894 [16896, 16895, 16894] by Demod 3957 with 23108 at 2 +Id : 28331, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?67206) ?67206)) ?67207))) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207, 67206] by Super 23366 with 28218 at 1,1,1,1,2 +Id : 28438, {_}: multiply (inverse (inverse ?67207)) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207] by Demod 28331 with 28218 at 1,1,1,2 +Id : 28698, {_}: multiply (inverse (inverse (multiply (inverse ?68177) ?68177))) ?68178 =>= ?68178 [68178, 68177] by Super 28218 with 28438 at 1,1,2 +Id : 23375, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16] by Demod 5 with 23108 at 1,2 +Id : 23376, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23375 with 23108 at 3 +Id : 23410, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642))))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59642, 59641, 59640] by Super 23376 with 23108 at 1,2,1,2,2 +Id : 23543, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23410 with 23108 at 1,1,2,1,2 +Id : 23544, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse ?59642) ?59642))) (inverse (multiply (inverse ?59642) ?59642)))) =?= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23543 with 23108 at 1,1,1,1,2,2 +Id : 23545, {_}: multiply (inverse (inverse (multiply ?59640 ?59642))) (inverse ?59642) =<= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23544 with 23376 at 2 +Id : 26221, {_}: multiply (inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682)))) (inverse (multiply (inverse ?63683) ?63683)) =>= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63683, 63682, 63681] by Super 3510 with 23545 at 3 +Id : 29246, {_}: multiply (inverse ?63085) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085] by Demod 25761 with 28698 at 1,2 +Id : 29249, {_}: inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682))) =<= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63682, 63681] by Demod 26221 with 29246 at 2 +Id : 29250, {_}: multiply (inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135)))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 23378 with 29249 at 1,2 +Id : 29258, {_}: inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135))) =>= ?17134 [17135, 17134] by Demod 29250 with 29246 at 2 +Id : 29298, {_}: inverse (inverse (multiply ?68838 (inverse (multiply (inverse ?68839) ?68839)))) =>= ?68838 [68839, 68838] by Super 29258 with 28698 at 2,1,1,2 +Id : 29251, {_}: inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) (multiply (inverse ?16896) ?16896))) =>= ?16894 [16896, 16895, 16894] by Demod 23366 with 29249 at 2 +Id : 29259, {_}: multiply ?16894 (inverse (multiply (inverse ?16895) ?16895)) =>= ?16894 [16895, 16894] by Demod 29251 with 29258 at 2 +Id : 29399, {_}: inverse (inverse ?68838) =>= ?68838 [68838] by Demod 29298 with 29259 at 1,1,2 +Id : 32788, {_}: multiply (multiply (inverse ?68177) ?68177) ?68178 =>= ?68178 [68178, 68177] by Demod 28698 with 29399 at 1,2 +Id : 32852, {_}: a2 === a2 [] by Demod 1 with 32788 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP410-1.p +23512: solved GRP410-1.p in 25.797611 using nrkbo +23512: status Unsatisfiable for GRP410-1.p +NO CLASH, using fixed ground order +23552: Facts: +23552: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23552: Goal: +23552: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23552: Order: +23552: nrkbo +23552: Leaf order: +23552: a3 2 0 2 1,1,2 +23552: b3 2 0 2 2,1,2 +23552: c3 2 0 2 2,2 +23552: inverse 5 1 0 +23552: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23553: Facts: +23553: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23553: Goal: +23553: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23553: Order: +23553: kbo +23553: Leaf order: +23553: a3 2 0 2 1,1,2 +23553: b3 2 0 2 2,1,2 +23553: c3 2 0 2 2,2 +23553: inverse 5 1 0 +23553: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23554: Facts: +23554: Id : 2, {_}: + multiply + (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) + (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23554: Goal: +23554: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23554: Order: +23554: lpo +23554: Leaf order: +23554: a3 2 0 2 1,1,2 +23554: b3 2 0 2 2,1,2 +23554: c3 2 0 2 2,2 +23554: inverse 5 1 0 +23554: multiply 10 2 4 0,2 +Statistics : +Max weight : 83 +Found proof, 26.764346s +% SZS status Unsatisfiable for GRP411-1.p +% SZS output start CNFRefutation for GRP411-1.p +Id : 3, {_}: multiply (multiply (inverse (multiply ?6 (inverse (multiply ?7 ?8)))) (multiply ?6 (inverse ?8))) (inverse (multiply (inverse ?8) ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8 +Id : 2, {_}: multiply (multiply (inverse (multiply ?2 (inverse (multiply ?3 ?4)))) (multiply ?2 (inverse ?4))) (inverse (multiply (inverse ?4) ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 5, {_}: multiply (multiply (inverse (multiply ?15 (inverse ?16))) (multiply ?15 (inverse (inverse (multiply (inverse ?17) ?17))))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16, 15] by Super 3 with 2 at 1,2,1,1,1,2 +Id : 104, {_}: multiply (inverse (multiply ?498 (inverse (multiply (multiply ?499 (inverse (multiply (inverse ?500) ?500))) ?500)))) (multiply ?498 (inverse ?500)) =>= ?499 [500, 499, 498] by Super 2 with 5 at 2 +Id : 161, {_}: multiply (multiply (inverse (multiply ?829 (inverse ?830))) (multiply ?829 (inverse (multiply ?831 (inverse ?832))))) (inverse (multiply (inverse (multiply ?831 (inverse ?832))) (multiply ?831 (inverse ?832)))) =>= inverse (multiply ?831 (inverse (multiply (multiply ?830 (inverse (multiply (inverse ?832) ?832))) ?832))) [832, 831, 830, 829] by Super 2 with 104 at 1,2,1,1,1,2 +Id : 218, {_}: multiply (inverse (multiply ?1090 (inverse (multiply (inverse (multiply ?1091 (inverse (multiply (multiply ?1092 (inverse (multiply (inverse ?1093) ?1093))) ?1093)))) (multiply ?1091 (inverse ?1093)))))) (multiply ?1090 (inverse (multiply ?1091 (inverse ?1093)))) =?= multiply (inverse (multiply ?1094 (inverse ?1092))) (multiply ?1094 (inverse (multiply ?1091 (inverse ?1093)))) [1094, 1093, 1092, 1091, 1090] by Super 104 with 161 at 1,1,2,1,1,2 +Id : 846, {_}: multiply (inverse (multiply ?3342 (inverse ?3343))) (multiply ?3342 (inverse (multiply ?3344 (inverse ?3345)))) =?= multiply (inverse (multiply ?3346 (inverse ?3343))) (multiply ?3346 (inverse (multiply ?3344 (inverse ?3345)))) [3346, 3345, 3344, 3343, 3342] by Demod 218 with 104 at 1,2,1,1,2 +Id : 210, {_}: inverse (multiply ?1043 (inverse (multiply (multiply (multiply ?1044 (multiply ?1043 (inverse ?1045))) (inverse (multiply (inverse ?1045) ?1045))) ?1045))) =>= ?1044 [1045, 1044, 1043] by Super 2 with 161 at 2 +Id : 856, {_}: multiply (inverse (multiply ?3416 (inverse ?3417))) (multiply ?3416 (inverse (multiply ?3418 (inverse (multiply (multiply (multiply ?3419 (multiply ?3418 (inverse ?3420))) (inverse (multiply (inverse ?3420) ?3420))) ?3420))))) =?= multiply (inverse (multiply ?3421 (inverse ?3417))) (multiply ?3421 ?3419) [3421, 3420, 3419, 3418, 3417, 3416] by Super 846 with 210 at 2,2,3 +Id : 1213, {_}: multiply (inverse (multiply ?5198 (inverse ?5199))) (multiply ?5198 ?5200) =?= multiply (inverse (multiply ?5201 (inverse ?5199))) (multiply ?5201 ?5200) [5201, 5200, 5199, 5198] by Demod 856 with 210 at 2,2,2 +Id : 1238, {_}: multiply (inverse (multiply ?5362 (inverse (multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) (inverse (multiply (inverse ?5365) ?5365))) ?5365)))) (multiply ?5362 ?5366) =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363, 5362] by Super 1213 with 210 at 1,3 +Id : 1228, {_}: multiply (inverse (multiply ?5296 (inverse (multiply ?5297 (inverse (multiply (multiply (multiply ?5298 (multiply ?5297 (inverse ?5299))) (inverse (multiply (inverse ?5299) ?5299))) ?5299)))))) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5299, 5298, 5297, 5296] by Super 1213 with 210 at 2,1,1,3 +Id : 1288, {_}: multiply (inverse (multiply ?5296 ?5298)) (multiply ?5296 ?5300) =?= multiply (inverse (multiply ?5301 ?5298)) (multiply ?5301 ?5300) [5301, 5300, 5298, 5296] by Demod 1228 with 210 at 2,1,1,2 +Id : 1314, {_}: multiply (inverse (multiply ?5709 (inverse (multiply (multiply ?5710 (inverse (multiply (inverse (multiply ?5711 ?5712)) (multiply ?5711 ?5712)))) (multiply ?5713 ?5712))))) (multiply ?5709 (inverse (multiply ?5713 ?5712))) =>= ?5710 [5713, 5712, 5711, 5710, 5709] by Super 104 with 1288 at 1,2,1,1,2,1,1,2 +Id : 2743, {_}: multiply ?12126 (inverse (multiply (inverse (multiply ?12127 ?12128)) (multiply ?12127 ?12128))) =?= multiply ?12126 (inverse (multiply (inverse (multiply ?12129 ?12128)) (multiply ?12129 ?12128))) [12129, 12128, 12127, 12126] by Super 2 with 1314 at 1,2 +Id : 6, {_}: multiply (multiply (inverse ?20) (multiply (multiply (inverse (multiply ?21 (inverse (multiply ?20 ?22)))) (multiply ?21 (inverse ?22))) (inverse ?22))) (inverse (multiply (inverse ?22) ?22)) =>= inverse ?22 [22, 21, 20] by Super 3 with 2 at 1,1,1,2 +Id : 2747, {_}: multiply ?12151 (inverse (multiply (inverse (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153)))) (multiply ?12152 (inverse (multiply (inverse ?12153) ?12153))))) =?= multiply ?12151 (inverse (multiply (inverse (multiply (multiply (inverse ?12154) (multiply (multiply (inverse (multiply ?12155 (inverse (multiply ?12154 ?12153)))) (multiply ?12155 (inverse ?12153))) (inverse ?12153))) (inverse (multiply (inverse ?12153) ?12153)))) (inverse ?12153))) [12155, 12154, 12153, 12152, 12151] by Super 2743 with 6 at 2,1,2,3 +Id : 3023, {_}: multiply ?13436 (inverse (multiply (inverse (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438)))) (multiply ?13437 (inverse (multiply (inverse ?13438) ?13438))))) =>= multiply ?13436 (inverse (multiply (inverse (inverse ?13438)) (inverse ?13438))) [13438, 13437, 13436] by Demod 2747 with 6 at 1,1,1,2,3 +Id : 3033, {_}: multiply ?13495 (inverse (multiply (inverse (multiply (multiply (inverse (multiply ?13496 (inverse (multiply ?13497 ?13498)))) (multiply ?13496 (inverse ?13498))) (inverse (multiply (inverse ?13498) ?13498)))) ?13497)) =>= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13496, 13495] by Super 3023 with 2 at 2,1,2,2 +Id : 3493, {_}: multiply ?14948 (inverse (multiply (inverse ?14949) ?14949)) =?= multiply ?14948 (inverse (multiply (inverse (inverse ?14950)) (inverse ?14950))) [14950, 14949, 14948] by Demod 3033 with 2 at 1,1,1,2,2 +Id : 3250, {_}: multiply ?13495 (inverse (multiply (inverse ?13497) ?13497)) =?= multiply ?13495 (inverse (multiply (inverse (inverse ?13498)) (inverse ?13498))) [13498, 13497, 13495] by Demod 3033 with 2 at 1,1,1,2,2 +Id : 3510, {_}: multiply ?15042 (inverse (multiply (inverse ?15043) ?15043)) =?= multiply ?15042 (inverse (multiply (inverse ?15044) ?15044)) [15044, 15043, 15042] by Super 3493 with 3250 at 3 +Id : 3957, {_}: multiply (inverse (multiply ?16893 (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896)))) (multiply ?16893 (inverse ?16896)) =>= ?16894 [16896, 16895, 16894, 16893] by Super 104 with 3510 at 1,1,2,1,1,2 +Id : 4003, {_}: multiply (multiply (inverse (multiply ?17133 (inverse (multiply ?17134 ?17135)))) (multiply ?17133 (inverse ?17135))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134, 17133] by Super 2 with 3510 at 2 +Id : 4810, {_}: multiply (multiply (inverse ?21607) ?21607) (inverse (multiply (inverse (multiply (inverse ?21608) ?21608)) (multiply (inverse ?21608) ?21608))) =>= inverse (multiply (inverse ?21608) ?21608) [21608, 21607] by Super 6 with 4003 at 2,1,2 +Id : 1364, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (multiply ?5999 (inverse ?5998))) (multiply ?5999 (inverse ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5999, 5998, 5997, 5996, 5995] by Super 161 with 1288 at 1,2,2 +Id : 4844, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (multiply (inverse (inverse ?21769)) (inverse ?21769)) [21769, 21768] by Super 4810 with 1364 at 2 +Id : 21277, {_}: multiply (inverse (multiply (inverse (inverse ?53833)) (inverse ?53833))) (multiply ?53834 (inverse ?53833)) =>= multiply ?53834 (inverse ?53833) [53834, 53833] by Super 3957 with 4844 at 1,2 +Id : 21278, {_}: multiply (inverse (multiply (inverse (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838))))) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53837, 53836] by Super 21277 with 210 at 2,2,2 +Id : 21547, {_}: multiply (inverse (multiply (inverse ?53837) (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))))) (multiply ?53839 ?53837) =>= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53839, 53838, 53836, 53837] by Demod 21278 with 210 at 1,1,1,1,2 +Id : 21548, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =?= multiply ?53839 (inverse (multiply ?53836 (inverse (multiply (multiply (multiply ?53837 (multiply ?53836 (inverse ?53838))) (inverse (multiply (inverse ?53838) ?53838))) ?53838)))) [53838, 53836, 53839, 53837] by Demod 21547 with 210 at 2,1,1,2 +Id : 21549, {_}: multiply (inverse (multiply (inverse ?53837) ?53837)) (multiply ?53839 ?53837) =>= multiply ?53839 ?53837 [53839, 53837] by Demod 21548 with 210 at 2,3 +Id : 22063, {_}: multiply (inverse (multiply ?55325 ?55326)) (multiply ?55325 ?55326) =>= multiply (inverse ?55326) ?55326 [55326, 55325] by Super 1288 with 21549 at 3 +Id : 22073, {_}: multiply (inverse (multiply (inverse (multiply ?55370 (inverse (multiply (multiply ?55371 (inverse (multiply (inverse ?55372) ?55372))) ?55373)))) (multiply ?55370 (inverse ?55373)))) ?55371 =>= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55372, 55371, 55370] by Super 22063 with 3957 at 2,2 +Id : 22230, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (multiply ?55370 (inverse ?55373))) (multiply ?55370 (inverse ?55373)) [55373, 55370, 55371] by Demod 22073 with 3957 at 1,1,2 +Id : 21784, {_}: multiply (inverse (multiply ?54500 ?54501)) (multiply ?54500 ?54501) =>= multiply (inverse ?54501) ?54501 [54501, 54500] by Super 1288 with 21549 at 3 +Id : 22543, {_}: multiply (inverse ?56820) ?56820 =?= multiply (inverse (inverse ?56821)) (inverse ?56821) [56821, 56820] by Demod 22230 with 21784 at 3 +Id : 22231, {_}: multiply (inverse ?55371) ?55371 =?= multiply (inverse (inverse ?55373)) (inverse ?55373) [55373, 55371] by Demod 22230 with 21784 at 3 +Id : 22585, {_}: multiply (inverse ?57023) ?57023 =?= multiply (inverse ?57024) ?57024 [57024, 57023] by Super 22543 with 22231 at 3 +Id : 22724, {_}: multiply (inverse (multiply (inverse ?57285) ?57285)) (multiply ?57286 ?57287) =>= multiply ?57286 ?57287 [57287, 57286, 57285] by Super 21549 with 22585 at 1,1,2 +Id : 23108, {_}: multiply (inverse (multiply ?58913 ?58914)) (multiply ?58913 ?58915) =>= multiply (inverse ?58914) ?58915 [58915, 58914, 58913] by Super 1288 with 22724 at 3 +Id : 23367, {_}: multiply (inverse (inverse (multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) (inverse (multiply (inverse ?5365) ?5365))) ?5365))) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 1238 with 23108 at 2 +Id : 23366, {_}: multiply (inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) ?16896))) (inverse ?16896) =>= ?16894 [16896, 16895, 16894] by Demod 3957 with 23108 at 2 +Id : 23375, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =?= multiply (inverse (multiply ?18 (inverse (multiply ?16 ?17)))) (multiply ?18 (inverse ?17)) [18, 17, 16] by Demod 5 with 23108 at 1,2 +Id : 23376, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse (multiply (inverse ?17) ?17))) (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23375 with 23108 at 3 +Id : 23410, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642))))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59642, 59641, 59640] by Super 23376 with 23108 at 1,2,1,2,2 +Id : 23543, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse (multiply ?59641 ?59642)) (multiply ?59641 ?59642)))) (inverse (multiply (inverse ?59642) ?59642)))) =>= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23410 with 23108 at 1,1,2,1,2 +Id : 23544, {_}: multiply (multiply (inverse (inverse ?59640)) (inverse (inverse (multiply (inverse ?59642) ?59642)))) (inverse (multiply (inverse (inverse (multiply (inverse ?59642) ?59642))) (inverse (multiply (inverse ?59642) ?59642)))) =?= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23543 with 23108 at 1,1,1,1,2,2 +Id : 23545, {_}: multiply (inverse (inverse (multiply ?59640 ?59642))) (inverse ?59642) =<= multiply (inverse (inverse (multiply ?59640 (multiply ?59641 ?59642)))) (inverse (multiply ?59641 ?59642)) [59641, 59642, 59640] by Demod 23544 with 23376 at 2 +Id : 26221, {_}: multiply (inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682)))) (inverse (multiply (inverse ?63683) ?63683)) =>= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63683, 63682, 63681] by Super 3510 with 23545 at 3 +Id : 23378, {_}: multiply (multiply (inverse (inverse (multiply ?17134 ?17135))) (inverse ?17135)) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 4003 with 23108 at 1,2 +Id : 1370, {_}: inverse (multiply ?6029 (inverse (multiply (multiply (multiply (inverse (multiply ?6030 ?6031)) (multiply ?6030 (inverse ?6032))) (inverse (multiply (inverse ?6032) ?6032))) ?6032))) =>= inverse (multiply ?6029 ?6031) [6032, 6031, 6030, 6029] by Super 210 with 1288 at 1,1,1,2,1,2 +Id : 4845, {_}: multiply (multiply (inverse ?21771) ?21771) (inverse (multiply (inverse ?21772) ?21772)) =?= inverse (multiply (inverse ?21773) ?21773) [21773, 21772, 21771] by Super 4810 with 3510 at 2 +Id : 7295, {_}: inverse (multiply ?28092 (inverse (multiply (inverse (multiply (inverse ?28093) ?28093)) ?28094))) =>= inverse (multiply ?28092 (inverse ?28094)) [28094, 28093, 28092] by Super 1370 with 4845 at 1,1,2,1,2 +Id : 22930, {_}: inverse (multiply (inverse ?58245) ?58245) =?= inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?58246) ?58246)) ?58247))) (inverse ?58247)) [58247, 58246, 58245] by Super 7295 with 22585 at 1,2 +Id : 8, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?26) (multiply (multiply (inverse (multiply ?27 (inverse (multiply ?26 ?28)))) (multiply ?27 (inverse ?28))) (inverse ?28))) (inverse (multiply ?29 (multiply (inverse ?28) ?28))))) (inverse ?28)) (inverse (multiply (inverse (multiply (inverse ?28) ?28)) (multiply (inverse ?28) ?28))) =>= ?29 [29, 28, 27, 26] by Super 2 with 6 at 2,1,2 +Id : 7694, {_}: inverse (multiply ?30248 (inverse (multiply (inverse (multiply (inverse ?30249) ?30249)) ?30250))) =>= inverse (multiply ?30248 (inverse ?30250)) [30250, 30249, 30248] by Super 1370 with 4845 at 1,1,2,1,2 +Id : 9751, {_}: inverse (multiply ?34833 (inverse (multiply (inverse (multiply ?34834 ?34835)) (multiply ?34834 ?34836)))) =>= inverse (multiply ?34833 (inverse (multiply (inverse ?34835) ?34836))) [34836, 34835, 34834, 34833] by Super 7694 with 1288 at 1,2,1,2 +Id : 9799, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (multiply ?35158 (inverse ?35159))) (multiply ?35158 ?35160)))) =?= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35158, 35157] by Super 9751 with 7295 at 1,1,2,1,2 +Id : 7715, {_}: inverse (multiply ?30362 (inverse (multiply (inverse (multiply ?30363 ?30364)) (multiply ?30363 ?30365)))) =>= inverse (multiply ?30362 (inverse (multiply (inverse ?30364) ?30365))) [30365, 30364, 30363, 30362] by Super 7694 with 1288 at 1,2,1,2 +Id : 10327, {_}: inverse (multiply ?35157 (inverse (multiply (inverse (inverse ?35159)) ?35160))) =<= inverse (multiply ?35157 (inverse (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?35161) ?35161)) ?35159))) ?35160))) [35161, 35160, 35159, 35157] by Demod 9799 with 7715 at 2 +Id : 14061, {_}: multiply (multiply (inverse (multiply (multiply (inverse ?43109) (multiply (multiply (inverse (multiply ?43110 (inverse (multiply ?43109 ?43111)))) (multiply ?43110 (inverse ?43111))) (inverse ?43111))) (inverse (multiply (inverse (inverse ?43112)) (multiply (inverse ?43111) ?43111))))) (inverse ?43111)) (inverse (multiply (inverse (multiply (inverse ?43111) ?43111)) (multiply (inverse ?43111) ?43111))) =?= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112, 43111, 43110, 43109] by Super 8 with 10327 at 1,1,2 +Id : 14495, {_}: inverse (inverse ?43112) =<= inverse (inverse (multiply (inverse (multiply (inverse ?43113) ?43113)) ?43112)) [43113, 43112] by Demod 14061 with 8 at 2 +Id : 23770, {_}: inverse (multiply (inverse ?60796) ?60796) =?= inverse (multiply (inverse (inverse ?60797)) (inverse ?60797)) [60797, 60796] by Demod 22930 with 14495 at 1,1,3 +Id : 23801, {_}: inverse (multiply (inverse ?60931) ?60931) =?= inverse (multiply (inverse ?60932) ?60932) [60932, 60931] by Super 23770 with 22585 at 1,3 +Id : 25761, {_}: multiply (multiply (inverse (inverse (multiply (inverse ?63084) ?63084))) (inverse ?63085)) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085, 63084] by Super 23378 with 23801 at 1,1,1,2 +Id : 27867, {_}: multiply (inverse (multiply (inverse ?66211) ?66211)) (inverse ?66212) =?= multiply (multiply (inverse (inverse (multiply (inverse ?66213) ?66213))) (inverse ?66212)) (inverse (multiply (inverse ?66214) ?66214)) [66214, 66213, 66212, 66211] by Super 22724 with 25761 at 2,2 +Id : 28152, {_}: multiply (inverse (multiply (inverse ?66849) ?66849)) (inverse ?66850) =>= inverse ?66850 [66850, 66849] by Demod 27867 with 25761 at 3 +Id : 28153, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =?= inverse (multiply ?66854 (inverse (multiply (multiply (multiply ?66853 (multiply ?66854 (inverse ?66855))) (inverse (multiply (inverse ?66855) ?66855))) ?66855))) [66855, 66854, 66853, 66852] by Super 28152 with 210 at 2,2 +Id : 28218, {_}: multiply (inverse (multiply (inverse ?66852) ?66852)) ?66853 =>= ?66853 [66853, 66852] by Demod 28153 with 210 at 3 +Id : 28331, {_}: multiply (inverse (inverse (multiply (inverse (multiply (inverse ?67206) ?67206)) ?67207))) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207, 67206] by Super 23366 with 28218 at 1,1,1,1,2 +Id : 28438, {_}: multiply (inverse (inverse ?67207)) (inverse ?67207) =?= inverse (multiply (inverse ?67208) ?67208) [67208, 67207] by Demod 28331 with 28218 at 1,1,1,2 +Id : 28698, {_}: multiply (inverse (inverse (multiply (inverse ?68177) ?68177))) ?68178 =>= ?68178 [68178, 68177] by Super 28218 with 28438 at 1,1,2 +Id : 29246, {_}: multiply (inverse ?63085) (inverse (multiply (inverse ?63086) ?63086)) =>= inverse ?63085 [63086, 63085] by Demod 25761 with 28698 at 1,2 +Id : 29249, {_}: inverse (inverse (multiply ?63681 (multiply (inverse ?63682) ?63682))) =<= multiply (inverse (inverse (multiply ?63681 ?63682))) (inverse ?63682) [63682, 63681] by Demod 26221 with 29246 at 2 +Id : 29251, {_}: inverse (inverse (multiply (multiply ?16894 (inverse (multiply (inverse ?16895) ?16895))) (multiply (inverse ?16896) ?16896))) =>= ?16894 [16896, 16895, 16894] by Demod 23366 with 29249 at 2 +Id : 29250, {_}: multiply (inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135)))) (inverse (multiply (inverse ?17136) ?17136)) =>= ?17134 [17136, 17135, 17134] by Demod 23378 with 29249 at 1,2 +Id : 29258, {_}: inverse (inverse (multiply ?17134 (multiply (inverse ?17135) ?17135))) =>= ?17134 [17135, 17134] by Demod 29250 with 29246 at 2 +Id : 29259, {_}: multiply ?16894 (inverse (multiply (inverse ?16895) ?16895)) =>= ?16894 [16895, 16894] by Demod 29251 with 29258 at 2 +Id : 29266, {_}: multiply (inverse (inverse (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) ?5365))) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 23367 with 29259 at 1,1,1,1,2 +Id : 29298, {_}: inverse (inverse (multiply ?68838 (inverse (multiply (inverse ?68839) ?68839)))) =>= ?68838 [68839, 68838] by Super 29258 with 28698 at 2,1,1,2 +Id : 29399, {_}: inverse (inverse ?68838) =>= ?68838 [68838] by Demod 29298 with 29259 at 1,1,2 +Id : 32787, {_}: multiply (multiply (multiply ?5363 (multiply ?5364 (inverse ?5365))) ?5365) ?5366 =>= multiply ?5363 (multiply ?5364 ?5366) [5366, 5365, 5364, 5363] by Demod 29266 with 29399 at 1,2 +Id : 32817, {_}: multiply (multiply (multiply ?69480 (multiply ?69481 ?69482)) (inverse ?69482)) ?69483 =>= multiply ?69480 (multiply ?69481 ?69483) [69483, 69482, 69481, 69480] by Super 32787 with 29399 at 2,2,1,1,2 +Id : 27049, {_}: multiply (inverse (inverse (multiply ?65328 (multiply (inverse ?65329) ?65329)))) (inverse (multiply (inverse ?65330) ?65330)) =>= multiply (inverse (inverse (multiply ?65328 ?65329))) (inverse ?65329) [65330, 65329, 65328] by Super 3510 with 23545 at 3 +Id : 27102, {_}: multiply (inverse (inverse (multiply (inverse ?65600) ?65600))) (inverse (multiply (inverse ?65601) ?65601)) =?= multiply (inverse (inverse (multiply (inverse (multiply (inverse ?65602) ?65602)) ?65600))) (inverse ?65600) [65602, 65601, 65600] by Super 27049 with 22724 at 1,1,1,2 +Id : 27480, {_}: multiply (inverse (inverse (multiply (inverse ?65600) ?65600))) (inverse (multiply (inverse ?65601) ?65601)) =>= multiply (inverse (inverse ?65600)) (inverse ?65600) [65601, 65600] by Demod 27102 with 14495 at 1,3 +Id : 27499, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (multiply (inverse (inverse ?17)) (inverse ?17))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 23376 with 27480 at 1,2,2 +Id : 28687, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?68131)) (inverse ?68131))) (inverse (inverse (multiply (inverse ?68132) ?68132)))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?68133) ?68133) ?68132))) (inverse ?68132) [68133, 68132, 68131] by Super 27499 with 28438 at 1,1,1,2 +Id : 28770, {_}: multiply (inverse (inverse (multiply (inverse ?68132) ?68132))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?68133) ?68133) ?68132))) (inverse ?68132) [68133, 68132] by Demod 28687 with 28218 at 1,2 +Id : 9, {_}: multiply (multiply (inverse (multiply ?31 (inverse (inverse ?32)))) (multiply ?31 (inverse (inverse (multiply (inverse ?32) ?32))))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (multiply ?34 (inverse (multiply ?33 ?32)))) (multiply ?34 (inverse ?32))) (inverse ?32)) [34, 33, 32, 31] by Super 2 with 6 at 1,2,1,1,1,2 +Id : 23370, {_}: multiply (multiply (inverse (inverse (inverse ?32))) (inverse (inverse (multiply (inverse ?32) ?32)))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (multiply ?34 (inverse (multiply ?33 ?32)))) (multiply ?34 (inverse ?32))) (inverse ?32)) [34, 33, 32] by Demod 9 with 23108 at 1,2 +Id : 23371, {_}: multiply (multiply (inverse (inverse (inverse ?32))) (inverse (inverse (multiply (inverse ?32) ?32)))) (inverse (multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse (multiply (inverse ?32) ?32)))) =?= multiply (inverse ?33) (multiply (multiply (inverse (inverse (multiply ?33 ?32))) (inverse ?32)) (inverse ?32)) [33, 32] by Demod 23370 with 23108 at 1,2,3 +Id : 23387, {_}: multiply (inverse (inverse (multiply (inverse ?32) ?32))) (inverse ?32) =<= multiply (inverse ?33) (multiply (multiply (inverse (inverse (multiply ?33 ?32))) (inverse ?32)) (inverse ?32)) [33, 32] by Demod 23371 with 23376 at 2 +Id : 25785, {_}: multiply (inverse (inverse (multiply (inverse ?63178) ?63178))) (inverse ?63178) =<= multiply (inverse (multiply (inverse ?63179) ?63179)) (multiply (multiply (inverse (inverse (multiply (multiply (inverse ?63180) ?63180) ?63178))) (inverse ?63178)) (inverse ?63178)) [63180, 63179, 63178] by Super 23387 with 23801 at 1,3 +Id : 25940, {_}: multiply (inverse (inverse (multiply (inverse ?63178) ?63178))) (inverse ?63178) =<= multiply (multiply (inverse (inverse (multiply (multiply (inverse ?63180) ?63180) ?63178))) (inverse ?63178)) (inverse ?63178) [63180, 63178] by Demod 25785 with 22724 at 3 +Id : 26391, {_}: multiply (inverse (inverse (multiply (multiply (inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074))) ?64075))) (inverse ?64075) =?= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074)) [64076, 64075, 64074] by Super 23366 with 25940 at 1,1,1,1,2 +Id : 26476, {_}: inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074))) =<= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) (multiply (inverse ?64074) ?64074)))) (inverse (multiply (inverse ?64074) ?64074)) [64076, 64074] by Demod 26391 with 23366 at 2 +Id : 26477, {_}: inverse (inverse (multiply (inverse (multiply (inverse ?64074) ?64074)) (multiply (inverse ?64074) ?64074))) =?= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) ?64074))) (inverse ?64074) [64076, 64074] by Demod 26476 with 23545 at 3 +Id : 26478, {_}: inverse (inverse (multiply (inverse ?64074) ?64074)) =<= multiply (inverse (inverse (multiply (multiply (inverse ?64076) ?64076) ?64074))) (inverse ?64074) [64076, 64074] by Demod 26477 with 14495 at 2 +Id : 28771, {_}: multiply (inverse (inverse (multiply (inverse ?68132) ?68132))) (inverse (multiply (inverse (inverse ?68132)) (inverse ?68132))) =>= inverse (inverse (multiply (inverse ?68132) ?68132)) [68132] by Demod 28770 with 26478 at 3 +Id : 28772, {_}: multiply (inverse (inverse ?68132)) (inverse ?68132) =>= inverse (inverse (multiply (inverse ?68132) ?68132)) [68132] by Demod 28771 with 27480 at 2 +Id : 28931, {_}: inverse (multiply ?21768 (inverse (multiply (multiply (multiply ?21768 (inverse ?21769)) (inverse (multiply (inverse ?21769) ?21769))) ?21769))) =>= inverse (inverse (inverse (multiply (inverse ?21769) ?21769))) [21769, 21768] by Demod 4844 with 28772 at 1,3 +Id : 29275, {_}: inverse (multiply ?21768 (inverse (multiply (multiply ?21768 (inverse ?21769)) ?21769))) =>= inverse (inverse (inverse (multiply (inverse ?21769) ?21769))) [21769, 21768] by Demod 28931 with 29259 at 1,1,2,1,2 +Id : 32786, {_}: inverse (multiply ?21768 (inverse (multiply (multiply ?21768 (inverse ?21769)) ?21769))) =>= inverse (multiply (inverse ?21769) ?21769) [21769, 21768] by Demod 29275 with 29399 at 3 +Id : 32802, {_}: inverse (multiply ?69432 (inverse (multiply (multiply ?69432 ?69433) (inverse ?69433)))) =>= inverse (multiply (inverse (inverse ?69433)) (inverse ?69433)) [69433, 69432] by Super 32786 with 29399 at 2,1,1,2,1,2 +Id : 21975, {_}: multiply (multiply (inverse (multiply ?5995 (inverse ?5996))) (multiply ?5995 (inverse (multiply ?5997 (inverse ?5998))))) (inverse (multiply (inverse (inverse ?5998)) (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996, 5995] by Demod 1364 with 21784 at 1,2,2 +Id : 23386, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (multiply (inverse (inverse ?5998)) (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996] by Demod 21975 with 23108 at 1,2 +Id : 28932, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply (multiply ?5996 (inverse (multiply (inverse ?5998) ?5998))) ?5998))) [5998, 5997, 5996] by Demod 23386 with 28772 at 1,2,2 +Id : 29265, {_}: multiply (multiply (inverse (inverse ?5996)) (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 28932 with 29259 at 1,1,2,1,3 +Id : 32767, {_}: multiply (multiply ?5996 (inverse (multiply ?5997 (inverse ?5998)))) (inverse (inverse (inverse (multiply (inverse ?5998) ?5998)))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 29265 with 29399 at 1,1,2 +Id : 32768, {_}: multiply (multiply ?5996 (inverse (multiply ?5997 (inverse ?5998)))) (inverse (multiply (inverse ?5998) ?5998)) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 32767 with 29399 at 2,2 +Id : 32797, {_}: multiply ?5996 (inverse (multiply ?5997 (inverse ?5998))) =>= inverse (multiply ?5997 (inverse (multiply ?5996 ?5998))) [5998, 5997, 5996] by Demod 32768 with 29259 at 2 +Id : 32841, {_}: inverse (inverse (multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)))) =>= inverse (multiply (inverse (inverse ?69433)) (inverse ?69433)) [69433, 69432] by Demod 32802 with 32797 at 1,2 +Id : 32842, {_}: inverse (inverse (multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)))) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32841 with 29399 at 1,1,3 +Id : 32843, {_}: multiply (multiply ?69432 ?69433) (inverse (multiply ?69432 ?69433)) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32842 with 29399 at 2 +Id : 10, {_}: multiply (multiply (inverse (inverse ?36)) (multiply (multiply (inverse ?37) (multiply (multiply (inverse (multiply ?38 (inverse (multiply ?37 ?36)))) (multiply ?38 (inverse ?36))) (inverse ?36))) (inverse ?36))) (inverse (multiply (inverse ?36) ?36)) =>= inverse ?36 [38, 37, 36] by Super 2 with 6 at 1,1,1,2 +Id : 37, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (multiply ?176 (inverse (multiply ?175 ?174)))) (multiply ?176 (inverse ?174))) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (multiply ?177 (inverse (inverse ?174)))) (multiply ?177 (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [177, 176, 175, 174] by Super 6 with 10 at 1,2,1,1,1,2,1,2 +Id : 23364, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (inverse (multiply ?175 ?174))) (inverse ?174)) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (multiply ?177 (inverse (inverse ?174)))) (multiply ?177 (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [177, 175, 174] by Demod 37 with 23108 at 1,2,1,2,1,1,1,2 +Id : 23365, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse ?175) (multiply (multiply (inverse (inverse (multiply ?175 ?174))) (inverse ?174)) (inverse ?174))) (inverse ?174)))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [175, 174] by Demod 23364 with 23108 at 1,2,1,2 +Id : 23401, {_}: multiply (multiply (inverse (multiply (inverse (inverse ?174)) (multiply (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174)) (inverse ?174)))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23365 with 23387 at 1,2,1,1,1,2 +Id : 23402, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23401 with 23387 at 1,1,1,2 +Id : 27500, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (multiply (inverse (inverse ?174)) (inverse ?174))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 23402 with 27480 at 1,2,2 +Id : 28930, {_}: multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?174) ?174))) (inverse ?174))) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 27500 with 28772 at 1,2,2 +Id : 29247, {_}: multiply (multiply (inverse (inverse ?174)) (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 28930 with 28698 at 1,1,1,2 +Id : 32772, {_}: multiply (multiply ?174 (multiply (multiply (inverse (inverse (inverse ?174))) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 29247 with 29399 at 1,1,2 +Id : 32773, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (inverse (inverse (multiply (inverse ?174) ?174)))) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32772 with 29399 at 1,1,2,1,2 +Id : 32774, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (inverse (inverse (multiply (inverse ?174) ?174))))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32773 with 29399 at 2,1,2,1,2 +Id : 32775, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (inverse (inverse (multiply (inverse ?174) ?174)))) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32774 with 29399 at 2,2,1,2 +Id : 32776, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)) =>= inverse (inverse (multiply (inverse ?174) ?174)) [174] by Demod 32775 with 29399 at 2,2 +Id : 32777, {_}: multiply (multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174))) (inverse (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32776 with 29399 at 3 +Id : 32792, {_}: multiply ?174 (multiply (multiply (inverse ?174) (multiply (inverse ?174) ?174)) (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32777 with 29259 at 2 +Id : 28933, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= multiply (inverse (inverse (multiply ?16 ?17))) (inverse ?17) [17, 16] by Demod 27499 with 28772 at 1,2,2 +Id : 29256, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= inverse (inverse (multiply ?16 (multiply (inverse ?17) ?17))) [17, 16] by Demod 28933 with 29249 at 3 +Id : 29262, {_}: multiply (multiply (inverse (inverse ?16)) (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 29256 with 29258 at 3 +Id : 32782, {_}: multiply (multiply ?16 (inverse (inverse (multiply (inverse ?17) ?17)))) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 29262 with 29399 at 1,1,2 +Id : 32783, {_}: multiply (multiply ?16 (multiply (inverse ?17) ?17)) (inverse (inverse (inverse (multiply (inverse ?17) ?17)))) =>= ?16 [17, 16] by Demod 32782 with 29399 at 2,1,2 +Id : 32784, {_}: multiply (multiply ?16 (multiply (inverse ?17) ?17)) (inverse (multiply (inverse ?17) ?17)) =>= ?16 [17, 16] by Demod 32783 with 29399 at 2,2 +Id : 32789, {_}: multiply ?16 (multiply (inverse ?17) ?17) =>= ?16 [17, 16] by Demod 32784 with 29259 at 2 +Id : 32793, {_}: multiply ?174 (multiply (inverse ?174) (multiply (inverse ?174) ?174)) =>= multiply (inverse ?174) ?174 [174] by Demod 32792 with 32789 at 2,2 +Id : 32794, {_}: multiply ?174 (inverse ?174) =?= multiply (inverse ?174) ?174 [174] by Demod 32793 with 32789 at 2,2 +Id : 32844, {_}: multiply (inverse (multiply ?69432 ?69433)) (multiply ?69432 ?69433) =>= inverse (multiply ?69433 (inverse ?69433)) [69433, 69432] by Demod 32843 with 32794 at 2 +Id : 32845, {_}: multiply (inverse ?69433) ?69433 =<= inverse (multiply ?69433 (inverse ?69433)) [69433] by Demod 32844 with 23108 at 2 +Id : 32878, {_}: inverse (multiply (inverse ?69602) ?69602) =>= multiply ?69602 (inverse ?69602) [69602] by Super 29399 with 32845 at 1,2 +Id : 32984, {_}: multiply ?16894 (multiply ?16895 (inverse ?16895)) =>= ?16894 [16895, 16894] by Demod 29259 with 32878 at 2,2 +Id : 38023, {_}: multiply ?72734 (multiply ?72735 (multiply ?72736 (inverse ?72736))) =?= multiply (multiply ?72734 (multiply ?72735 ?72737)) (inverse ?72737) [72737, 72736, 72735, 72734] by Super 32984 with 32817 at 2 +Id : 38122, {_}: multiply ?72734 ?72735 =<= multiply (multiply ?72734 (multiply ?72735 ?72737)) (inverse ?72737) [72737, 72735, 72734] by Demod 38023 with 32984 at 2,2 +Id : 40272, {_}: multiply (multiply ?69480 ?69481) ?69483 =?= multiply ?69480 (multiply ?69481 ?69483) [69483, 69481, 69480] by Demod 32817 with 38122 at 1,2 +Id : 40468, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 40272 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP411-1.p +23552: solved GRP411-1.p in 26.617662 using nrkbo +23552: status Unsatisfiable for GRP411-1.p +NO CLASH, using fixed ground order +23570: Facts: +23570: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23570: Goal: +23570: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23570: Order: +23570: nrkbo +23570: Leaf order: +23570: b2 2 0 2 1,1,1,2 +23570: a2 2 0 2 2,2 +23570: inverse 8 1 1 0,1,1,2 +23570: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +23571: Facts: +23571: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23571: Goal: +23571: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23571: Order: +23571: kbo +23571: Leaf order: +23571: b2 2 0 2 1,1,1,2 +23571: a2 2 0 2 2,2 +23571: inverse 8 1 1 0,1,1,2 +23571: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +23572: Facts: +23572: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23572: Goal: +23572: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23572: Order: +23572: lpo +23572: Leaf order: +23572: b2 2 0 2 1,1,1,2 +23572: a2 2 0 2 2,2 +23572: inverse 8 1 1 0,1,1,2 +23572: multiply 8 2 2 0,2 +Statistics : +Max weight : 117 +Found proof, 75.766748s +% SZS status Unsatisfiable for GRP419-1.p +% SZS output start CNFRefutation for GRP419-1.p +Id : 3, {_}: inverse (multiply (inverse (multiply ?6 (inverse (multiply (inverse ?7) (inverse (multiply ?8 (inverse (multiply (inverse ?8) ?8)))))))) (multiply ?6 ?8)) =>= ?7 [8, 7, 6] by single_axiom ?6 ?7 ?8 +Id : 2, {_}: inverse (multiply (inverse (multiply ?2 (inverse (multiply (inverse ?3) (inverse (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) (multiply ?2 ?4)) =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 31, {_}: inverse (multiply (inverse (multiply ?219 (inverse (multiply (inverse ?220) (inverse (multiply (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)) (inverse (multiply ?222 (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)))))))))) (multiply ?219 (multiply (inverse (multiply ?221 (inverse (multiply (inverse ?222) (inverse (multiply ?223 (inverse (multiply (inverse ?223) ?223)))))))) (multiply ?221 ?223)))) =>= ?220 [223, 222, 221, 220, 219] by Super 3 with 2 at 1,1,2,1,2,1,2,1,1,1,2 +Id : 5, {_}: inverse (multiply (inverse (multiply ?16 (inverse (multiply ?17 (inverse (multiply ?18 (inverse (multiply (inverse ?18) ?18)))))))) (multiply ?16 ?18)) =?= multiply (inverse (multiply ?19 (inverse (multiply (inverse ?17) (inverse (multiply ?20 (inverse (multiply (inverse ?20) ?20)))))))) (multiply ?19 ?20) [20, 19, 18, 17, 16] by Super 3 with 2 at 1,1,2,1,1,1,2 +Id : 39, {_}: inverse (multiply (inverse (multiply ?290 (inverse (multiply (inverse ?291) (inverse (multiply (multiply (inverse (multiply ?292 (inverse (multiply (inverse ?293) (inverse (multiply ?294 (inverse (multiply (inverse ?294) ?294)))))))) (multiply ?292 ?294)) (inverse (multiply ?293 (multiply (inverse (multiply ?292 (inverse (multiply (inverse ?293) (inverse (multiply ?294 (inverse (multiply (inverse ?294) ?294)))))))) (multiply ?292 ?294)))))))))) (multiply ?290 (inverse (multiply (inverse (multiply ?295 (inverse (multiply ?293 (inverse (multiply ?296 (inverse (multiply (inverse ?296) ?296)))))))) (multiply ?295 ?296))))) =>= ?291 [296, 295, 294, 293, 292, 291, 290] by Super 31 with 5 at 2,2,1,2 +Id : 11, {_}: multiply (inverse (multiply ?51 (inverse (multiply (inverse (inverse ?52)) (inverse (multiply ?53 (inverse (multiply (inverse ?53) ?53)))))))) (multiply ?51 ?53) =>= ?52 [53, 52, 51] by Super 2 with 5 at 2 +Id : 131, {_}: inverse (multiply (inverse (multiply (inverse (multiply ?678 (inverse (multiply (inverse (inverse ?679)) (inverse (multiply ?680 (inverse (multiply (inverse ?680) ?680)))))))) (inverse (multiply (inverse ?681) (inverse (multiply (multiply ?678 ?680) (inverse (multiply (inverse (multiply ?678 ?680)) (multiply ?678 ?680))))))))) ?679) =>= ?681 [681, 680, 679, 678] by Super 2 with 11 at 2,1,2 +Id : 592, {_}: inverse (multiply (inverse (multiply ?3887 ?3888)) (multiply ?3887 ?3889)) =?= multiply (inverse (multiply ?3890 (inverse (multiply (inverse (inverse (inverse (multiply ?3889 (inverse (multiply (inverse ?3889) ?3889)))))) (inverse (multiply ?3891 (inverse (multiply (inverse ?3891) ?3891)))))))) (inverse (multiply (inverse ?3888) (inverse (multiply (multiply ?3890 ?3891) (inverse (multiply (inverse (multiply ?3890 ?3891)) (multiply ?3890 ?3891))))))) [3891, 3890, 3889, 3888, 3887] by Super 2 with 131 at 2,1,1,1,2 +Id : 1723, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?12104 ?12105)) (multiply ?12104 ?12106)))) (inverse (multiply ?12106 (inverse (multiply (inverse ?12106) ?12106))))) =>= ?12105 [12106, 12105, 12104] by Super 131 with 592 at 1,1,1,2 +Id : 139, {_}: multiply (inverse (multiply ?714 (inverse (multiply (inverse (inverse ?715)) (inverse (multiply ?716 (inverse (multiply (inverse ?716) ?716)))))))) (multiply ?714 ?716) =>= ?715 [716, 715, 714] by Super 2 with 5 at 2 +Id : 140, {_}: multiply (inverse (multiply (inverse (multiply ?718 (inverse (multiply (inverse (inverse ?719)) (inverse (multiply ?720 (inverse (multiply (inverse ?720) ?720)))))))) (inverse (multiply (inverse (inverse ?721)) (inverse (multiply (multiply ?718 ?720) (inverse (multiply (inverse (multiply ?718 ?720)) (multiply ?718 ?720))))))))) ?719 =>= ?721 [721, 720, 719, 718] by Super 139 with 11 at 2,2 +Id : 1734, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?12189 (inverse ?12190))) (multiply ?12189 ?12191)))) (inverse (multiply ?12191 (inverse (multiply (inverse ?12191) ?12191)))) =>= ?12190 [12191, 12190, 12189] by Super 140 with 592 at 1,1,2 +Id : 10, {_}: inverse (inverse (multiply (inverse (multiply ?47 (inverse (multiply ?48 (inverse (multiply ?49 (inverse (multiply (inverse ?49) ?49)))))))) (multiply ?47 ?49))) =>= ?48 [49, 48, 47] by Super 2 with 5 at 1,2 +Id : 1746, {_}: inverse (multiply (inverse (multiply ?12293 ?12294)) (multiply ?12293 ?12295)) =?= multiply (inverse (multiply ?12296 (inverse (multiply (inverse (inverse (inverse (multiply ?12295 (inverse (multiply (inverse ?12295) ?12295)))))) (inverse (multiply ?12297 (inverse (multiply (inverse ?12297) ?12297)))))))) (inverse (multiply (inverse ?12294) (inverse (multiply (multiply ?12296 ?12297) (inverse (multiply (inverse (multiply ?12296 ?12297)) (multiply ?12296 ?12297))))))) [12297, 12296, 12295, 12294, 12293] by Super 2 with 131 at 2,1,1,1,2 +Id : 1828, {_}: inverse (multiply (inverse (multiply ?13070 ?13071)) (multiply ?13070 ?13072)) =?= inverse (multiply (inverse (multiply ?13073 ?13071)) (multiply ?13073 ?13072)) [13073, 13072, 13071, 13070] by Super 1746 with 592 at 3 +Id : 6984, {_}: inverse (inverse (multiply (inverse (multiply ?54958 (inverse (multiply ?54959 (inverse (multiply (multiply ?54960 ?54961) (inverse (multiply (inverse (multiply ?54962 ?54961)) (multiply ?54962 ?54961))))))))) (multiply ?54958 (multiply ?54960 ?54961)))) =>= ?54959 [54962, 54961, 54960, 54959, 54958] by Super 10 with 1828 at 2,1,2,1,2,1,1,1,1,2 +Id : 6987, {_}: inverse (inverse (multiply (inverse (multiply ?54980 (inverse (multiply ?54981 (inverse (multiply (multiply (inverse (multiply (inverse (multiply ?54982 (inverse (multiply (inverse (inverse ?54983)) (inverse (multiply ?54984 (inverse (multiply (inverse ?54984) ?54984)))))))) (inverse (multiply (inverse (inverse ?54985)) (inverse (multiply (multiply ?54982 ?54984) (inverse (multiply (inverse (multiply ?54982 ?54984)) (multiply ?54982 ?54984))))))))) ?54983) (inverse (multiply (inverse (multiply ?54986 ?54983)) (multiply ?54986 ?54983))))))))) (multiply ?54980 ?54985))) =>= ?54981 [54986, 54985, 54984, 54983, 54982, 54981, 54980] by Super 6984 with 140 at 2,2,1,1,2 +Id : 7283, {_}: inverse (inverse (multiply (inverse (multiply ?56997 (inverse (multiply ?56998 (inverse (multiply ?56999 (inverse (multiply (inverse (multiply ?57000 ?57001)) (multiply ?57000 ?57001))))))))) (multiply ?56997 ?56999))) =>= ?56998 [57001, 57000, 56999, 56998, 56997] by Demod 6987 with 140 at 1,1,2,1,2,1,1,1,1,2 +Id : 7302, {_}: inverse (inverse (multiply (inverse (multiply ?57173 (inverse (multiply ?57174 (inverse (multiply ?57175 (inverse (multiply (inverse (multiply (inverse (multiply ?57176 (inverse (multiply (inverse (inverse ?57177)) (inverse (multiply ?57178 (inverse (multiply (inverse ?57178) ?57178)))))))) (multiply ?57176 ?57178))) ?57177)))))))) (multiply ?57173 ?57175))) =>= ?57174 [57178, 57177, 57176, 57175, 57174, 57173] by Super 7283 with 11 at 2,1,2,1,2,1,2,1,1,1,1,2 +Id : 7433, {_}: inverse (inverse (multiply (inverse (multiply ?57173 (inverse (multiply ?57174 (inverse (multiply ?57175 (inverse (multiply (inverse ?57177) ?57177)))))))) (multiply ?57173 ?57175))) =>= ?57174 [57177, 57175, 57174, 57173] by Demod 7302 with 2 at 1,1,2,1,2,1,2,1,1,1,1,2 +Id : 7485, {_}: multiply ?58076 (inverse (multiply ?58077 (inverse (multiply (inverse ?58077) ?58077)))) =?= multiply ?58076 (inverse (multiply ?58077 (inverse (multiply (inverse ?58078) ?58078)))) [58078, 58077, 58076] by Super 1734 with 7433 at 1,2 +Id : 8374, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?64683 (inverse (multiply ?64684 (inverse (multiply (inverse ?64685) ?64685)))))) (multiply ?64683 ?64686)))) (inverse (multiply ?64686 (inverse (multiply (inverse ?64686) ?64686)))) =?= multiply ?64684 (inverse (multiply (inverse ?64684) ?64684)) [64686, 64685, 64684, 64683] by Super 1734 with 7485 at 1,1,1,1,1,2 +Id : 8749, {_}: multiply ?64684 (inverse (multiply (inverse ?64685) ?64685)) =?= multiply ?64684 (inverse (multiply (inverse ?64684) ?64684)) [64685, 64684] by Demod 8374 with 1734 at 2 +Id : 8815, {_}: inverse (multiply (inverse (inverse (multiply (inverse (multiply ?67872 (inverse (multiply (inverse ?67872) ?67872)))) (multiply ?67872 ?67873)))) (inverse (multiply ?67873 (inverse (multiply (inverse ?67873) ?67873))))) =?= inverse (multiply (inverse ?67874) ?67874) [67874, 67873, 67872] by Super 1723 with 8749 at 1,1,1,1,1,1,2 +Id : 9225, {_}: inverse (multiply (inverse ?67872) ?67872) =?= inverse (multiply (inverse ?67874) ?67874) [67874, 67872] by Demod 8815 with 1723 at 2 +Id : 9030, {_}: multiply (inverse (inverse (multiply (inverse (multiply ?69262 (inverse (multiply (inverse ?69262) ?69262)))) (multiply ?69262 ?69263)))) (inverse (multiply ?69263 (inverse (multiply (inverse ?69263) ?69263)))) =?= multiply (inverse ?69264) ?69264 [69264, 69263, 69262] by Super 1734 with 8749 at 1,1,1,1,1,2 +Id : 9183, {_}: multiply (inverse ?69262) ?69262 =?= multiply (inverse ?69264) ?69264 [69264, 69262] by Demod 9030 with 1734 at 2 +Id : 12179, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?88672) ?88672))) (inverse (multiply ?88673 (inverse (multiply (inverse ?88673) ?88673))))) =>= ?88673 [88673, 88672] by Super 1723 with 9183 at 1,1,1,1,2 +Id : 12213, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?88894) ?88894))) (inverse (multiply ?88895 (inverse (multiply (inverse ?88896) ?88896))))) =>= ?88895 [88896, 88895, 88894] by Super 12179 with 9183 at 1,2,1,2,1,2 +Id : 13701, {_}: inverse (multiply (inverse ?97964) ?97964) =?= inverse (inverse (multiply (inverse ?97965) ?97965)) [97965, 97964] by Super 9225 with 12213 at 3 +Id : 34411, {_}: inverse (multiply (inverse (multiply (inverse ?202408) ?202408)) (inverse (multiply ?202409 (inverse (multiply (inverse ?202409) ?202409))))) =>= ?202409 [202409, 202408] by Super 1723 with 13701 at 1,1,2 +Id : 9086, {_}: multiply ?69615 (inverse (multiply (inverse ?69616) ?69616)) =?= multiply ?69615 (inverse (multiply (inverse ?69615) ?69615)) [69616, 69615] by Demod 8374 with 1734 at 2 +Id : 9126, {_}: multiply ?69879 (inverse (multiply (inverse ?69880) ?69880)) =?= multiply ?69879 (inverse (multiply (inverse ?69881) ?69881)) [69881, 69880, 69879] by Super 9086 with 8749 at 3 +Id : 56, {_}: inverse (multiply (inverse (multiply ?444 (inverse (multiply (inverse ?445) (inverse (multiply (inverse (multiply (inverse (multiply ?446 (inverse (multiply ?447 (inverse (multiply ?448 (inverse (multiply (inverse ?448) ?448)))))))) (multiply ?446 ?448))) (inverse (multiply ?447 (multiply (inverse (multiply ?449 (inverse (multiply (inverse ?447) (inverse (multiply ?450 (inverse (multiply (inverse ?450) ?450)))))))) (multiply ?449 ?450)))))))))) (multiply ?444 (multiply (inverse (multiply ?449 (inverse (multiply (inverse ?447) (inverse (multiply ?450 (inverse (multiply (inverse ?450) ?450)))))))) (multiply ?449 ?450)))) =>= ?445 [450, 449, 448, 447, 446, 445, 444] by Super 31 with 5 at 1,1,2,1,2,1,1,1,2 +Id : 14563, {_}: inverse (multiply (inverse (multiply ?103053 (inverse (multiply (inverse (inverse (multiply (inverse ?103054) ?103054))) (inverse (multiply (inverse (multiply (inverse (multiply ?103055 (inverse (multiply ?103056 (inverse (multiply ?103057 (inverse (multiply (inverse ?103057) ?103057)))))))) (multiply ?103055 ?103057))) (inverse (multiply ?103056 (multiply (inverse (multiply ?103058 (inverse (multiply (inverse ?103056) (inverse (multiply ?103059 (inverse (multiply (inverse ?103059) ?103059)))))))) (multiply ?103058 ?103059)))))))))) (multiply ?103053 (multiply (inverse (multiply ?103058 (inverse (multiply (inverse ?103056) (inverse (multiply ?103059 (inverse (multiply (inverse ?103059) ?103059)))))))) (multiply ?103058 ?103059)))) =?= multiply (inverse ?103060) ?103060 [103060, 103059, 103058, 103057, 103056, 103055, 103054, 103053] by Super 56 with 13701 at 1,1,2,1,1,1,2 +Id : 14713, {_}: inverse (multiply (inverse ?103054) ?103054) =?= multiply (inverse ?103060) ?103060 [103060, 103054] by Demod 14563 with 56 at 2 +Id : 15410, {_}: multiply ?107836 (inverse (multiply (inverse ?107837) ?107837)) =?= multiply ?107836 (multiply (inverse ?107838) ?107838) [107838, 107837, 107836] by Super 9126 with 14713 at 2,3 +Id : 34485, {_}: inverse (multiply (inverse (multiply (inverse ?202808) ?202808)) (inverse (multiply (inverse (multiply (inverse ?202809) ?202809)) (inverse (multiply (inverse (inverse (multiply (inverse ?202809) ?202809))) (multiply (inverse ?202810) ?202810)))))) =>= inverse (multiply (inverse ?202809) ?202809) [202810, 202809, 202808] by Super 34411 with 15410 at 1,2,1,2,1,2 +Id : 14824, {_}: multiply (inverse ?103830) ?103830 =?= inverse (inverse (multiply (inverse ?103831) ?103831)) [103831, 103830] by Super 12213 with 14713 at 2 +Id : 24848, {_}: inverse (multiply (multiply (inverse ?160661) ?160661) (inverse (multiply ?160662 (inverse (multiply (inverse ?160662) ?160662))))) =>= ?160662 [160662, 160661] by Super 1723 with 14824 at 1,1,2 +Id : 25277, {_}: inverse (multiply (multiply (inverse ?163120) ?163120) (inverse (multiply ?163121 (multiply (inverse ?163122) ?163122)))) =>= ?163121 [163122, 163121, 163120] by Super 24848 with 14713 at 2,1,2,1,2 +Id : 25479, {_}: inverse (multiply (inverse (multiply (inverse ?164337) ?164337)) (inverse (multiply ?164338 (multiply (inverse ?164339) ?164339)))) =>= ?164338 [164339, 164338, 164337] by Super 25277 with 14713 at 1,1,2 +Id : 35006, {_}: inverse (multiply (inverse (multiply (inverse ?204646) ?204646)) (inverse (inverse (multiply (inverse ?204647) ?204647)))) =>= inverse (multiply (inverse ?204647) ?204647) [204647, 204646] by Demod 34485 with 25479 at 2,1,2 +Id : 35218, {_}: inverse (multiply (multiply (inverse ?205705) ?205705) (inverse (inverse (multiply (inverse ?205706) ?205706)))) =>= inverse (multiply (inverse ?205706) ?205706) [205706, 205705] by Super 35006 with 14713 at 1,1,2 +Id : 35602, {_}: inverse (multiply (inverse (multiply ?206697 (inverse (multiply (inverse (multiply (inverse ?206698) ?206698)) (inverse (multiply (multiply (inverse (multiply ?206699 (inverse (multiply (inverse ?206700) (inverse (multiply ?206701 (inverse (multiply (inverse ?206701) ?206701)))))))) (multiply ?206699 ?206701)) (inverse (multiply ?206700 (multiply (inverse (multiply ?206699 (inverse (multiply (inverse ?206700) (inverse (multiply ?206701 (inverse (multiply (inverse ?206701) ?206701)))))))) (multiply ?206699 ?206701)))))))))) (multiply ?206697 (inverse (multiply (inverse (multiply ?206702 (inverse (multiply ?206700 (inverse (multiply ?206703 (inverse (multiply (inverse ?206703) ?206703)))))))) (multiply ?206702 ?206703))))) =?= multiply (multiply (inverse ?206704) ?206704) (inverse (inverse (multiply (inverse ?206698) ?206698))) [206704, 206703, 206702, 206701, 206700, 206699, 206698, 206697] by Super 39 with 35218 at 1,1,2,1,1,1,2 +Id : 35866, {_}: multiply (inverse ?206698) ?206698 =<= multiply (multiply (inverse ?206704) ?206704) (inverse (inverse (multiply (inverse ?206698) ?206698))) [206704, 206698] by Demod 35602 with 39 at 2 +Id : 36115, {_}: inverse (multiply (inverse (multiply (multiply (inverse ?208195) ?208195) (inverse (multiply (inverse ?208196) (inverse (multiply (inverse (inverse (multiply (inverse ?208197) ?208197))) (inverse (multiply (inverse (inverse (inverse (multiply (inverse ?208197) ?208197)))) (inverse (inverse (multiply (inverse ?208197) ?208197))))))))))) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196, 208195] by Super 2 with 35866 at 2,1,2 +Id : 15929, {_}: inverse (multiply (multiply (inverse ?110579) ?110579) (inverse (multiply ?110580 (inverse (multiply (inverse ?110580) ?110580))))) =>= ?110580 [110580, 110579] by Super 1723 with 14824 at 1,1,2 +Id : 24931, {_}: inverse (multiply (multiply (inverse ?161104) ?161104) (inverse (multiply ?161105 (multiply (inverse ?161106) ?161106)))) =>= ?161105 [161106, 161105, 161104] by Super 24848 with 14713 at 2,1,2,1,2 +Id : 25816, {_}: inverse (multiply (multiply (inverse ?166039) ?166039) (inverse (multiply (inverse ?166040) ?166040))) =>= multiply (inverse ?166040) ?166040 [166040, 166039] by Super 15929 with 24931 at 2,1,2 +Id : 25967, {_}: inverse (multiply (inverse (inverse (multiply (inverse ?166851) ?166851))) (inverse (multiply (inverse ?166852) ?166852))) =>= multiply (inverse ?166852) ?166852 [166852, 166851] by Super 25816 with 14824 at 1,1,2 +Id : 36557, {_}: inverse (multiply (inverse (multiply (multiply (inverse ?208195) ?208195) (inverse (multiply (inverse ?208196) (multiply (inverse (inverse (inverse (multiply (inverse ?208197) ?208197)))) (inverse (inverse (multiply (inverse ?208197) ?208197)))))))) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196, 208195] by Demod 36115 with 25967 at 2,1,2,1,1,1,2 +Id : 36558, {_}: inverse (multiply (inverse ?208196) (multiply (inverse ?208197) ?208197)) =>= ?208196 [208197, 208196] by Demod 36557 with 24931 at 1,1,2 +Id : 37252, {_}: inverse (multiply (multiply (inverse ?211410) ?211410) ?211411) =>= inverse ?211411 [211411, 211410] by Super 24931 with 36558 at 2,1,2 +Id : 40835, {_}: inverse (multiply (inverse ?231064) (multiply (inverse ?231065) ?231065)) =?= multiply (multiply (inverse ?231066) ?231066) ?231064 [231066, 231065, 231064] by Super 36558 with 37252 at 1,1,2 +Id : 40960, {_}: ?231064 =<= multiply (multiply (inverse ?231066) ?231066) ?231064 [231066, 231064] by Demod 40835 with 36558 at 2 +Id : 42184, {_}: a2 === a2 [] by Demod 1 with 40960 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP419-1.p +23570: solved GRP419-1.p in 75.644727 using nrkbo +23570: status Unsatisfiable for GRP419-1.p +NO CLASH, using fixed ground order +23595: Facts: +23595: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23595: Goal: +23595: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23595: Order: +23595: nrkbo +23595: Leaf order: +23595: b2 2 0 2 1,1,1,2 +23595: a2 2 0 2 2,2 +23595: inverse 8 1 1 0,1,1,2 +23595: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +23596: Facts: +23596: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23596: Goal: +23596: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23596: Order: +23596: kbo +23596: Leaf order: +23596: b2 2 0 2 1,1,1,2 +23596: a2 2 0 2 2,2 +23596: inverse 8 1 1 0,1,1,2 +23596: multiply 8 2 2 0,2 +NO CLASH, using fixed ground order +23597: Facts: +23597: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23597: Goal: +23597: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23597: Order: +23597: lpo +23597: Leaf order: +23597: b2 2 0 2 1,1,1,2 +23597: a2 2 0 2 2,2 +23597: inverse 8 1 1 0,1,1,2 +23597: multiply 8 2 2 0,2 +% SZS status Timeout for GRP422-1.p +NO CLASH, using fixed ground order +23629: Facts: +23629: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23629: Goal: +23629: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23629: Order: +23629: nrkbo +23629: Leaf order: +23629: a3 2 0 2 1,1,2 +23629: b3 2 0 2 2,1,2 +23629: c3 2 0 2 2,2 +23629: inverse 7 1 0 +23629: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23630: Facts: +23630: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23630: Goal: +23630: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23630: Order: +23630: kbo +23630: Leaf order: +23630: a3 2 0 2 1,1,2 +23630: b3 2 0 2 2,1,2 +23630: c3 2 0 2 2,2 +23630: inverse 7 1 0 +23630: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23631: Facts: +23631: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (multiply (inverse ?4) + (inverse (multiply (inverse ?4) ?4))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23631: Goal: +23631: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23631: Order: +23631: lpo +23631: Leaf order: +23631: a3 2 0 2 1,1,2 +23631: b3 2 0 2 2,1,2 +23631: c3 2 0 2 2,2 +23631: inverse 7 1 0 +23631: multiply 10 2 4 0,2 +% SZS status Timeout for GRP423-1.p +NO CLASH, using fixed ground order +23653: Facts: +23653: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23653: Goal: +23653: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23653: Order: +23653: nrkbo +23653: Leaf order: +23653: a3 2 0 2 1,1,2 +23653: b3 2 0 2 2,1,2 +23653: c3 2 0 2 2,2 +23653: inverse 5 1 0 +23653: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23654: Facts: +23654: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23654: Goal: +23654: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23654: Order: +23654: kbo +23654: Leaf order: +23654: a3 2 0 2 1,1,2 +23654: b3 2 0 2 2,1,2 +23654: c3 2 0 2 2,2 +23654: inverse 5 1 0 +23654: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23655: Facts: +23655: Id : 2, {_}: + multiply ?2 + (inverse + (multiply + (multiply + (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) + ?5) (inverse (multiply ?3 ?5)))) + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23655: Goal: +23655: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23655: Order: +23655: lpo +23655: Leaf order: +23655: a3 2 0 2 1,1,2 +23655: b3 2 0 2 2,1,2 +23655: c3 2 0 2 2,2 +23655: inverse 5 1 0 +23655: multiply 10 2 4 0,2 +Statistics : +Max weight : 62 +Found proof, 11.852538s +% SZS status Unsatisfiable for GRP429-1.p +% SZS output start CNFRefutation for GRP429-1.p +Id : 2, {_}: multiply ?2 (inverse (multiply (multiply (inverse (multiply (inverse ?3) (multiply (inverse ?2) ?4))) ?5) (inverse (multiply ?3 ?5)))) =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 3, {_}: multiply ?7 (inverse (multiply (multiply (inverse (multiply (inverse ?8) (multiply (inverse ?7) ?9))) ?10) (inverse (multiply ?8 ?10)))) =>= ?9 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10 +Id : 6, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (inverse (multiply (inverse ?29) (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27))) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 30, 29, 28, 27, 26] by Super 3 with 2 at 1,1,2,2 +Id : 5, {_}: multiply ?19 (inverse (multiply (multiply (inverse (multiply (inverse ?20) ?21)) ?22) (inverse (multiply ?20 ?22)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?23) (multiply (inverse (inverse ?19)) ?21))) ?24) (inverse (multiply ?23 ?24))) [24, 23, 22, 21, 20, 19] by Super 3 with 2 at 2,1,1,1,1,2,2 +Id : 28, {_}: multiply (inverse ?215) (multiply ?215 (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216, 215] by Super 2 with 5 at 2,2 +Id : 29, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?220) (multiply (inverse (inverse ?221)) (multiply (inverse ?221) ?222)))) ?223) (inverse (multiply ?220 ?223))) =>= ?222 [223, 222, 221, 220] by Super 2 with 5 at 2 +Id : 287, {_}: multiply (inverse ?2293) (multiply ?2293 ?2294) =?= multiply (inverse (inverse ?2295)) (multiply (inverse ?2295) ?2294) [2295, 2294, 2293] by Super 28 with 29 at 2,2,2 +Id : 136, {_}: multiply (inverse ?1148) (multiply ?1148 ?1149) =?= multiply (inverse (inverse ?1150)) (multiply (inverse ?1150) ?1149) [1150, 1149, 1148] by Super 28 with 29 at 2,2,2 +Id : 301, {_}: multiply (inverse ?2384) (multiply ?2384 ?2385) =?= multiply (inverse ?2386) (multiply ?2386 ?2385) [2386, 2385, 2384] by Super 287 with 136 at 3 +Id : 356, {_}: multiply (inverse ?2583) (multiply ?2583 (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584, 2583] by Super 28 with 301 at 1,1,1,1,2,2,2 +Id : 679, {_}: multiply ?5168 (inverse (multiply (multiply (inverse (multiply (inverse ?5169) (multiply ?5169 ?5170))) ?5171) (inverse (multiply (inverse ?5168) ?5171)))) =>= ?5170 [5171, 5170, 5169, 5168] by Super 2 with 301 at 1,1,1,1,2,2 +Id : 2910, {_}: multiply ?23936 (inverse (multiply (multiply (inverse (multiply (inverse ?23937) (multiply ?23937 ?23938))) (multiply ?23936 ?23939)) (inverse (multiply (inverse ?23940) (multiply ?23940 ?23939))))) =>= ?23938 [23940, 23939, 23938, 23937, 23936] by Super 679 with 301 at 1,2,1,2,2 +Id : 2996, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse (multiply (inverse ?24705) (multiply ?24705 (inverse (multiply (multiply (inverse (multiply (inverse ?24706) ?24704)) ?24707) (inverse (multiply ?24706 ?24707))))))))) =>= ?24703 [24707, 24706, 24705, 24704, 24703, 24702] by Super 2910 with 28 at 1,1,2,2 +Id : 3034, {_}: multiply (multiply (inverse ?24702) (multiply ?24702 ?24703)) (inverse (multiply ?24704 (inverse ?24704))) =>= ?24703 [24704, 24703, 24702] by Demod 2996 with 28 at 1,2,1,2,2 +Id : 3426, {_}: multiply (inverse (multiply (inverse ?29536) (multiply ?29536 ?29537))) ?29537 =?= multiply (inverse (multiply (inverse ?29538) (multiply ?29538 ?29539))) ?29539 [29539, 29538, 29537, 29536] by Super 356 with 3034 at 2,2 +Id : 3726, {_}: multiply (inverse (inverse (multiply (inverse ?31745) (multiply ?31745 (inverse (multiply (multiply (inverse (multiply (inverse ?31746) ?31747)) ?31748) (inverse (multiply ?31746 ?31748)))))))) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31748, 31747, 31746, 31745] by Super 28 with 3426 at 2,2 +Id : 3919, {_}: multiply (inverse (inverse ?31747)) (multiply (inverse (multiply (inverse ?31749) (multiply ?31749 ?31750))) ?31750) =>= ?31747 [31750, 31749, 31747] by Demod 3726 with 28 at 1,1,1,2 +Id : 91, {_}: multiply (inverse ?821) (multiply ?821 (inverse (multiply (multiply (inverse (multiply (inverse ?822) ?823)) ?824) (inverse (multiply ?822 ?824))))) =>= ?823 [824, 823, 822, 821] by Super 2 with 5 at 2,2 +Id : 107, {_}: multiply (inverse ?949) (multiply ?949 (multiply ?950 (inverse (multiply (multiply (inverse (multiply (inverse ?951) ?952)) ?953) (inverse (multiply ?951 ?953)))))) =>= multiply (inverse (inverse ?950)) ?952 [953, 952, 951, 950, 949] by Super 91 with 5 at 2,2,2 +Id : 3966, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse (multiply (inverse ?33636) (multiply ?33636 (inverse (multiply (multiply (inverse (multiply (inverse ?33637) ?33638)) ?33639) (inverse (multiply ?33637 ?33639))))))))) ?33638 [33639, 33638, 33637, 33636, 33635] by Super 107 with 3919 at 2,2 +Id : 4117, {_}: multiply (inverse (inverse (inverse ?33635))) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 3966 with 28 at 1,1,1,1,3 +Id : 4346, {_}: multiply (inverse (inverse ?35898)) (multiply (inverse (multiply (inverse (inverse (inverse (inverse ?35899)))) (multiply (inverse (inverse (inverse ?35900))) ?35900))) ?35899) =>= ?35898 [35900, 35899, 35898] by Super 3919 with 4117 at 2,1,1,2,2 +Id : 3965, {_}: multiply (inverse ?33628) (multiply ?33628 (multiply ?33629 (inverse (multiply (multiply (inverse ?33630) ?33631) (inverse (multiply (inverse ?33630) ?33631)))))) =?= multiply (inverse (inverse ?33629)) (multiply (inverse (multiply (inverse ?33632) (multiply ?33632 ?33633))) ?33633) [33633, 33632, 33631, 33630, 33629, 33628] by Super 107 with 3919 at 1,1,1,1,2,2,2,2 +Id : 6632, {_}: multiply (inverse ?52916) (multiply ?52916 (multiply ?52917 (inverse (multiply (multiply (inverse ?52918) ?52919) (inverse (multiply (inverse ?52918) ?52919)))))) =>= ?52917 [52919, 52918, 52917, 52916] by Demod 3965 with 3919 at 3 +Id : 6641, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply (multiply (inverse ?52994) (inverse (multiply (multiply (inverse (multiply (inverse ?52995) (multiply (inverse (inverse ?52994)) ?52996))) ?52997) (inverse (multiply ?52995 ?52997))))) (inverse ?52996))))) =>= ?52993 [52997, 52996, 52995, 52994, 52993, 52992] by Super 6632 with 2 at 1,2,1,2,2,2,2 +Id : 6773, {_}: multiply (inverse ?52992) (multiply ?52992 (multiply ?52993 (inverse (multiply ?52996 (inverse ?52996))))) =>= ?52993 [52996, 52993, 52992] by Demod 6641 with 2 at 1,1,2,2,2,2 +Id : 6832, {_}: multiply (inverse (inverse ?53817)) (multiply (inverse ?53818) (multiply ?53818 (inverse (multiply ?53819 (inverse ?53819))))) =>= ?53817 [53819, 53818, 53817] by Super 4346 with 6773 at 1,1,2,2 +Id : 4, {_}: multiply ?12 (inverse (multiply (multiply (inverse (multiply (inverse ?13) (multiply (inverse ?12) ?14))) (inverse (multiply (multiply (inverse (multiply (inverse ?15) (multiply (inverse ?13) ?16))) ?17) (inverse (multiply ?15 ?17))))) (inverse ?16))) =>= ?14 [17, 16, 15, 14, 13, 12] by Super 3 with 2 at 1,2,1,2,2 +Id : 9, {_}: multiply ?44 (inverse (multiply (multiply (inverse (multiply (inverse ?45) ?46)) ?47) (inverse (multiply ?45 ?47)))) =?= inverse (multiply (multiply (inverse (multiply (inverse ?48) (multiply (inverse (inverse ?44)) ?46))) (inverse (multiply (multiply (inverse (multiply (inverse ?49) (multiply (inverse ?48) ?50))) ?51) (inverse (multiply ?49 ?51))))) (inverse ?50)) [51, 50, 49, 48, 47, 46, 45, 44] by Super 2 with 4 at 2,1,1,1,1,2,2 +Id : 7754, {_}: multiply ?63171 (inverse (multiply (multiply (inverse (multiply (inverse ?63172) (multiply (inverse ?63171) (inverse (multiply ?63173 (inverse ?63173)))))) ?63174) (inverse (multiply ?63172 ?63174)))) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63174, 63173, 63172, 63171] by Super 9 with 6832 at 1,1,1,1,3 +Id : 7872, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply (multiply (inverse ?63175) (inverse (multiply (multiply (inverse (multiply (inverse ?63176) (multiply (inverse (inverse ?63175)) ?63177))) ?63178) (inverse (multiply ?63176 ?63178))))) (inverse ?63177)) [63178, 63177, 63176, 63175, 63173] by Demod 7754 with 2 at 2 +Id : 7873, {_}: inverse (multiply ?63173 (inverse ?63173)) =?= inverse (multiply ?63177 (inverse ?63177)) [63177, 63173] by Demod 7872 with 2 at 1,1,3 +Id : 8249, {_}: multiply (inverse (inverse (multiply ?66459 (inverse ?66459)))) (multiply (inverse ?66460) (multiply ?66460 (inverse (multiply ?66461 (inverse ?66461))))) =?= multiply ?66462 (inverse ?66462) [66462, 66461, 66460, 66459] by Super 6832 with 7873 at 1,1,2 +Id : 8282, {_}: multiply ?66459 (inverse ?66459) =?= multiply ?66462 (inverse ?66462) [66462, 66459] by Demod 8249 with 6832 at 2 +Id : 8520, {_}: multiply (multiply (inverse ?67970) (multiply ?67971 (inverse ?67971))) (inverse (multiply ?67972 (inverse ?67972))) =>= inverse ?67970 [67972, 67971, 67970] by Super 3034 with 8282 at 2,1,2 +Id : 380, {_}: multiply ?2743 (inverse (multiply (multiply (inverse ?2744) (multiply ?2744 ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2744, 2743] by Super 2 with 301 at 1,1,2,2 +Id : 8912, {_}: multiply ?70596 (inverse (multiply (multiply (inverse ?70597) (multiply ?70597 (inverse (multiply ?70598 (inverse ?70598))))) (inverse (multiply ?70599 (inverse ?70599))))) =>= inverse (inverse ?70596) [70599, 70598, 70597, 70596] by Super 380 with 8520 at 2,1,2,1,2,2 +Id : 9021, {_}: multiply ?70596 (inverse (inverse (multiply ?70598 (inverse ?70598)))) =>= inverse (inverse ?70596) [70598, 70596] by Demod 8912 with 3034 at 1,2,2 +Id : 9165, {_}: multiply (inverse (inverse ?72171)) (multiply (inverse (multiply (inverse ?72172) (inverse (inverse ?72172)))) (inverse (inverse (multiply ?72173 (inverse ?72173))))) =>= ?72171 [72173, 72172, 72171] by Super 3919 with 9021 at 2,1,1,2,2 +Id : 10068, {_}: multiply (inverse (inverse ?76580)) (inverse (inverse (inverse (multiply (inverse ?76581) (inverse (inverse ?76581)))))) =>= ?76580 [76581, 76580] by Demod 9165 with 9021 at 2,2 +Id : 9180, {_}: multiply ?72234 (inverse ?72234) =?= inverse (inverse (inverse (multiply ?72235 (inverse ?72235)))) [72235, 72234] by Super 8282 with 9021 at 3 +Id : 10100, {_}: multiply (inverse (inverse ?76745)) (multiply ?76746 (inverse ?76746)) =>= ?76745 [76746, 76745] by Super 10068 with 9180 at 2,2 +Id : 10663, {_}: multiply ?82289 (inverse (multiply ?82290 (inverse ?82290))) =>= inverse (inverse ?82289) [82290, 82289] by Super 8520 with 10100 at 1,2 +Id : 10913, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (inverse (multiply (inverse ?83564) (multiply ?83564 (inverse (multiply ?83565 (inverse ?83565)))))))) =>= ?83563 [83565, 83564, 83563] by Super 3919 with 10663 at 2,2 +Id : 10892, {_}: inverse (inverse (multiply (inverse ?24702) (multiply ?24702 ?24703))) =>= ?24703 [24703, 24702] by Demod 3034 with 10663 at 2 +Id : 11238, {_}: multiply (inverse (inverse ?83563)) (inverse (inverse (multiply ?83565 (inverse ?83565)))) =>= ?83563 [83565, 83563] by Demod 10913 with 10892 at 1,2,2 +Id : 11239, {_}: inverse (inverse (inverse (inverse ?83563))) =>= ?83563 [83563] by Demod 11238 with 9021 at 2 +Id : 138, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1160) (multiply (inverse (inverse ?1161)) (multiply (inverse ?1161) ?1162)))) ?1163) (inverse (multiply ?1160 ?1163))) =>= ?1162 [1163, 1162, 1161, 1160] by Super 2 with 5 at 2 +Id : 145, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?1214) (multiply (inverse (inverse ?1215)) (multiply (inverse ?1215) ?1216)))) ?1217) (inverse (multiply ?1214 ?1217))))) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1217, 1216, 1215, 1214, 1213] by Super 138 with 29 at 1,2,2,1,1,1,1,2 +Id : 168, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?1213) (multiply (inverse ?1216) (multiply ?1216 ?1218)))) ?1219) (inverse (multiply ?1213 ?1219))) =>= ?1218 [1219, 1218, 1216, 1213] by Demod 145 with 29 at 1,1,2,1,1,1,1,2 +Id : 777, {_}: multiply (inverse ?5891) (multiply ?5891 (multiply ?5892 (inverse (multiply (multiply (inverse (multiply (inverse ?5893) ?5894)) ?5895) (inverse (multiply ?5893 ?5895)))))) =>= multiply (inverse (inverse ?5892)) ?5894 [5895, 5894, 5893, 5892, 5891] by Super 91 with 5 at 2,2,2 +Id : 813, {_}: multiply (inverse ?6211) (multiply ?6211 (multiply ?6212 ?6213)) =?= multiply (inverse (inverse ?6212)) (multiply (inverse ?6214) (multiply ?6214 ?6213)) [6214, 6213, 6212, 6211] by Super 777 with 168 at 2,2,2,2 +Id : 1401, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11491) (multiply ?11491 (multiply ?11492 ?11493)))) ?11494) (inverse (multiply (inverse ?11492) ?11494))) =>= ?11493 [11494, 11493, 11492, 11491] by Super 168 with 813 at 1,1,1,1,2 +Id : 1427, {_}: inverse (multiply (multiply (inverse (multiply (inverse ?11709) (multiply ?11709 (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710, 11709] by Super 1401 with 301 at 2,2,1,1,1,1,2 +Id : 10889, {_}: multiply (inverse ?52992) (multiply ?52992 (inverse (inverse ?52993))) =>= ?52993 [52993, 52992] by Demod 6773 with 10663 at 2,2,2 +Id : 11440, {_}: multiply (inverse ?85947) (multiply ?85947 ?85948) =>= inverse (inverse ?85948) [85948, 85947] by Super 10889 with 11239 at 2,2,2 +Id : 12070, {_}: inverse (multiply (multiply (inverse (inverse (inverse (multiply (inverse ?11710) (multiply ?11710 ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711, 11710] by Demod 1427 with 11440 at 1,1,1,1,2 +Id : 12071, {_}: inverse (multiply (multiply (inverse (inverse (inverse (inverse (inverse ?11711))))) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12070 with 11440 at 1,1,1,1,1,1,2 +Id : 12086, {_}: inverse (multiply (multiply (inverse ?11711) ?11712) (inverse (multiply (inverse (inverse ?11713)) ?11712))) =>= multiply ?11713 ?11711 [11713, 11712, 11711] by Demod 12071 with 11239 at 1,1,1,2 +Id : 11284, {_}: multiply ?84907 (inverse (multiply (inverse (inverse (inverse ?84908))) ?84908)) =>= inverse (inverse ?84907) [84908, 84907] by Super 10663 with 11239 at 2,1,2,2 +Id : 12456, {_}: inverse (inverse (inverse (multiply (inverse ?89511) ?89512))) =>= multiply (inverse ?89512) ?89511 [89512, 89511] by Super 12086 with 11284 at 1,2 +Id : 12807, {_}: inverse (multiply (inverse ?89891) ?89892) =>= multiply (inverse ?89892) ?89891 [89892, 89891] by Super 11239 with 12456 at 1,2 +Id : 13084, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (inverse (multiply (inverse (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?27)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 6 with 12807 at 1,1,1,2,1,2,1,2,2 +Id : 13085, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (inverse (multiply (inverse ?28) (multiply (inverse ?26) ?30)))) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13084 with 12807 at 1,1,1,1,2,1,2,1,2,2 +Id : 13086, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (inverse (multiply (inverse ?26) ?30)) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13085 with 12807 at 2,1,1,1,1,2,1,2,1,2,2 +Id : 13087, {_}: multiply ?26 (inverse (multiply ?27 (inverse (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31)))))))) =>= ?30 [31, 29, 30, 28, 27, 26] by Demod 13086 with 12807 at 1,2,1,1,1,1,2,1,2,1,2,2 +Id : 12072, {_}: multiply ?2743 (inverse (multiply (inverse (inverse ?2745)) (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745))))) =>= ?2747 [2747, 2746, 2745, 2743] by Demod 380 with 11440 at 1,1,2,2 +Id : 13068, {_}: multiply ?2743 (multiply (inverse (inverse (multiply ?2746 (multiply (multiply (inverse ?2746) (multiply (inverse ?2743) ?2747)) ?2745)))) (inverse ?2745)) =>= ?2747 [2745, 2747, 2746, 2743] by Demod 12072 with 12807 at 2,2 +Id : 358, {_}: multiply (inverse ?2595) (multiply ?2595 (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596, 2595] by Super 28 with 301 at 1,1,2,2,2 +Id : 12055, {_}: inverse (inverse (inverse (multiply (multiply (inverse ?2596) (multiply ?2596 ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597, 2596] by Demod 358 with 11440 at 2 +Id : 12056, {_}: inverse (inverse (inverse (multiply (inverse (inverse ?2597)) (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))))) =>= ?2599 [2599, 2598, 2597] by Demod 12055 with 11440 at 1,1,1,1,2 +Id : 12778, {_}: multiply (inverse (inverse (multiply ?2598 (multiply (multiply (inverse ?2598) ?2599) ?2597)))) (inverse ?2597) =>= ?2599 [2597, 2599, 2598] by Demod 12056 with 12456 at 2 +Id : 13130, {_}: multiply ?2743 (multiply (inverse ?2743) ?2747) =>= ?2747 [2747, 2743] by Demod 13068 with 12778 at 2,2 +Id : 12068, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?2584) (multiply ?2584 ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585, 2584] by Demod 356 with 11440 at 2 +Id : 12069, {_}: inverse (inverse (inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12068 with 11440 at 1,1,1,1,1,1,2 +Id : 12343, {_}: inverse (inverse (inverse (inverse (inverse (multiply (inverse (inverse (inverse ?88665))) ?88666))))) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Super 12069 with 11284 at 1,1,1,2 +Id : 12705, {_}: inverse (multiply (inverse (inverse (inverse ?88665))) ?88666) =>= multiply (inverse (inverse (inverse ?88666))) ?88665 [88666, 88665] by Demod 12343 with 11239 at 2 +Id : 13398, {_}: multiply (inverse ?88666) (inverse (inverse ?88665)) =?= multiply (inverse (inverse (inverse ?88666))) ?88665 [88665, 88666] by Demod 12705 with 12807 at 2 +Id : 13591, {_}: multiply (inverse ?93455) (inverse (inverse (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456))) =>= ?93456 [93456, 93455] by Super 13130 with 13398 at 2 +Id : 13688, {_}: multiply (inverse ?93455) (inverse (multiply (inverse ?93456) (inverse (inverse (inverse ?93455))))) =>= ?93456 [93456, 93455] by Demod 13591 with 12807 at 1,2,2 +Id : 13689, {_}: multiply (inverse ?93455) (multiply (inverse (inverse (inverse (inverse ?93455)))) ?93456) =>= ?93456 [93456, 93455] by Demod 13688 with 12807 at 2,2 +Id : 13690, {_}: multiply (inverse ?93455) (multiply ?93455 ?93456) =>= ?93456 [93456, 93455] by Demod 13689 with 11239 at 1,2,2 +Id : 13691, {_}: inverse (inverse ?93456) =>= ?93456 [93456] by Demod 13690 with 11440 at 2 +Id : 14259, {_}: inverse (multiply ?94937 ?94938) =<= multiply (inverse ?94938) (inverse ?94937) [94938, 94937] by Super 12807 with 13691 at 1,1,2 +Id : 14272, {_}: inverse (multiply ?94994 (inverse ?94995)) =>= multiply ?94995 (inverse ?94994) [94995, 94994] by Super 14259 with 13691 at 1,3 +Id : 15113, {_}: multiply ?26 (multiply (multiply ?28 (inverse (multiply (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31) (inverse (multiply ?29 ?31))))) (inverse ?27)) =>= ?30 [31, 29, 30, 27, 28, 26] by Demod 13087 with 14272 at 2,2 +Id : 15114, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (multiply (inverse ?27) (multiply (multiply (inverse ?30) ?26) ?28)) ?29) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15113 with 14272 at 2,1,2,2 +Id : 14099, {_}: inverse (multiply ?94283 ?94284) =<= multiply (inverse ?94284) (inverse ?94283) [94284, 94283] by Super 12807 with 13691 at 1,1,2 +Id : 15376, {_}: multiply ?101449 (inverse (multiply ?101450 ?101449)) =>= inverse ?101450 [101450, 101449] by Super 13130 with 14099 at 2,2 +Id : 14196, {_}: multiply ?94524 (inverse (multiply ?94525 ?94524)) =>= inverse ?94525 [94525, 94524] by Super 13130 with 14099 at 2,2 +Id : 15386, {_}: multiply (inverse (multiply ?101486 ?101487)) (inverse (inverse ?101486)) =>= inverse ?101487 [101487, 101486] by Super 15376 with 14196 at 1,2,2 +Id : 15574, {_}: inverse (multiply (inverse ?101486) (multiply ?101486 ?101487)) =>= inverse ?101487 [101487, 101486] by Demod 15386 with 14099 at 2 +Id : 16040, {_}: multiply (inverse (multiply ?103094 ?103095)) ?103094 =>= inverse ?103095 [103095, 103094] by Demod 15574 with 12807 at 2 +Id : 12061, {_}: inverse (inverse (inverse (multiply (multiply (inverse (multiply (inverse ?216) ?217)) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 217, 216] by Demod 28 with 11440 at 2 +Id : 13066, {_}: inverse (inverse (inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))))) =>= ?217 [218, 216, 217] by Demod 12061 with 12807 at 1,1,1,1,1,2 +Id : 14035, {_}: inverse (multiply (multiply (multiply (inverse ?217) ?216) ?218) (inverse (multiply ?216 ?218))) =>= ?217 [218, 216, 217] by Demod 13066 with 13691 at 2 +Id : 15129, {_}: multiply (multiply ?216 ?218) (inverse (multiply (multiply (inverse ?217) ?216) ?218)) =>= ?217 [217, 218, 216] by Demod 14035 with 14272 at 2 +Id : 16059, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= inverse (inverse (multiply (multiply (inverse ?103200) ?103201) ?103202)) [103202, 103201, 103200] by Super 16040 with 15129 at 1,1,2 +Id : 16156, {_}: multiply (inverse ?103200) (multiply ?103201 ?103202) =<= multiply (multiply (inverse ?103200) ?103201) ?103202 [103202, 103201, 103200] by Demod 16059 with 13691 at 3 +Id : 17066, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29)) ?31)))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 15114 with 16156 at 1,1,2,2,1,2,2 +Id : 17067, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (multiply (inverse ?30) ?26) ?28) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17066 with 16156 at 1,2,2,1,2,2 +Id : 17068, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (multiply (inverse ?30) (multiply ?26 ?28)) ?29) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17067 with 16156 at 1,1,2,1,2,2,1,2,2 +Id : 17069, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (multiply (inverse ?30) (multiply (multiply ?26 ?28) ?29)) ?31))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17068 with 16156 at 1,2,1,2,2,1,2,2 +Id : 17070, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (inverse (multiply (inverse ?27) (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31)))))) (inverse ?27)) =>= ?30 [30, 27, 31, 29, 28, 26] by Demod 17069 with 16156 at 2,1,2,2,1,2,2 +Id : 17075, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (inverse ?30) (multiply (multiply (multiply ?26 ?28) ?29) ?31))) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17070 with 12807 at 2,2,1,2,2 +Id : 17076, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) ?30) ?27))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17075 with 12807 at 1,2,2,1,2,2 +Id : 17077, {_}: multiply ?26 (multiply (multiply ?28 (multiply (multiply ?29 ?31) (multiply (inverse (multiply (multiply (multiply ?26 ?28) ?29) ?31)) (multiply ?30 ?27)))) (inverse ?27)) =>= ?30 [27, 30, 31, 29, 28, 26] by Demod 17076 with 16156 at 2,2,1,2,2 +Id : 14023, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse (inverse (inverse ?33638))) ?33638 [33638, 33635] by Demod 4117 with 13691 at 1,2 +Id : 14024, {_}: multiply (inverse ?33635) ?33635 =?= multiply (inverse ?33638) ?33638 [33638, 33635] by Demod 14023 with 13691 at 1,3 +Id : 14053, {_}: multiply (inverse ?93965) ?93965 =?= multiply ?93966 (inverse ?93966) [93966, 93965] by Super 14024 with 13691 at 1,3 +Id : 19206, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply (multiply ?108861 ?108862) (multiply ?108863 (inverse ?108863)))) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108863, 108862, 108861, 108860, 108859] by Super 17077 with 14053 at 2,2,1,2,2 +Id : 14021, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= inverse (inverse ?70596) [70598, 70596] by Demod 9021 with 13691 at 2,2 +Id : 14022, {_}: multiply ?70596 (multiply ?70598 (inverse ?70598)) =>= ?70596 [70598, 70596] by Demod 14021 with 13691 at 3 +Id : 19669, {_}: multiply ?108859 (multiply (multiply ?108860 (multiply ?108861 ?108862)) (inverse ?108862)) =>= multiply (multiply ?108859 ?108860) ?108861 [108862, 108861, 108860, 108859] by Demod 19206 with 14022 at 2,1,2,2 +Id : 14028, {_}: inverse (multiply (multiply (inverse (inverse (inverse ?2585))) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 12069 with 13691 at 2 +Id : 14029, {_}: inverse (multiply (multiply (inverse ?2585) ?2586) (inverse (multiply ?2587 ?2586))) =>= multiply ?2587 ?2585 [2587, 2586, 2585] by Demod 14028 with 13691 at 1,1,1,2 +Id : 15108, {_}: multiply (multiply ?2587 ?2586) (inverse (multiply (inverse ?2585) ?2586)) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 14029 with 14272 at 2 +Id : 15134, {_}: multiply (multiply ?2587 ?2586) (multiply (inverse ?2586) ?2585) =>= multiply ?2587 ?2585 [2585, 2586, 2587] by Demod 15108 with 12807 at 2,2 +Id : 15575, {_}: multiply (inverse (multiply ?101486 ?101487)) ?101486 =>= inverse ?101487 [101487, 101486] by Demod 15574 with 12807 at 2 +Id : 16032, {_}: multiply (multiply ?103052 (multiply ?103053 ?103054)) (inverse ?103054) =>= multiply ?103052 ?103053 [103054, 103053, 103052] by Super 15134 with 15575 at 2,2 +Id : 32860, {_}: multiply ?108859 (multiply ?108860 ?108861) =?= multiply (multiply ?108859 ?108860) ?108861 [108861, 108860, 108859] by Demod 19669 with 16032 at 2,2 +Id : 33337, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 32860 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP429-1.p +23653: solved GRP429-1.p in 11.596724 using nrkbo +23653: status Unsatisfiable for GRP429-1.p +NO CLASH, using fixed ground order +23669: Facts: +23669: Id : 2, {_}: + inverse + (multiply ?2 + (multiply ?3 + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?5 (multiply ?2 ?3)))))) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23669: Goal: +23669: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23669: Order: +23669: nrkbo +23669: Leaf order: +23669: a3 2 0 2 1,1,2 +23669: b3 2 0 2 2,1,2 +23669: c3 2 0 2 2,2 +23669: inverse 3 1 0 +23669: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23670: Facts: +23670: Id : 2, {_}: + inverse + (multiply ?2 + (multiply ?3 + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?5 (multiply ?2 ?3)))))) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23670: Goal: +23670: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23670: Order: +23670: kbo +23670: Leaf order: +23670: a3 2 0 2 1,1,2 +23670: b3 2 0 2 2,1,2 +23670: c3 2 0 2 2,2 +23670: inverse 3 1 0 +23670: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +23671: Facts: +23671: Id : 2, {_}: + inverse + (multiply ?2 + (multiply ?3 + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?5 (multiply ?2 ?3)))))) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23671: Goal: +23671: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23671: Order: +23671: lpo +23671: Leaf order: +23671: a3 2 0 2 1,1,2 +23671: b3 2 0 2 2,1,2 +23671: c3 2 0 2 2,2 +23671: inverse 3 1 0 +23671: multiply 10 2 4 0,2 +Statistics : +Max weight : 52 +Found proof, 56.465480s +% SZS status Unsatisfiable for GRP444-1.p +% SZS output start CNFRefutation for GRP444-1.p +Id : 3, {_}: inverse (multiply ?7 (multiply ?8 (multiply (multiply ?9 (inverse ?9)) (inverse (multiply ?10 (multiply ?7 ?8)))))) =>= ?10 [10, 9, 8, 7] by single_axiom ?7 ?8 ?9 ?10 +Id : 2, {_}: inverse (multiply ?2 (multiply ?3 (multiply (multiply ?4 (inverse ?4)) (inverse (multiply ?5 (multiply ?2 ?3)))))) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 5, {_}: inverse (multiply ?18 (multiply ?19 (multiply (multiply (multiply ?20 (multiply ?21 (multiply (multiply ?22 (inverse ?22)) (inverse (multiply ?23 (multiply ?20 ?21)))))) ?23) (inverse (multiply ?24 (multiply ?18 ?19)))))) =>= ?24 [24, 23, 22, 21, 20, 19, 18] by Super 3 with 2 at 2,1,2,2,1,2 +Id : 4, {_}: inverse (multiply ?12 (multiply (multiply (multiply ?13 (inverse ?13)) (inverse (multiply ?14 (multiply ?15 ?12)))) (multiply (multiply ?16 (inverse ?16)) ?14))) =>= ?15 [16, 15, 14, 13, 12] by Super 3 with 2 at 2,2,2,1,2 +Id : 7, {_}: inverse (multiply (multiply (multiply ?28 (inverse ?28)) (inverse (multiply ?29 (multiply ?30 ?31)))) (multiply (multiply (multiply ?32 (inverse ?32)) ?29) (multiply (multiply ?33 (inverse ?33)) ?30))) =>= ?31 [33, 32, 31, 30, 29, 28] by Super 2 with 4 at 2,2,2,1,2 +Id : 9, {_}: inverse (multiply ?44 (multiply (multiply (multiply ?45 (inverse ?45)) (inverse (multiply ?46 (multiply ?47 ?44)))) (multiply (multiply ?48 (inverse ?48)) ?46))) =>= ?47 [48, 47, 46, 45, 44] by Super 3 with 2 at 2,2,2,1,2 +Id : 13, {_}: inverse (multiply (multiply (multiply ?76 (inverse ?76)) ?77) (multiply (multiply (multiply ?78 (inverse ?78)) ?79) (multiply (multiply ?80 (inverse ?80)) ?81))) =?= multiply (multiply ?82 (inverse ?82)) (inverse (multiply ?77 (multiply ?79 ?81))) [82, 81, 80, 79, 78, 77, 76] by Super 9 with 4 at 2,1,2,1,2 +Id : 178, {_}: multiply (multiply ?1864 (inverse ?1864)) (inverse (multiply (inverse (multiply ?1865 (multiply ?1866 ?1867))) (multiply ?1865 ?1866))) =>= ?1867 [1867, 1866, 1865, 1864] by Super 7 with 13 at 2 +Id : 184, {_}: multiply (multiply ?1909 (inverse ?1909)) (inverse (multiply ?1910 (multiply ?1911 (multiply (multiply ?1912 (inverse ?1912)) (inverse (multiply ?1913 (multiply ?1910 ?1911))))))) =?= multiply (multiply ?1914 (inverse ?1914)) ?1913 [1914, 1913, 1912, 1911, 1910, 1909] by Super 178 with 4 at 1,1,2,2 +Id : 205, {_}: multiply (multiply ?1909 (inverse ?1909)) ?1913 =?= multiply (multiply ?1914 (inverse ?1914)) ?1913 [1914, 1913, 1909] by Demod 184 with 2 at 2,2 +Id : 277, {_}: inverse (multiply ?2556 (multiply ?2557 (multiply (multiply (multiply ?2558 (multiply ?2559 (multiply (multiply ?2560 (inverse ?2560)) (inverse (multiply ?2561 (multiply ?2558 ?2559)))))) ?2561) (inverse (multiply (multiply ?2562 (inverse ?2562)) (multiply ?2556 ?2557)))))) =?= multiply ?2563 (inverse ?2563) [2563, 2562, 2561, 2560, 2559, 2558, 2557, 2556] by Super 5 with 205 at 1,2,2,2,1,2 +Id : 348, {_}: multiply ?2562 (inverse ?2562) =?= multiply ?2563 (inverse ?2563) [2563, 2562] by Demod 277 with 5 at 2 +Id : 1129, {_}: inverse (multiply ?9239 (multiply (inverse ?9239) (multiply (multiply ?9240 (inverse ?9240)) (inverse (multiply ?9241 (multiply ?9242 (inverse ?9242))))))) =>= ?9241 [9242, 9241, 9240, 9239] by Super 2 with 348 at 2,1,2,2,2,1,2 +Id : 86, {_}: multiply (multiply ?817 (inverse ?817)) (inverse (multiply (inverse (multiply ?818 (multiply ?819 ?820))) (multiply ?818 ?819))) =>= ?820 [820, 819, 818, 817] by Super 7 with 13 at 2 +Id : 1168, {_}: inverse (multiply ?9548 (multiply (inverse ?9548) ?9549)) =?= inverse (multiply ?9550 (multiply (inverse ?9550) ?9549)) [9550, 9549, 9548] by Super 1129 with 86 at 2,2,1,2 +Id : 3826, {_}: inverse (multiply (inverse ?28880) (multiply ?28881 (multiply (multiply ?28882 (inverse ?28882)) (inverse (multiply ?28883 (multiply (inverse ?28883) ?28881)))))) =>= ?28880 [28883, 28882, 28881, 28880] by Super 2 with 1168 at 2,2,2,1,2 +Id : 529, {_}: multiply (multiply ?4511 (inverse ?4511)) (inverse (multiply (inverse (multiply ?4512 (multiply (inverse ?4512) ?4513))) (multiply ?4514 (inverse ?4514)))) =>= ?4513 [4514, 4513, 4512, 4511] by Super 86 with 348 at 2,1,2,2 +Id : 3910, {_}: inverse (multiply (inverse ?29502) (multiply (inverse (inverse (inverse (multiply ?29503 (multiply (inverse ?29503) ?29504))))) ?29504)) =>= ?29502 [29504, 29503, 29502] by Super 3826 with 529 at 2,2,1,2 +Id : 5137, {_}: inverse (multiply (inverse (inverse (inverse (multiply ?39280 (multiply (inverse ?39280) ?39281))))) (multiply ?39281 (multiply (multiply ?39282 (inverse ?39282)) ?39283))) =>= inverse ?39283 [39283, 39282, 39281, 39280] by Super 2 with 3910 at 2,2,2,1,2 +Id : 17340, {_}: inverse (inverse (multiply ?127629 (multiply (inverse (inverse (inverse (multiply ?127630 (multiply (inverse ?127630) ?127631))))) ?127631))) =>= ?127629 [127631, 127630, 127629] by Super 2 with 5137 at 2 +Id : 5128, {_}: multiply (multiply ?39206 (inverse ?39206)) (multiply (inverse (inverse (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))))) (multiply ?39208 ?39209)) =>= ?39209 [39209, 39208, 39207, 39206] by Super 86 with 3910 at 2,2 +Id : 3928, {_}: inverse (multiply (inverse (multiply ?29660 (multiply (inverse ?29660) ?29661))) (multiply ?29662 (multiply (multiply ?29663 (inverse ?29663)) (inverse (multiply ?29664 (multiply (inverse ?29664) ?29662)))))) =?= multiply ?29665 (multiply (inverse ?29665) ?29661) [29665, 29664, 29663, 29662, 29661, 29660] by Super 3826 with 1168 at 1,1,2 +Id : 1246, {_}: inverse (multiply (inverse ?10029) (multiply ?10030 (multiply (multiply ?10031 (inverse ?10031)) (inverse (multiply ?10032 (multiply (inverse ?10032) ?10030)))))) =>= ?10029 [10032, 10031, 10030, 10029] by Super 2 with 1168 at 2,2,2,1,2 +Id : 3958, {_}: multiply ?29660 (multiply (inverse ?29660) ?29661) =?= multiply ?29665 (multiply (inverse ?29665) ?29661) [29665, 29661, 29660] by Demod 3928 with 1246 at 2 +Id : 531, {_}: multiply (multiply ?4521 (inverse ?4521)) (inverse (multiply (inverse (multiply ?4522 (multiply ?4523 (inverse ?4523)))) (multiply ?4522 ?4524))) =>= inverse ?4524 [4524, 4523, 4522, 4521] by Super 86 with 348 at 2,1,1,1,2,2 +Id : 737, {_}: multiply (multiply ?5774 (inverse ?5774)) (inverse (multiply (inverse (multiply ?5775 (multiply ?5776 (inverse ?5776)))) (multiply ?5775 ?5777))) =>= inverse ?5777 [5777, 5776, 5775, 5774] by Super 86 with 348 at 2,1,1,1,2,2 +Id : 1911, {_}: multiply (multiply ?15350 (inverse ?15350)) (inverse (multiply (inverse (multiply ?15351 (multiply ?15352 (inverse ?15352)))) (multiply ?15353 (inverse ?15353)))) =>= inverse (inverse ?15351) [15353, 15352, 15351, 15350] by Super 737 with 348 at 2,1,2,2 +Id : 1956, {_}: multiply (multiply ?15717 (inverse ?15717)) (inverse (multiply (inverse (multiply (multiply ?15718 (inverse ?15718)) (multiply ?15719 (inverse ?15719)))) (multiply ?15720 (inverse ?15720)))) =?= inverse (inverse (multiply ?15721 (inverse ?15721))) [15721, 15720, 15719, 15718, 15717] by Super 1911 with 205 at 1,1,1,2,2 +Id : 740, {_}: multiply (multiply ?5792 (inverse ?5792)) (inverse (multiply (inverse (multiply ?5793 (multiply ?5794 (inverse ?5794)))) (multiply ?5795 (inverse ?5795)))) =>= inverse (inverse ?5793) [5795, 5794, 5793, 5792] by Super 737 with 348 at 2,1,2,2 +Id : 2009, {_}: inverse (inverse (multiply ?15718 (inverse ?15718))) =?= inverse (inverse (multiply ?15721 (inverse ?15721))) [15721, 15718] by Demod 1956 with 740 at 2 +Id : 2083, {_}: multiply ?16427 (inverse ?16427) =?= multiply (inverse (multiply ?16428 (inverse ?16428))) (inverse (inverse (multiply ?16429 (inverse ?16429)))) [16429, 16428, 16427] by Super 348 with 2009 at 2,3 +Id : 2187, {_}: multiply (multiply ?17062 (inverse ?17062)) (inverse (multiply (inverse (multiply (inverse (multiply ?17063 (inverse ?17063))) (multiply ?17064 (inverse ?17064)))) (multiply ?17065 (inverse ?17065)))) =?= inverse (inverse (inverse (multiply ?17066 (inverse ?17066)))) [17066, 17065, 17064, 17063, 17062] by Super 531 with 2083 at 2,1,2,2 +Id : 2437, {_}: inverse (inverse (inverse (multiply ?17063 (inverse ?17063)))) =?= inverse (inverse (inverse (multiply ?17066 (inverse ?17066)))) [17066, 17063] by Demod 2187 with 740 at 2 +Id : 2507, {_}: multiply ?19079 (inverse ?19079) =?= multiply (inverse (inverse (multiply ?19080 (inverse ?19080)))) (inverse (inverse (inverse (multiply ?19081 (inverse ?19081))))) [19081, 19080, 19079] by Super 348 with 2437 at 2,3 +Id : 5155, {_}: multiply (multiply ?39417 (inverse ?39417)) (multiply (inverse (inverse (inverse (multiply ?39418 (multiply (inverse ?39418) ?39419))))) (multiply ?39420 (inverse ?39420))) =>= inverse ?39419 [39420, 39419, 39418, 39417] by Super 531 with 3910 at 2,2 +Id : 21348, {_}: inverse (inverse (inverse (multiply ?158881 (inverse ?158881)))) =?= multiply ?158882 (inverse ?158882) [158882, 158881] by Super 17340 with 5155 at 1,1,2 +Id : 21903, {_}: multiply ?162370 (inverse ?162370) =?= multiply (inverse (inverse (multiply ?162371 (inverse ?162371)))) (multiply ?162372 (inverse ?162372)) [162372, 162371, 162370] by Super 2507 with 21348 at 2,3 +Id : 27319, {_}: multiply ?194055 (multiply (inverse ?194055) (inverse (inverse (inverse (inverse (multiply ?194056 (inverse ?194056))))))) =?= multiply ?194057 (inverse ?194057) [194057, 194056, 194055] by Super 3958 with 21903 at 3 +Id : 38543, {_}: multiply (multiply ?266891 (inverse ?266891)) (multiply (inverse (inverse (inverse (multiply ?266892 (multiply (inverse ?266892) ?266893))))) (multiply ?266894 (inverse ?266894))) =?= multiply (inverse ?266893) (inverse (inverse (inverse (inverse (multiply ?266895 (inverse ?266895)))))) [266895, 266894, 266893, 266892, 266891] by Super 5128 with 27319 at 2,2,2 +Id : 39135, {_}: inverse ?270165 =<= multiply (inverse ?270165) (inverse (inverse (inverse (inverse (multiply ?270166 (inverse ?270166)))))) [270166, 270165] by Demod 38543 with 5155 at 2 +Id : 39578, {_}: inverse ?271815 =<= multiply (inverse ?271815) (inverse (multiply ?271816 (inverse ?271816))) [271816, 271815] by Super 39135 with 21348 at 1,2,3 +Id : 39704, {_}: inverse (multiply ?272432 (multiply ?272433 (multiply (multiply ?272434 (inverse ?272434)) (inverse (multiply ?272435 (multiply ?272432 ?272433)))))) =?= multiply ?272435 (inverse (multiply ?272436 (inverse ?272436))) [272436, 272435, 272434, 272433, 272432] by Super 39578 with 2 at 1,3 +Id : 39842, {_}: ?272435 =<= multiply ?272435 (inverse (multiply ?272436 (inverse ?272436))) [272436, 272435] by Demod 39704 with 2 at 2 +Id : 40136, {_}: inverse (inverse (multiply ?274147 (multiply (inverse (inverse (inverse (multiply ?274148 (inverse ?274148))))) (inverse (multiply ?274149 (inverse ?274149)))))) =>= ?274147 [274149, 274148, 274147] by Super 17340 with 39842 at 2,1,1,1,1,2,1,1,2 +Id : 42233, {_}: inverse (inverse (multiply ?290970 (inverse (inverse (inverse (multiply ?290971 (inverse ?290971))))))) =>= ?290970 [290971, 290970] by Demod 40136 with 39842 at 2,1,1,2 +Id : 42325, {_}: inverse (inverse (multiply ?291465 (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))))))) =>= ?291465 [291466, 291465] by Super 42233 with 21348 at 1,1,1,2,1,1,2 +Id : 3911, {_}: inverse (multiply (inverse ?29506) (multiply (inverse (inverse (inverse (multiply ?29507 (multiply ?29508 (inverse ?29508)))))) (inverse (inverse ?29507)))) =>= ?29506 [29508, 29507, 29506] by Super 3826 with 740 at 2,2,1,2 +Id : 42355, {_}: inverse (inverse (multiply ?291566 (multiply ?291567 (inverse ?291567)))) =>= ?291566 [291567, 291566] by Super 42233 with 21348 at 2,1,1,2 +Id : 42465, {_}: inverse (multiply (inverse ?29506) (multiply (inverse ?29507) (inverse (inverse ?29507)))) =>= ?29506 [29507, 29506] by Demod 3911 with 42355 at 1,1,2,1,2 +Id : 42659, {_}: inverse (multiply (inverse ?292844) (multiply (inverse (inverse (multiply ?292845 (multiply ?292846 (inverse ?292846))))) (inverse ?292845))) =>= ?292844 [292846, 292845, 292844] by Super 42465 with 42355 at 1,2,2,1,2 +Id : 42797, {_}: inverse (multiply (inverse ?292844) (multiply ?292845 (inverse ?292845))) =>= ?292844 [292845, 292844] by Demod 42659 with 42355 at 1,2,1,2 +Id : 42874, {_}: multiply (multiply ?5792 (inverse ?5792)) (multiply ?5793 (multiply ?5794 (inverse ?5794))) =>= inverse (inverse ?5793) [5794, 5793, 5792] by Demod 740 with 42797 at 2,2 +Id : 46254, {_}: ?309013 =<= multiply ?309013 (inverse (multiply (inverse (multiply ?309014 (multiply ?309015 (inverse ?309015)))) ?309014)) [309015, 309014, 309013] by Super 39842 with 42355 at 2,1,2,3 +Id : 46402, {_}: ?309842 =<= multiply ?309842 (multiply (multiply ?309843 (inverse ?309843)) (multiply ?309844 (inverse ?309844))) [309844, 309843, 309842] by Super 46254 with 42797 at 2,3 +Id : 46563, {_}: multiply ?309963 (inverse ?309963) =?= inverse (inverse (multiply ?309964 (inverse ?309964))) [309964, 309963] by Super 42874 with 46402 at 2 +Id : 47597, {_}: inverse (inverse (multiply ?315584 (inverse (inverse (inverse (inverse (multiply ?315585 (inverse ?315585)))))))) =>= ?315584 [315585, 315584] by Super 42325 with 46563 at 1,1,1,1,2,1,1,2 +Id : 39281, {_}: inverse (multiply ?270847 (multiply ?270848 (multiply (multiply ?270849 (inverse ?270849)) (inverse (multiply ?270850 (multiply ?270847 ?270848)))))) =?= multiply ?270850 (inverse (inverse (inverse (inverse (multiply ?270851 (inverse ?270851)))))) [270851, 270850, 270849, 270848, 270847] by Super 39135 with 2 at 1,3 +Id : 39433, {_}: ?270850 =<= multiply ?270850 (inverse (inverse (inverse (inverse (multiply ?270851 (inverse ?270851)))))) [270851, 270850] by Demod 39281 with 2 at 2 +Id : 47849, {_}: inverse (inverse ?315584) =>= ?315584 [315584] by Demod 47597 with 39433 at 1,1,2 +Id : 48100, {_}: multiply (multiply ?5792 (inverse ?5792)) (multiply ?5793 (multiply ?5794 (inverse ?5794))) =>= ?5793 [5794, 5793, 5792] by Demod 42874 with 47849 at 3 +Id : 48103, {_}: multiply ?291465 (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))))) =>= ?291465 [291466, 291465] by Demod 42325 with 47849 at 2 +Id : 48104, {_}: multiply ?291465 (inverse (inverse (inverse (inverse (multiply ?291466 (inverse ?291466)))))) =>= ?291465 [291466, 291465] by Demod 48103 with 47849 at 2,2 +Id : 48105, {_}: multiply ?291465 (inverse (inverse (multiply ?291466 (inverse ?291466)))) =>= ?291465 [291466, 291465] by Demod 48104 with 47849 at 2,2 +Id : 48106, {_}: multiply ?291465 (multiply ?291466 (inverse ?291466)) =>= ?291465 [291466, 291465] by Demod 48105 with 47849 at 2,2 +Id : 48126, {_}: multiply (multiply ?5792 (inverse ?5792)) ?5793 =>= ?5793 [5793, 5792] by Demod 48100 with 48106 at 2,2 +Id : 48146, {_}: inverse (multiply ?2 (multiply ?3 (inverse (multiply ?5 (multiply ?2 ?3))))) =>= ?5 [5, 3, 2] by Demod 2 with 48126 at 2,2,1,2 +Id : 48243, {_}: multiply (multiply (inverse ?316807) ?316807) ?316808 =>= ?316808 [316808, 316807] by Super 48126 with 47849 at 2,1,2 +Id : 48369, {_}: inverse (multiply (multiply (inverse ?317633) ?317633) (multiply ?317634 (inverse (multiply ?317635 ?317634)))) =>= ?317635 [317635, 317634, 317633] by Super 48146 with 48243 at 2,1,2,2,1,2 +Id : 48458, {_}: inverse (multiply ?317634 (inverse (multiply ?317635 ?317634))) =>= ?317635 [317635, 317634] by Demod 48369 with 48243 at 1,2 +Id : 49027, {_}: inverse ?319864 =<= multiply ?319865 (inverse (multiply ?319864 ?319865)) [319865, 319864] by Super 47849 with 48458 at 1,2 +Id : 48054, {_}: multiply (multiply ?39206 (inverse ?39206)) (multiply (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))) (multiply ?39208 ?39209)) =>= ?39209 [39209, 39208, 39207, 39206] by Demod 5128 with 47849 at 1,2,2 +Id : 48214, {_}: multiply (inverse (multiply ?39207 (multiply (inverse ?39207) ?39208))) (multiply ?39208 ?39209) =>= ?39209 [39209, 39208, 39207] by Demod 48054 with 48126 at 2 +Id : 42875, {_}: multiply (multiply ?4511 (inverse ?4511)) (multiply ?4512 (multiply (inverse ?4512) ?4513)) =>= ?4513 [4513, 4512, 4511] by Demod 529 with 42797 at 2,2 +Id : 48128, {_}: multiply ?4512 (multiply (inverse ?4512) ?4513) =>= ?4513 [4513, 4512] by Demod 42875 with 48126 at 2 +Id : 48215, {_}: multiply (inverse ?39208) (multiply ?39208 ?39209) =>= ?39209 [39209, 39208] by Demod 48214 with 48128 at 1,1,2 +Id : 49034, {_}: inverse (inverse ?319885) =<= multiply (multiply ?319885 ?319886) (inverse ?319886) [319886, 319885] by Super 49027 with 48215 at 1,2,3 +Id : 49824, {_}: ?323338 =<= multiply (multiply ?323338 ?323339) (inverse ?323339) [323339, 323338] by Demod 49034 with 47849 at 2 +Id : 48152, {_}: inverse (multiply (inverse (multiply ?818 (multiply ?819 ?820))) (multiply ?818 ?819)) =>= ?820 [820, 819, 818] by Demod 86 with 48126 at 2 +Id : 48896, {_}: inverse ?319286 =<= multiply ?319287 (inverse (multiply ?319286 ?319287)) [319287, 319286] by Super 47849 with 48458 at 1,2 +Id : 49169, {_}: multiply (inverse ?320479) (inverse ?320480) =>= inverse (multiply ?320480 ?320479) [320480, 320479] by Super 48215 with 48896 at 2,2 +Id : 49171, {_}: multiply (inverse ?320486) ?320487 =<= inverse (multiply (inverse ?320487) ?320486) [320487, 320486] by Super 49169 with 47849 at 2,2 +Id : 49369, {_}: multiply (inverse (multiply ?818 ?819)) (multiply ?818 (multiply ?819 ?820)) =>= ?820 [820, 819, 818] by Demod 48152 with 49171 at 2 +Id : 49850, {_}: inverse (multiply ?323494 ?323495) =<= multiply ?323496 (inverse (multiply ?323494 (multiply ?323495 ?323496))) [323496, 323495, 323494] by Super 49824 with 49369 at 1,3 +Id : 49041, {_}: inverse ?319906 =<= multiply (inverse (multiply ?319907 ?319906)) (inverse (inverse ?319907)) [319907, 319906] by Super 49027 with 48896 at 1,2,3 +Id : 49999, {_}: inverse ?323996 =<= multiply (inverse (multiply ?323997 ?323996)) ?323997 [323997, 323996] by Demod 49041 with 47849 at 2,3 +Id : 50016, {_}: inverse (multiply ?324063 (inverse (multiply ?324064 (multiply ?324065 ?324063)))) =>= multiply ?324064 ?324065 [324065, 324064, 324063] by Super 49999 with 48146 at 1,3 +Id : 49025, {_}: multiply ?319858 (inverse ?319859) =<= inverse (multiply ?319859 (inverse ?319858)) [319859, 319858] by Super 48128 with 48896 at 2,2 +Id : 53578, {_}: multiply (multiply ?332164 (multiply ?332165 ?332166)) (inverse ?332166) =>= multiply ?332164 ?332165 [332166, 332165, 332164] by Demod 50016 with 49025 at 2 +Id : 49088, {_}: inverse ?319906 =<= multiply (inverse (multiply ?319907 ?319906)) ?319907 [319907, 319906] by Demod 49041 with 47849 at 2,3 +Id : 53621, {_}: multiply (inverse ?332348) (inverse ?332349) =<= multiply (inverse (multiply (multiply ?332350 ?332349) ?332348)) ?332350 [332350, 332349, 332348] by Super 53578 with 49088 at 1,2 +Id : 48971, {_}: multiply (inverse ?319476) (inverse ?319477) =>= inverse (multiply ?319477 ?319476) [319477, 319476] by Super 48215 with 48896 at 2,2 +Id : 53698, {_}: inverse (multiply ?332349 ?332348) =<= multiply (inverse (multiply (multiply ?332350 ?332349) ?332348)) ?332350 [332350, 332348, 332349] by Demod 53621 with 48971 at 2 +Id : 55617, {_}: inverse (multiply (inverse (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719)) ?335716) =>= multiply ?335717 (inverse (inverse (multiply ?335718 ?335719))) [335719, 335718, 335717, 335716] by Super 49850 with 53698 at 1,2,3 +Id : 55728, {_}: multiply (inverse ?335716) (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719) =>= multiply ?335717 (inverse (inverse (multiply ?335718 ?335719))) [335719, 335718, 335717, 335716] by Demod 55617 with 49171 at 2 +Id : 55729, {_}: multiply (inverse ?335716) (multiply (multiply (multiply ?335716 ?335717) ?335718) ?335719) =>= multiply ?335717 (multiply ?335718 ?335719) [335719, 335718, 335717, 335716] by Demod 55728 with 47849 at 2,3 +Id : 53403, {_}: inverse (multiply ?331872 ?331873) =<= multiply ?331874 (inverse (multiply ?331872 (multiply ?331873 ?331874))) [331874, 331873, 331872] by Super 49824 with 49369 at 1,3 +Id : 49375, {_}: multiply (inverse ?321009) (multiply (inverse ?321010) ?321011) =>= inverse (multiply (multiply (inverse ?321011) ?321010) ?321009) [321011, 321010, 321009] by Super 48971 with 49171 at 2,2 +Id : 53436, {_}: inverse (multiply (inverse ?332006) (inverse ?332007)) =<= multiply ?332008 (inverse (inverse (multiply (multiply (inverse ?332008) ?332007) ?332006))) [332008, 332007, 332006] by Super 53403 with 49375 at 1,2,3 +Id : 53542, {_}: multiply ?332007 (inverse (inverse ?332006)) =<= multiply ?332008 (inverse (inverse (multiply (multiply (inverse ?332008) ?332007) ?332006))) [332008, 332006, 332007] by Demod 53436 with 49025 at 2 +Id : 53543, {_}: multiply ?332007 (inverse (inverse ?332006)) =<= multiply ?332008 (multiply (multiply (inverse ?332008) ?332007) ?332006) [332008, 332006, 332007] by Demod 53542 with 47849 at 2,3 +Id : 53544, {_}: multiply ?332007 ?332006 =<= multiply ?332008 (multiply (multiply (inverse ?332008) ?332007) ?332006) [332008, 332006, 332007] by Demod 53543 with 47849 at 2,2 +Id : 54357, {_}: multiply (inverse ?333550) (multiply ?333551 ?333552) =<= multiply (multiply (inverse ?333550) ?333551) ?333552 [333552, 333551, 333550] by Super 48215 with 53544 at 2,2 +Id : 53440, {_}: inverse (multiply (inverse (multiply (multiply ?332022 ?332023) ?332024)) ?332022) =>= multiply ?332023 (inverse (inverse ?332024)) [332024, 332023, 332022] by Super 53403 with 49088 at 1,2,3 +Id : 53553, {_}: multiply (inverse ?332022) (multiply (multiply ?332022 ?332023) ?332024) =>= multiply ?332023 (inverse (inverse ?332024)) [332024, 332023, 332022] by Demod 53440 with 49171 at 2 +Id : 53554, {_}: multiply (inverse ?332022) (multiply (multiply ?332022 ?332023) ?332024) =>= multiply ?332023 ?332024 [332024, 332023, 332022] by Demod 53553 with 47849 at 2,3 +Id : 54857, {_}: multiply (inverse ?334428) (multiply (multiply (multiply ?334428 ?334429) ?334430) ?334431) =>= multiply (multiply ?334429 ?334430) ?334431 [334431, 334430, 334429, 334428] by Super 54357 with 53554 at 1,3 +Id : 81835, {_}: multiply (multiply ?335717 ?335718) ?335719 =?= multiply ?335717 (multiply ?335718 ?335719) [335719, 335718, 335717] by Demod 55729 with 54857 at 2 +Id : 82672, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 81835 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP444-1.p +23669: solved GRP444-1.p in 49.195074 using nrkbo +23669: status Unsatisfiable for GRP444-1.p +NO CLASH, using fixed ground order +23734: Facts: +23734: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23734: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +23734: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +23734: Goal: +23734: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23734: Order: +23734: nrkbo +23734: Leaf order: +23734: b2 2 0 2 1,1,1,2 +23734: a2 2 0 2 2,2 +23734: inverse 2 1 1 0,1,1,2 +23734: multiply 3 2 2 0,2 +23734: divide 13 2 0 +NO CLASH, using fixed ground order +23735: Facts: +23735: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23735: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +23735: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +23735: Goal: +23735: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23735: Order: +23735: kbo +23735: Leaf order: +23735: b2 2 0 2 1,1,1,2 +23735: a2 2 0 2 2,2 +23735: inverse 2 1 1 0,1,1,2 +23735: multiply 3 2 2 0,2 +23735: divide 13 2 0 +NO CLASH, using fixed ground order +23736: Facts: +23736: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +23736: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +23736: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +23736: Goal: +23736: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23736: Order: +23736: lpo +23736: Leaf order: +23736: b2 2 0 2 1,1,1,2 +23736: a2 2 0 2 2,2 +23736: inverse 2 1 1 0,1,1,2 +23736: multiply 3 2 2 0,2 +23736: divide 13 2 0 +Statistics : +Max weight : 38 +Found proof, 0.373646s +% SZS status Unsatisfiable for GRP452-1.p +% SZS output start CNFRefutation for GRP452-1.p +Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15 +Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91 +Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11 +Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8 +Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3 +Id : 41, {_}: multiply (divide ?104 ?104) ?105 =>= inverse (inverse ?105) [105, 104] by Super 29 with 4 at 3 +Id : 43, {_}: multiply (multiply (inverse ?110) ?110) ?111 =>= inverse (inverse ?111) [111, 110] by Super 41 with 29 at 1,2 +Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2 +Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3 +Id : 205, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2 +Id : 206, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 205 with 4 at 1,2,1,1,1,2 +Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3 +Id : 207, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 206 with 36 at 2,1,1,1,2 +Id : 208, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 207 with 29 at 1,1,1,2 +Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2 +Id : 61, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2 +Id : 62, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 61 with 4 at 3 +Id : 63, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 62 with 4 at 1,2,2,1,3 +Id : 68, {_}: divide (inverse (divide ?170 ?171)) ?172 =<= inverse (divide ?173 (divide ?171 (divide (inverse ?173) (divide (inverse ?170) ?172)))) [173, 172, 171, 170] by Demod 63 with 4 at 1,2,2,2,1,3 +Id : 75, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (divide (divide ?216 ?216) (divide ?214 (inverse (divide (inverse ?213) ?215)))) [216, 215, 214, 213] by Super 68 with 36 at 2,2,1,3 +Id : 85, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (inverse (divide ?214 (inverse (divide (inverse ?213) ?215)))) [215, 214, 213] by Demod 75 with 4 at 1,3 +Id : 329, {_}: divide (inverse (divide ?884 ?885)) ?886 =<= inverse (inverse (multiply ?885 (divide (inverse ?884) ?886))) [886, 885, 884] by Demod 85 with 29 at 1,1,3 +Id : 336, {_}: divide (inverse (divide (divide ?919 ?919) ?920)) ?921 =>= inverse (inverse (multiply ?920 (inverse ?921))) [921, 920, 919] by Super 329 with 36 at 2,1,1,3 +Id : 348, {_}: divide (inverse (inverse ?920)) ?921 =<= inverse (inverse (multiply ?920 (inverse ?921))) [921, 920] by Demod 336 with 4 at 1,1,2 +Id : 435, {_}: divide (inverse (inverse ?1126)) ?1127 =<= inverse (inverse (multiply ?1126 (inverse ?1127))) [1127, 1126] by Demod 336 with 4 at 1,1,2 +Id : 439, {_}: divide (inverse (inverse (divide ?1144 ?1144))) ?1145 =>= inverse (inverse (inverse (inverse (inverse ?1145)))) [1145, 1144] by Super 435 with 32 at 1,1,3 +Id : 46, {_}: inverse ?115 =<= divide (inverse (inverse (divide ?116 ?116))) ?115 [116, 115] by Super 4 with 36 at 1,3 +Id : 452, {_}: inverse ?1145 =<= inverse (inverse (inverse (inverse (inverse ?1145)))) [1145] by Demod 439 with 46 at 2 +Id : 461, {_}: multiply ?1187 (inverse (inverse (inverse (inverse ?1188)))) =>= divide ?1187 (inverse ?1188) [1188, 1187] by Super 29 with 452 at 2,3 +Id : 480, {_}: multiply ?1187 (inverse (inverse (inverse (inverse ?1188)))) =>= multiply ?1187 ?1188 [1188, 1187] by Demod 461 with 29 at 3 +Id : 490, {_}: divide (inverse (inverse ?1237)) (inverse (inverse (inverse ?1238))) =>= inverse (inverse (multiply ?1237 ?1238)) [1238, 1237] by Super 348 with 480 at 1,1,3 +Id : 543, {_}: multiply (inverse (inverse ?1237)) (inverse (inverse ?1238)) =>= inverse (inverse (multiply ?1237 ?1238)) [1238, 1237] by Demod 490 with 29 at 2 +Id : 564, {_}: divide (inverse (inverse (inverse (inverse ?1361)))) (inverse ?1362) =>= inverse (inverse (inverse (inverse (multiply ?1361 ?1362)))) [1362, 1361] by Super 348 with 543 at 1,1,3 +Id : 586, {_}: multiply (inverse (inverse (inverse (inverse ?1361)))) ?1362 =>= inverse (inverse (inverse (inverse (multiply ?1361 ?1362)))) [1362, 1361] by Demod 564 with 29 at 2 +Id : 608, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?1454 ?1455))))))) ?1455 =>= inverse (inverse (inverse (inverse ?1454))) [1455, 1454] by Super 208 with 586 at 1,1,1,2 +Id : 633, {_}: divide (inverse (inverse (multiply ?1454 ?1455))) ?1455 =>= inverse (inverse (inverse (inverse ?1454))) [1455, 1454] by Demod 608 with 452 at 1,2 +Id : 634, {_}: ?1454 =<= inverse (inverse (inverse (inverse ?1454))) [1454] by Demod 633 with 208 at 2 +Id : 755, {_}: multiply ?1763 (inverse (inverse (inverse ?1764))) =>= divide ?1763 ?1764 [1764, 1763] by Super 29 with 634 at 2,3 +Id : 797, {_}: divide (inverse (inverse ?1873)) (inverse (inverse ?1874)) =>= inverse (inverse (divide ?1873 ?1874)) [1874, 1873] by Super 348 with 755 at 1,1,3 +Id : 816, {_}: multiply (inverse (inverse ?1873)) (inverse ?1874) =>= inverse (inverse (divide ?1873 ?1874)) [1874, 1873] by Demod 797 with 29 at 2 +Id : 868, {_}: divide (inverse (inverse (inverse (inverse (divide ?1957 ?1958))))) (inverse ?1958) =>= inverse (inverse ?1957) [1958, 1957] by Super 208 with 816 at 1,1,1,2 +Id : 892, {_}: multiply (inverse (inverse (inverse (inverse (divide ?1957 ?1958))))) ?1958 =>= inverse (inverse ?1957) [1958, 1957] by Demod 868 with 29 at 2 +Id : 915, {_}: multiply (divide ?2055 ?2056) ?2056 =>= inverse (inverse ?2055) [2056, 2055] by Demod 892 with 634 at 1,2 +Id : 921, {_}: multiply (multiply ?2076 ?2077) (inverse ?2077) =>= inverse (inverse ?2076) [2077, 2076] by Super 915 with 29 at 1,2 +Id : 872, {_}: multiply (inverse (inverse ?1970)) (inverse ?1971) =>= inverse (inverse (divide ?1970 ?1971)) [1971, 1970] by Demod 797 with 29 at 2 +Id : 885, {_}: multiply ?2028 (inverse ?2029) =<= inverse (inverse (divide (inverse (inverse ?2028)) ?2029)) [2029, 2028] by Super 872 with 634 at 1,2 +Id : 86, {_}: divide (inverse (divide ?213 ?214)) ?215 =<= inverse (inverse (multiply ?214 (divide (inverse ?213) ?215))) [215, 214, 213] by Demod 85 with 29 at 1,1,3 +Id : 64, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 63 with 4 at 1,2,2,2,1,3 +Id : 893, {_}: multiply (divide ?1957 ?1958) ?1958 =>= inverse (inverse ?1957) [1958, 1957] by Demod 892 with 634 at 1,2 +Id : 910, {_}: inverse (inverse ?2040) =<= divide (divide ?2040 (inverse (inverse (inverse ?2041)))) ?2041 [2041, 2040] by Super 755 with 893 at 2 +Id : 1447, {_}: inverse (inverse ?3326) =<= divide (multiply ?3326 (inverse (inverse ?3327))) ?3327 [3327, 3326] by Demod 910 with 29 at 1,3 +Id : 51, {_}: multiply (inverse (inverse (divide ?133 ?133))) ?134 =>= inverse (inverse ?134) [134, 133] by Super 32 with 36 at 1,2 +Id : 1463, {_}: inverse (inverse (inverse (inverse (divide ?3389 ?3389)))) =?= divide (inverse (inverse (inverse (inverse ?3390)))) ?3390 [3390, 3389] by Super 1447 with 51 at 1,3 +Id : 1498, {_}: divide ?3389 ?3389 =?= divide (inverse (inverse (inverse (inverse ?3390)))) ?3390 [3390, 3389] by Demod 1463 with 634 at 2 +Id : 1499, {_}: divide ?3389 ?3389 =?= divide ?3390 ?3390 [3390, 3389] by Demod 1498 with 634 at 1,3 +Id : 1548, {_}: divide (inverse (divide ?3530 (divide (inverse ?3531) (divide (inverse ?3530) ?3532)))) ?3532 =?= inverse (divide ?3531 (divide ?3533 ?3533)) [3533, 3532, 3531, 3530] by Super 64 with 1499 at 2,1,3 +Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2 +Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2 +Id : 1619, {_}: inverse ?3531 =<= inverse (divide ?3531 (divide ?3533 ?3533)) [3533, 3531] by Demod 1548 with 31 at 2 +Id : 1667, {_}: divide ?3815 (divide ?3816 ?3816) =>= inverse (inverse (inverse (inverse ?3815))) [3816, 3815] by Super 634 with 1619 at 1,1,1,3 +Id : 1711, {_}: divide ?3815 (divide ?3816 ?3816) =>= ?3815 [3816, 3815] by Demod 1667 with 634 at 3 +Id : 1774, {_}: divide (inverse (divide ?4058 ?4059)) (divide ?4060 ?4060) =>= inverse (inverse (multiply ?4059 (inverse ?4058))) [4060, 4059, 4058] by Super 86 with 1711 at 2,1,1,3 +Id : 1809, {_}: inverse (divide ?4058 ?4059) =<= inverse (inverse (multiply ?4059 (inverse ?4058))) [4059, 4058] by Demod 1774 with 1711 at 2 +Id : 1810, {_}: inverse (divide ?4058 ?4059) =<= divide (inverse (inverse ?4059)) ?4058 [4059, 4058] by Demod 1809 with 348 at 3 +Id : 1856, {_}: multiply ?2028 (inverse ?2029) =<= inverse (inverse (inverse (divide ?2029 ?2028))) [2029, 2028] by Demod 885 with 1810 at 1,1,3 +Id : 52, {_}: inverse ?136 =<= divide (inverse (divide ?137 ?137)) ?136 [137, 136] by Super 35 with 4 at 1,3 +Id : 55, {_}: inverse ?145 =<= divide (inverse (inverse (inverse (divide ?146 ?146)))) ?145 [146, 145] by Super 52 with 36 at 1,1,3 +Id : 1858, {_}: inverse ?145 =<= inverse (divide ?145 (inverse (divide ?146 ?146))) [146, 145] by Demod 55 with 1810 at 3 +Id : 1862, {_}: inverse ?145 =<= inverse (multiply ?145 (divide ?146 ?146)) [146, 145] by Demod 1858 with 29 at 1,3 +Id : 1778, {_}: multiply ?4073 (divide ?4074 ?4074) =>= inverse (inverse ?4073) [4074, 4073] by Super 893 with 1711 at 1,2 +Id : 2425, {_}: inverse ?145 =<= inverse (inverse (inverse ?145)) [145] by Demod 1862 with 1778 at 1,3 +Id : 2428, {_}: multiply ?2028 (inverse ?2029) =>= inverse (divide ?2029 ?2028) [2029, 2028] by Demod 1856 with 2425 at 3 +Id : 2431, {_}: inverse (divide ?2077 (multiply ?2076 ?2077)) =>= inverse (inverse ?2076) [2076, 2077] by Demod 921 with 2428 at 2 +Id : 1860, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 208 with 1810 at 2 +Id : 2432, {_}: ?2076 =<= inverse (inverse ?2076) [2076] by Demod 2431 with 1860 at 2 +Id : 2437, {_}: multiply (multiply (inverse ?110) ?110) ?111 =>= ?111 [111, 110] by Demod 43 with 2432 at 3 +Id : 2539, {_}: a2 === a2 [] by Demod 1 with 2437 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP452-1.p +23734: solved GRP452-1.p in 0.388023 using nrkbo +23734: status Unsatisfiable for GRP452-1.p +NO CLASH, using fixed ground order +23741: Facts: +23741: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +NO CLASH, using fixed ground order +23742: Facts: +23742: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23742: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23742: Goal: +23742: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23742: Order: +23742: kbo +23742: Leaf order: +23742: a1 2 0 2 1,1,2 +23742: b1 2 0 2 1,1,3 +23742: inverse 4 1 2 0,1,2 +23742: multiply 3 2 2 0,2 +23742: divide 7 2 0 +NO CLASH, using fixed ground order +23743: Facts: +23743: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23743: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23743: Goal: +23743: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23743: Order: +23743: lpo +23743: Leaf order: +23743: a1 2 0 2 1,1,2 +23743: b1 2 0 2 1,1,3 +23743: inverse 4 1 2 0,1,2 +23743: multiply 3 2 2 0,2 +23743: divide 7 2 0 +23741: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23741: Goal: +23741: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23741: Order: +23741: nrkbo +23741: Leaf order: +23741: a1 2 0 2 1,1,2 +23741: b1 2 0 2 1,1,3 +23741: inverse 4 1 2 0,1,2 +23741: multiply 3 2 2 0,2 +23741: divide 7 2 0 +% SZS status Timeout for GRP469-1.p +NO CLASH, using fixed ground order +23763: Facts: +23763: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23763: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23763: Goal: +23763: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23763: Order: +23763: nrkbo +23763: Leaf order: +23763: b2 2 0 2 1,1,1,2 +23763: a2 2 0 2 2,2 +23763: inverse 3 1 1 0,1,1,2 +23763: multiply 3 2 2 0,2 +23763: divide 7 2 0 +NO CLASH, using fixed ground order +23764: Facts: +23764: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23764: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23764: Goal: +23764: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23764: Order: +23764: kbo +23764: Leaf order: +23764: b2 2 0 2 1,1,1,2 +23764: a2 2 0 2 2,2 +23764: inverse 3 1 1 0,1,1,2 +23764: multiply 3 2 2 0,2 +23764: divide 7 2 0 +NO CLASH, using fixed ground order +23765: Facts: +23765: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23765: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23765: Goal: +23765: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23765: Order: +23765: lpo +23765: Leaf order: +23765: b2 2 0 2 1,1,1,2 +23765: a2 2 0 2 2,2 +23765: inverse 3 1 1 0,1,1,2 +23765: multiply 3 2 2 0,2 +23765: divide 7 2 0 +% SZS status Timeout for GRP470-1.p +NO CLASH, using fixed ground order +23801: Facts: +23801: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23801: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23801: Goal: +23801: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23801: Order: +23801: nrkbo +23801: Leaf order: +23801: a3 2 0 2 1,1,2 +23801: b3 2 0 2 2,1,2 +23801: c3 2 0 2 2,2 +23801: inverse 2 1 0 +23801: multiply 5 2 4 0,2 +23801: divide 7 2 0 +NO CLASH, using fixed ground order +23802: Facts: +23802: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23802: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23802: Goal: +23802: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23802: Order: +23802: kbo +23802: Leaf order: +23802: a3 2 0 2 1,1,2 +23802: b3 2 0 2 2,1,2 +23802: c3 2 0 2 2,2 +23802: inverse 2 1 0 +23802: multiply 5 2 4 0,2 +23802: divide 7 2 0 +NO CLASH, using fixed ground order +23803: Facts: +23803: Id : 2, {_}: + divide (inverse (divide ?2 (divide ?3 (divide ?4 ?5)))) + (divide (divide ?5 ?4) ?2) + =>= + ?3 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23803: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23803: Goal: +23803: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23803: Order: +23803: lpo +23803: Leaf order: +23803: a3 2 0 2 1,1,2 +23803: b3 2 0 2 2,1,2 +23803: c3 2 0 2 2,2 +23803: inverse 2 1 0 +23803: multiply 5 2 4 0,2 +23803: divide 7 2 0 +% SZS status Timeout for GRP471-1.p +NO CLASH, using fixed ground order +23910: Facts: +23910: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23910: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23910: Goal: +23910: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23910: Order: +23910: nrkbo +23910: Leaf order: +23910: a1 2 0 2 1,1,2 +23910: b1 2 0 2 1,1,3 +23910: inverse 4 1 2 0,1,2 +23910: multiply 3 2 2 0,2 +23910: divide 7 2 0 +NO CLASH, using fixed ground order +23911: Facts: +23911: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23911: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23911: Goal: +23911: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23911: Order: +23911: kbo +23911: Leaf order: +23911: a1 2 0 2 1,1,2 +23911: b1 2 0 2 1,1,3 +23911: inverse 4 1 2 0,1,2 +23911: multiply 3 2 2 0,2 +23911: divide 7 2 0 +NO CLASH, using fixed ground order +23912: Facts: +23912: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23912: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23912: Goal: +23912: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23912: Order: +23912: lpo +23912: Leaf order: +23912: a1 2 0 2 1,1,2 +23912: b1 2 0 2 1,1,3 +23912: inverse 4 1 2 0,1,2 +23912: multiply 3 2 2 0,2 +23912: divide 7 2 0 +% SZS status Timeout for GRP475-1.p +NO CLASH, using fixed ground order +23945: Facts: +23945: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23945: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23945: Goal: +23945: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23945: Order: +23945: nrkbo +23945: Leaf order: +23945: b2 2 0 2 1,1,1,2 +23945: a2 2 0 2 2,2 +23945: inverse 3 1 1 0,1,1,2 +23945: multiply 3 2 2 0,2 +23945: divide 7 2 0 +NO CLASH, using fixed ground order +23946: Facts: +23946: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23946: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23946: Goal: +23946: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23946: Order: +23946: kbo +23946: Leaf order: +23946: b2 2 0 2 1,1,1,2 +23946: a2 2 0 2 2,2 +23946: inverse 3 1 1 0,1,1,2 +23946: multiply 3 2 2 0,2 +23946: divide 7 2 0 +NO CLASH, using fixed ground order +23947: Facts: +23947: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23947: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23947: Goal: +23947: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23947: Order: +23947: lpo +23947: Leaf order: +23947: b2 2 0 2 1,1,1,2 +23947: a2 2 0 2 2,2 +23947: inverse 3 1 1 0,1,1,2 +23947: multiply 3 2 2 0,2 +23947: divide 7 2 0 +Statistics : +Max weight : 50 +Found proof, 11.024829s +% SZS status Unsatisfiable for GRP476-1.p +% SZS output start CNFRefutation for GRP476-1.p +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2 +Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2 +Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3 +Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2 +Id : 863, {_}: multiply (divide (inverse (divide (divide (divide ?4853 ?4854) (inverse ?4855)) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Super 18 with 20 at 1,2 +Id : 978, {_}: multiply (divide (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 863 with 3 at 1,1,1,1,2 +Id : 1168, {_}: divide (divide (inverse (divide (divide (divide ?6497 ?6498) ?6499) ?6500)) (divide ?6498 ?6497)) ?6499 =>= ?6500 [6500, 6499, 6498, 6497] by Super 17 with 20 at 1,2 +Id : 1637, {_}: divide (divide (inverse (divide (divide (divide (inverse ?8641) ?8642) ?8643) ?8644)) (multiply ?8642 ?8641)) ?8643 =>= ?8644 [8644, 8643, 8642, 8641] by Super 1168 with 3 at 2,1,2 +Id : 1659, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?8819) ?8820) ?8821) ?8822)) (multiply (inverse ?8820) ?8819)) ?8821 =>= ?8822 [8822, 8821, 8820, 8819] by Super 1637 with 3 at 1,1,1,1,1,2 +Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2 +Id : 292, {_}: divide (inverse (divide (divide ?1415 ?1416) (divide ?1417 ?1416))) (multiply (divide ?1418 ?1419) (divide (divide (divide ?1419 ?1418) ?1420) (divide ?1415 ?1420))) =>= ?1417 [1420, 1419, 1418, 1417, 1416, 1415] by Demod 7 with 3 at 2,2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 117, {_}: inverse (divide (divide (divide ?560 ?561) ?562) (divide (divide ?563 (divide ?561 ?560)) ?562)) =>= ?563 [563, 562, 561, 560] by Super 2 with 6 at 2 +Id : 329, {_}: divide ?1764 (multiply (divide ?1765 ?1766) (divide (divide (divide ?1766 ?1765) ?1767) (divide (divide ?1768 ?1769) ?1767))) =>= divide ?1764 (divide ?1769 ?1768) [1769, 1768, 1767, 1766, 1765, 1764] by Super 292 with 117 at 1,2 +Id : 13692, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?74151) ?74152) ?74153) (divide ?74154 ?74155))) (multiply (inverse ?74152) ?74151)) ?74153 =?= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154, 74153, 74152, 74151] by Super 1659 with 329 at 1,1,1,2 +Id : 13926, {_}: divide ?74154 ?74155 =<= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154] by Demod 13692 with 1659 at 2 +Id : 1195, {_}: divide (divide (inverse (multiply (divide (divide ?6697 ?6698) ?6699) ?6700)) (divide ?6698 ?6697)) ?6699 =>= inverse ?6700 [6700, 6699, 6698, 6697] by Super 1168 with 3 at 1,1,1,2 +Id : 14284, {_}: divide (divide (inverse (divide ?76258 ?76259)) (divide ?76260 ?76261)) ?76262 =<= inverse (divide (divide (divide ?76262 (divide ?76261 ?76260)) ?76263) (divide (divide ?76259 ?76258) ?76263)) [76263, 76262, 76261, 76260, 76259, 76258] by Super 1195 with 13926 at 1,1,1,2 +Id : 14590, {_}: divide (divide (divide (inverse (divide ?77679 ?77680)) (divide ?77681 ?77682)) ?77683) (divide (divide ?77682 ?77681) ?77683) =>= divide ?77680 ?77679 [77683, 77682, 77681, 77680, 77679] by Super 2 with 14284 at 1,2 +Id : 21451, {_}: divide ?110293 ?110294 =<= multiply (divide (divide ?110293 ?110294) (inverse (divide ?110295 ?110296))) (divide ?110296 ?110295) [110296, 110295, 110294, 110293] by Super 13926 with 14590 at 2,3 +Id : 22065, {_}: divide ?114187 ?114188 =<= multiply (multiply (divide ?114187 ?114188) (divide ?114189 ?114190)) (divide ?114190 ?114189) [114190, 114189, 114188, 114187] by Demod 21451 with 3 at 1,3 +Id : 22122, {_}: divide (inverse (divide (divide (divide ?114646 ?114647) ?114648) (divide ?114649 ?114648))) (divide ?114647 ?114646) =?= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649, 114648, 114647, 114646] by Super 22065 with 2 at 1,1,3 +Id : 22268, {_}: ?114649 =<= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649] by Demod 22122 with 2 at 2 +Id : 202, {_}: inverse (divide (divide (divide ?946 ?947) ?948) (divide (divide ?949 (divide ?947 ?946)) ?948)) =>= ?949 [949, 948, 947, 946] by Super 2 with 6 at 2 +Id : 213, {_}: inverse (divide (divide (divide ?1024 ?1025) (inverse ?1026)) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Super 202 with 3 at 2,1,2 +Id : 232, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 213 with 3 at 1,1,2 +Id : 21617, {_}: divide (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (inverse (divide ?111844 ?111845)) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Super 14284 with 14590 at 1,3 +Id : 21801, {_}: multiply (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (divide ?111844 ?111845) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Demod 21617 with 3 at 2 +Id : 24938, {_}: inverse (divide (inverse (divide ?127750 ?127751)) (multiply (divide ?127752 (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753)))) (divide ?127751 ?127750))) =>= ?127752 [127754, 127753, 127752, 127751, 127750] by Super 232 with 21801 at 1,1,2 +Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2 +Id : 21516, {_}: divide (inverse (divide ?110895 ?110896)) (multiply (divide ?110897 ?110898) (divide ?110896 ?110895)) =>= divide ?110898 ?110897 [110898, 110897, 110896, 110895] by Super 9 with 14590 at 1,1,2 +Id : 25207, {_}: inverse (divide (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753))) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 24938 with 21516 at 1,2 +Id : 25208, {_}: inverse (divide (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 25207 with 3 at 1,1,2 +Id : 25416, {_}: multiply (divide ?129668 (divide ?129669 ?129670)) (divide ?129669 ?129670) =>= ?129668 [129670, 129669, 129668] by Super 232 with 25208 at 2 +Id : 25599, {_}: divide ?130543 (divide ?130544 ?130545) =>= multiply ?130543 (divide ?130545 ?130544) [130545, 130544, 130543] by Super 22268 with 25416 at 1,3 +Id : 25966, {_}: multiply (multiply (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4853 ?4854)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 978 with 25599 at 1,2 +Id : 26300, {_}: multiply (multiply (inverse (multiply (multiply (divide ?133704 ?133705) ?133706) (divide ?133707 ?133708))) (divide ?133704 ?133705)) ?133706 =>= divide ?133708 ?133707 [133708, 133707, 133706, 133705, 133704] by Super 25966 with 25599 at 1,1,1,2 +Id : 1261, {_}: multiply (divide (inverse (divide (multiply (divide ?6852 ?6853) ?6854) ?6855)) (divide ?6853 ?6852)) ?6854 =>= ?6855 [6855, 6854, 6853, 6852] by Demod 863 with 3 at 1,1,1,1,2 +Id : 1287, {_}: multiply (divide (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7048 ?7047)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Super 1261 with 3 at 1,1,1,2 +Id : 25965, {_}: multiply (multiply (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7047 ?7048)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Demod 1287 with 25599 at 1,2 +Id : 26721, {_}: inverse (divide ?134526 ?134527) =>= divide ?134527 ?134526 [134527, 134526] by Demod 26300 with 25965 at 2 +Id : 26764, {_}: inverse (multiply ?134789 ?134790) =<= divide (inverse ?134790) ?134789 [134790, 134789] by Super 26721 with 3 at 1,2 +Id : 26966, {_}: multiply (inverse ?135418) ?135419 =<= inverse (multiply (inverse ?135419) ?135418) [135419, 135418] by Super 3 with 26764 at 3 +Id : 26405, {_}: inverse (divide ?133707 ?133708) =>= divide ?133708 ?133707 [133708, 133707] by Demod 26300 with 25965 at 2 +Id : 26641, {_}: divide ?127752 (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) =>= ?127752 [127754, 127753, 127752] by Demod 25208 with 26405 at 2 +Id : 656, {_}: inverse (divide (divide (divide (inverse ?3361) ?3362) ?3363) (divide (divide ?3364 (multiply ?3362 ?3361)) ?3363)) =>= ?3364 [3364, 3363, 3362, 3361] by Super 202 with 3 at 2,1,2,1,2 +Id : 272, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (multiply (divide ?32 ?33) (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34))) =>= ?31 [34, 33, 32, 31, 30, 29] by Demod 7 with 3 at 2,2 +Id : 661, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?3396 ?3397) ?3398) (divide ?3399 ?3398))) (divide ?3397 ?3396)) ?3400) (divide ?3401 ?3400)) =?= inverse (divide (divide ?3399 ?3402) (divide ?3401 ?3402)) [3402, 3401, 3400, 3399, 3398, 3397, 3396] by Super 656 with 272 at 1,2,1,2 +Id : 5809, {_}: inverse (divide (divide ?31363 ?31364) (divide ?31365 ?31364)) =?= inverse (divide (divide ?31363 ?31366) (divide ?31365 ?31366)) [31366, 31365, 31364, 31363] by Demod 661 with 2 at 1,1,1,2 +Id : 5810, {_}: inverse (divide (divide ?31368 ?31369) (divide (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))) ?31369)) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Super 5809 with 2 at 2,1,3 +Id : 25948, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 5810 with 25599 at 1,2 +Id : 25949, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25948 with 25599 at 1,1,3 +Id : 25950, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25949 with 25599 at 1,2,2,1,2 +Id : 26071, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25950 with 3 at 2,1,2 +Id : 26655, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 26071 with 26405 at 3 +Id : 5834, {_}: inverse (divide (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31561 ?31560)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Super 5809 with 2 at 1,1,3 +Id : 25943, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 5834 with 25599 at 1,2 +Id : 25944, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25943 with 25599 at 1,3 +Id : 25945, {_}: inverse (multiply (divide (inverse (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25944 with 25599 at 1,1,1,1,2 +Id : 26832, {_}: inverse (multiply (inverse (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)))) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31559, 31558, 31557, 31556, 31560] by Demod 25945 with 26764 at 1,1,2 +Id : 27298, {_}: multiply (inverse (divide ?31560 ?31561)) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31561, 31560] by Demod 26832 with 26966 at 2 +Id : 27299, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27298 with 26405 at 1,2 +Id : 27300, {_}: inverse (inverse (multiply ?31373 (divide (divide ?31371 ?31370) ?31368))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 26655 with 27299 at 1,2 +Id : 26900, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= divide ?134958 (inverse ?134959) [134959, 134958] by Super 26405 with 26764 at 1,2 +Id : 27254, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= multiply ?134958 ?134959 [134959, 134958] by Demod 26900 with 3 at 3 +Id : 27506, {_}: multiply ?31373 (divide (divide ?31371 ?31370) ?31368) =<= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 27300 with 27254 at 2 +Id : 27507, {_}: multiply ?127752 (divide (divide ?127753 ?127754) (divide ?127753 ?127754)) =>= ?127752 [127754, 127753, 127752] by Demod 26641 with 27506 at 2 +Id : 27516, {_}: multiply ?127752 (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) =>= ?127752 [127754, 127753, 127752] by Demod 27507 with 25599 at 2,2 +Id : 22416, {_}: ?115848 =<= multiply (multiply ?115848 (divide ?115849 ?115850)) (divide ?115850 ?115849) [115850, 115849, 115848] by Demod 22122 with 2 at 2 +Id : 22472, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (divide (inverse ?116248) ?116247) [116248, 116247, 116246] by Super 22416 with 3 at 2,1,3 +Id : 26848, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (inverse (multiply ?116247 ?116248)) [116248, 116247, 116246] by Demod 22472 with 26764 at 2,3 +Id : 27552, {_}: inverse (inverse (multiply ?137012 ?137013)) =>= multiply ?137012 ?137013 [137013, 137012] by Demod 26900 with 3 at 3 +Id : 25980, {_}: multiply (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 2 with 25599 at 2 +Id : 25981, {_}: multiply (inverse (multiply (divide (divide ?2 ?3) ?4) (divide ?4 ?5))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 25980 with 25599 at 1,1,2 +Id : 27556, {_}: inverse (inverse ?137032) =<= multiply (inverse (multiply (divide (divide ?137033 ?137034) ?137035) (divide ?137035 ?137032))) (divide ?137033 ?137034) [137035, 137034, 137033, 137032] by Super 27552 with 25981 at 1,1,2 +Id : 27632, {_}: inverse (inverse ?137032) =>= ?137032 [137032] by Demod 27556 with 25981 at 3 +Id : 27734, {_}: multiply ?137511 (inverse ?137512) =>= divide ?137511 ?137512 [137512, 137511] by Super 3 with 27632 at 2,3 +Id : 27823, {_}: ?116246 =<= divide (multiply ?116246 (multiply ?116247 ?116248)) (multiply ?116247 ?116248) [116248, 116247, 116246] by Demod 26848 with 27734 at 3 +Id : 22, {_}: divide (inverse (divide (divide (multiply (divide ?98 ?99) (divide (divide (divide ?99 ?98) ?100) (divide ?101 ?100))) ?102) (divide ?103 ?102))) ?101 =>= ?103 [103, 102, 101, 100, 99, 98] by Demod 5 with 3 at 1,1,1,1,2 +Id : 26, {_}: divide (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (inverse (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139))) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Super 22 with 2 at 2,2,1,1,1,1,2 +Id : 42, {_}: multiply (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Demod 26 with 3 at 2 +Id : 26984, {_}: inverse (multiply (divide ?135518 ?135519) ?135520) =<= multiply (inverse ?135520) (divide ?135519 ?135518) [135520, 135519, 135518] by Super 25599 with 26764 at 2 +Id : 31736, {_}: inverse (multiply (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) =>= ?138 [138, 137, 133, 132, 134, 135, 139, 136] by Demod 42 with 26984 at 2 +Id : 26724, {_}: inverse (multiply ?134539 (divide ?134540 ?134541)) =>= divide (divide ?134541 ?134540) ?134539 [134541, 134540, 134539] by Super 26721 with 25599 at 1,2 +Id : 31737, {_}: divide (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31736 with 26724 at 2 +Id : 31738, {_}: multiply (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31737 with 25599 at 2 +Id : 31739, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31738 with 25599 at 1,2 +Id : 31740, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31739 with 25599 at 2,2 +Id : 31741, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (divide (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?132 ?133)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31740 with 27506 at 2,1,2 +Id : 31742, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31741 with 25599 at 2,2,1,2 +Id : 31743, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (divide (divide ?134 ?135) (divide ?133 ?132))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 132, 133, 135, 134, 136, 137, 138] by Demod 31742 with 25599 at 1,2,2,1,2 +Id : 31744, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (multiply (divide ?134 ?135) (divide ?132 ?133))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 133, 132, 135, 134, 136, 137, 138] by Demod 31743 with 25599 at 2,1,2,2,1,2 +Id : 31832, {_}: ?147291 =<= divide (multiply ?147291 (multiply (multiply (divide ?147292 ?147293) (multiply ?147293 (multiply (multiply ?147294 (multiply (divide ?147295 ?147296) (divide ?147297 ?147298))) (divide ?147298 ?147297)))) (multiply (divide (divide ?147296 ?147295) ?147299) (divide ?147299 ?147294)))) ?147292 [147299, 147298, 147297, 147296, 147295, 147294, 147293, 147292, 147291] by Super 27823 with 31744 at 2,3 +Id : 32203, {_}: ?147291 =<= divide (multiply ?147291 ?147292) ?147292 [147292, 147291] by Demod 31832 with 31744 at 2,1,3 +Id : 33094, {_}: inverse ?153200 =<= divide ?153201 (multiply ?153200 ?153201) [153201, 153200] by Super 26405 with 32203 at 1,2 +Id : 33479, {_}: multiply ?154885 (multiply (divide (multiply ?154886 ?154887) ?154887) (inverse ?154886)) =>= ?154885 [154887, 154886, 154885] by Super 27516 with 33094 at 2,2,2 +Id : 33980, {_}: multiply ?154885 (divide (divide (multiply ?154886 ?154887) ?154887) ?154886) =>= ?154885 [154887, 154886, 154885] by Demod 33479 with 27734 at 2,2 +Id : 33981, {_}: multiply ?154885 (divide ?154886 ?154886) =>= ?154885 [154886, 154885] by Demod 33980 with 32203 at 1,2,2 +Id : 34313, {_}: multiply (inverse (divide ?156478 ?156478)) ?156479 =>= inverse (inverse ?156479) [156479, 156478] by Super 26966 with 33981 at 1,3 +Id : 34773, {_}: multiply (divide ?156478 ?156478) ?156479 =>= inverse (inverse ?156479) [156479, 156478] by Demod 34313 with 26405 at 1,2 +Id : 36051, {_}: multiply (divide ?160644 ?160644) ?160645 =>= ?160645 [160645, 160644] by Demod 34773 with 27632 at 3 +Id : 36066, {_}: multiply (multiply (inverse ?160721) ?160721) ?160722 =>= ?160722 [160722, 160721] by Super 36051 with 3 at 1,2 +Id : 39894, {_}: a2 === a2 [] by Demod 1 with 36066 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP476-1.p +23945: solved GRP476-1.p in 11.032689 using nrkbo +23945: status Unsatisfiable for GRP476-1.p +NO CLASH, using fixed ground order +23952: Facts: +23952: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23952: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23952: Goal: +23952: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23952: Order: +23952: nrkbo +23952: Leaf order: +23952: a3 2 0 2 1,1,2 +23952: b3 2 0 2 2,1,2 +23952: c3 2 0 2 2,2 +23952: inverse 2 1 0 +23952: multiply 5 2 4 0,2 +23952: divide 7 2 0 +NO CLASH, using fixed ground order +23953: Facts: +23953: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23953: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23953: Goal: +23953: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23953: Order: +23953: kbo +23953: Leaf order: +23953: a3 2 0 2 1,1,2 +23953: b3 2 0 2 2,1,2 +23953: c3 2 0 2 2,2 +23953: inverse 2 1 0 +23953: multiply 5 2 4 0,2 +23953: divide 7 2 0 +NO CLASH, using fixed ground order +23954: Facts: +23954: Id : 2, {_}: + divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) + (divide ?3 ?2) + =>= + ?5 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23954: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23954: Goal: +23954: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +23954: Order: +23954: lpo +23954: Leaf order: +23954: a3 2 0 2 1,1,2 +23954: b3 2 0 2 2,1,2 +23954: c3 2 0 2 2,2 +23954: inverse 2 1 0 +23954: multiply 5 2 4 0,2 +23954: divide 7 2 0 +Statistics : +Max weight : 50 +Found proof, 32.327095s +% SZS status Unsatisfiable for GRP477-1.p +% SZS output start CNFRefutation for GRP477-1.p +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?3 ?2) =>= ?5 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?11) ?12) (divide ?13 ?12))) (divide ?11 ?10) =>= ?13 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 5, {_}: divide (inverse (divide (divide (divide (divide ?15 ?16) (inverse (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17)))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2 +Id : 17, {_}: divide (inverse (divide (divide (multiply (divide ?15 ?16) (divide (divide (divide ?16 ?15) ?17) (divide ?18 ?17))) ?19) (divide ?20 ?19))) ?18 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,1,2 +Id : 20, {_}: divide (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?81 ?80) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Super 2 with 17 at 2,1,1,2 +Id : 1168, {_}: divide (divide (inverse (divide (divide (divide ?6497 ?6498) ?6499) ?6500)) (divide ?6498 ?6497)) ?6499 =>= ?6500 [6500, 6499, 6498, 6497] by Super 17 with 20 at 1,2 +Id : 1637, {_}: divide (divide (inverse (divide (divide (divide (inverse ?8641) ?8642) ?8643) ?8644)) (multiply ?8642 ?8641)) ?8643 =>= ?8644 [8644, 8643, 8642, 8641] by Super 1168 with 3 at 2,1,2 +Id : 1659, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?8819) ?8820) ?8821) ?8822)) (multiply (inverse ?8820) ?8819)) ?8821 =>= ?8822 [8822, 8821, 8820, 8819] by Super 1637 with 3 at 1,1,1,1,1,2 +Id : 7, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (divide (divide ?32 ?33) (inverse (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34)))) =>= ?31 [34, 33, 32, 31, 30, 29] by Super 4 with 2 at 1,1,1,1,2 +Id : 292, {_}: divide (inverse (divide (divide ?1415 ?1416) (divide ?1417 ?1416))) (multiply (divide ?1418 ?1419) (divide (divide (divide ?1419 ?1418) ?1420) (divide ?1415 ?1420))) =>= ?1417 [1420, 1419, 1418, 1417, 1416, 1415] by Demod 7 with 3 at 2,2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?23) (divide ?24 ?25)) ?26)) (divide ?23 ?22) =?= inverse (divide (divide (divide ?25 ?24) ?27) (divide ?26 ?27)) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 117, {_}: inverse (divide (divide (divide ?560 ?561) ?562) (divide (divide ?563 (divide ?561 ?560)) ?562)) =>= ?563 [563, 562, 561, 560] by Super 2 with 6 at 2 +Id : 329, {_}: divide ?1764 (multiply (divide ?1765 ?1766) (divide (divide (divide ?1766 ?1765) ?1767) (divide (divide ?1768 ?1769) ?1767))) =>= divide ?1764 (divide ?1769 ?1768) [1769, 1768, 1767, 1766, 1765, 1764] by Super 292 with 117 at 1,2 +Id : 13692, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?74151) ?74152) ?74153) (divide ?74154 ?74155))) (multiply (inverse ?74152) ?74151)) ?74153 =?= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154, 74153, 74152, 74151] by Super 1659 with 329 at 1,1,1,2 +Id : 13926, {_}: divide ?74154 ?74155 =<= multiply (divide ?74156 ?74157) (divide (divide (divide ?74157 ?74156) ?74158) (divide (divide ?74155 ?74154) ?74158)) [74158, 74157, 74156, 74155, 74154] by Demod 13692 with 1659 at 2 +Id : 1195, {_}: divide (divide (inverse (multiply (divide (divide ?6697 ?6698) ?6699) ?6700)) (divide ?6698 ?6697)) ?6699 =>= inverse ?6700 [6700, 6699, 6698, 6697] by Super 1168 with 3 at 1,1,1,2 +Id : 14284, {_}: divide (divide (inverse (divide ?76258 ?76259)) (divide ?76260 ?76261)) ?76262 =<= inverse (divide (divide (divide ?76262 (divide ?76261 ?76260)) ?76263) (divide (divide ?76259 ?76258) ?76263)) [76263, 76262, 76261, 76260, 76259, 76258] by Super 1195 with 13926 at 1,1,1,2 +Id : 14590, {_}: divide (divide (divide (inverse (divide ?77679 ?77680)) (divide ?77681 ?77682)) ?77683) (divide (divide ?77682 ?77681) ?77683) =>= divide ?77680 ?77679 [77683, 77682, 77681, 77680, 77679] by Super 2 with 14284 at 1,2 +Id : 21451, {_}: divide ?110293 ?110294 =<= multiply (divide (divide ?110293 ?110294) (inverse (divide ?110295 ?110296))) (divide ?110296 ?110295) [110296, 110295, 110294, 110293] by Super 13926 with 14590 at 2,3 +Id : 22065, {_}: divide ?114187 ?114188 =<= multiply (multiply (divide ?114187 ?114188) (divide ?114189 ?114190)) (divide ?114190 ?114189) [114190, 114189, 114188, 114187] by Demod 21451 with 3 at 1,3 +Id : 22122, {_}: divide (inverse (divide (divide (divide ?114646 ?114647) ?114648) (divide ?114649 ?114648))) (divide ?114647 ?114646) =?= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649, 114648, 114647, 114646] by Super 22065 with 2 at 1,1,3 +Id : 22416, {_}: ?115848 =<= multiply (multiply ?115848 (divide ?115849 ?115850)) (divide ?115850 ?115849) [115850, 115849, 115848] by Demod 22122 with 2 at 2 +Id : 22444, {_}: ?116047 =<= multiply (multiply ?116047 (divide (inverse ?116048) ?116049)) (multiply ?116049 ?116048) [116049, 116048, 116047] by Super 22416 with 3 at 2,3 +Id : 18, {_}: multiply (inverse (divide (divide (multiply (divide ?64 ?65) (divide (divide (divide ?65 ?64) ?66) (divide (inverse ?67) ?66))) ?68) (divide ?69 ?68))) ?67 =>= ?69 [69, 68, 67, 66, 65, 64] by Super 3 with 17 at 3 +Id : 863, {_}: multiply (divide (inverse (divide (divide (divide ?4853 ?4854) (inverse ?4855)) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Super 18 with 20 at 1,2 +Id : 978, {_}: multiply (divide (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4854 ?4853)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 863 with 3 at 1,1,1,1,2 +Id : 22268, {_}: ?114649 =<= multiply (multiply ?114649 (divide ?114650 ?114651)) (divide ?114651 ?114650) [114651, 114650, 114649] by Demod 22122 with 2 at 2 +Id : 202, {_}: inverse (divide (divide (divide ?946 ?947) ?948) (divide (divide ?949 (divide ?947 ?946)) ?948)) =>= ?949 [949, 948, 947, 946] by Super 2 with 6 at 2 +Id : 213, {_}: inverse (divide (divide (divide ?1024 ?1025) (inverse ?1026)) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Super 202 with 3 at 2,1,2 +Id : 232, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (divide ?1027 (divide ?1025 ?1024)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 213 with 3 at 1,1,2 +Id : 21617, {_}: divide (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (inverse (divide ?111844 ?111845)) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Super 14284 with 14590 at 1,3 +Id : 21801, {_}: multiply (divide (inverse (divide ?111842 ?111843)) (divide ?111843 ?111842)) (divide ?111844 ?111845) =>= inverse (divide ?111845 ?111844) [111845, 111844, 111843, 111842] by Demod 21617 with 3 at 2 +Id : 24938, {_}: inverse (divide (inverse (divide ?127750 ?127751)) (multiply (divide ?127752 (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753)))) (divide ?127751 ?127750))) =>= ?127752 [127754, 127753, 127752, 127751, 127750] by Super 232 with 21801 at 1,1,2 +Id : 9, {_}: divide (inverse (divide (divide (divide (inverse ?38) ?39) ?40) (divide ?41 ?40))) (multiply ?39 ?38) =>= ?41 [41, 40, 39, 38] by Super 2 with 3 at 2,2 +Id : 21516, {_}: divide (inverse (divide ?110895 ?110896)) (multiply (divide ?110897 ?110898) (divide ?110896 ?110895)) =>= divide ?110898 ?110897 [110898, 110897, 110896, 110895] by Super 9 with 14590 at 1,1,2 +Id : 25207, {_}: inverse (divide (divide (divide ?127753 ?127754) (inverse (divide ?127754 ?127753))) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 24938 with 21516 at 1,2 +Id : 25208, {_}: inverse (divide (multiply (divide ?127753 ?127754) (divide ?127754 ?127753)) ?127752) =>= ?127752 [127752, 127754, 127753] by Demod 25207 with 3 at 1,1,2 +Id : 25416, {_}: multiply (divide ?129668 (divide ?129669 ?129670)) (divide ?129669 ?129670) =>= ?129668 [129670, 129669, 129668] by Super 232 with 25208 at 2 +Id : 25599, {_}: divide ?130543 (divide ?130544 ?130545) =>= multiply ?130543 (divide ?130545 ?130544) [130545, 130544, 130543] by Super 22268 with 25416 at 1,3 +Id : 25966, {_}: multiply (multiply (inverse (divide (multiply (divide ?4853 ?4854) ?4855) ?4856)) (divide ?4853 ?4854)) ?4855 =>= ?4856 [4856, 4855, 4854, 4853] by Demod 978 with 25599 at 1,2 +Id : 26300, {_}: multiply (multiply (inverse (multiply (multiply (divide ?133704 ?133705) ?133706) (divide ?133707 ?133708))) (divide ?133704 ?133705)) ?133706 =>= divide ?133708 ?133707 [133708, 133707, 133706, 133705, 133704] by Super 25966 with 25599 at 1,1,1,2 +Id : 1261, {_}: multiply (divide (inverse (divide (multiply (divide ?6852 ?6853) ?6854) ?6855)) (divide ?6853 ?6852)) ?6854 =>= ?6855 [6855, 6854, 6853, 6852] by Demod 863 with 3 at 1,1,1,1,2 +Id : 1287, {_}: multiply (divide (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7048 ?7047)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Super 1261 with 3 at 1,1,1,2 +Id : 25965, {_}: multiply (multiply (inverse (multiply (multiply (divide ?7047 ?7048) ?7049) ?7050)) (divide ?7047 ?7048)) ?7049 =>= inverse ?7050 [7050, 7049, 7048, 7047] by Demod 1287 with 25599 at 1,2 +Id : 26721, {_}: inverse (divide ?134526 ?134527) =>= divide ?134527 ?134526 [134527, 134526] by Demod 26300 with 25965 at 2 +Id : 26764, {_}: inverse (multiply ?134789 ?134790) =<= divide (inverse ?134790) ?134789 [134790, 134789] by Super 26721 with 3 at 1,2 +Id : 26849, {_}: ?116047 =<= multiply (multiply ?116047 (inverse (multiply ?116049 ?116048))) (multiply ?116049 ?116048) [116048, 116049, 116047] by Demod 22444 with 26764 at 2,1,3 +Id : 26405, {_}: inverse (divide ?133707 ?133708) =>= divide ?133708 ?133707 [133708, 133707] by Demod 26300 with 25965 at 2 +Id : 26900, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= divide ?134958 (inverse ?134959) [134959, 134958] by Super 26405 with 26764 at 1,2 +Id : 27552, {_}: inverse (inverse (multiply ?137012 ?137013)) =>= multiply ?137012 ?137013 [137013, 137012] by Demod 26900 with 3 at 3 +Id : 25980, {_}: multiply (inverse (divide (divide (divide ?2 ?3) ?4) (divide ?5 ?4))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 2 with 25599 at 2 +Id : 25981, {_}: multiply (inverse (multiply (divide (divide ?2 ?3) ?4) (divide ?4 ?5))) (divide ?2 ?3) =>= ?5 [5, 4, 3, 2] by Demod 25980 with 25599 at 1,1,2 +Id : 27556, {_}: inverse (inverse ?137032) =<= multiply (inverse (multiply (divide (divide ?137033 ?137034) ?137035) (divide ?137035 ?137032))) (divide ?137033 ?137034) [137035, 137034, 137033, 137032] by Super 27552 with 25981 at 1,1,2 +Id : 27632, {_}: inverse (inverse ?137032) =>= ?137032 [137032] by Demod 27556 with 25981 at 3 +Id : 27734, {_}: multiply ?137511 (inverse ?137512) =>= divide ?137511 ?137512 [137512, 137511] by Super 3 with 27632 at 2,3 +Id : 27821, {_}: ?116047 =<= multiply (divide ?116047 (multiply ?116049 ?116048)) (multiply ?116049 ?116048) [116048, 116049, 116047] by Demod 26849 with 27734 at 1,3 +Id : 22, {_}: divide (inverse (divide (divide (multiply (divide ?98 ?99) (divide (divide (divide ?99 ?98) ?100) (divide ?101 ?100))) ?102) (divide ?103 ?102))) ?101 =>= ?103 [103, 102, 101, 100, 99, 98] by Demod 5 with 3 at 1,1,1,1,2 +Id : 26, {_}: divide (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (inverse (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139))) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Super 22 with 2 at 2,2,1,1,1,1,2 +Id : 42, {_}: multiply (inverse (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 138, 137, 136, 135, 134, 133, 132] by Demod 26 with 3 at 2 +Id : 26984, {_}: inverse (multiply (divide ?135518 ?135519) ?135520) =<= multiply (inverse ?135520) (divide ?135519 ?135518) [135520, 135519, 135518] by Super 25599 with 26764 at 2 +Id : 31736, {_}: inverse (multiply (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) (divide (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137) (divide ?138 ?137))) =>= ?138 [138, 137, 133, 132, 134, 135, 139, 136] by Demod 42 with 26984 at 2 +Id : 26724, {_}: inverse (multiply ?134539 (divide ?134540 ?134541)) =>= divide (divide ?134541 ?134540) ?134539 [134541, 134540, 134539] by Super 26721 with 25599 at 1,2 +Id : 31737, {_}: divide (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide ?136 ?139) (divide (divide ?135 ?134) ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31736 with 26724 at 2 +Id : 31738, {_}: multiply (divide (divide ?138 ?137) (divide (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)) ?137)) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31737 with 25599 at 2 +Id : 31739, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (divide (divide (divide ?135 ?134) ?139) (divide ?136 ?139)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31738 with 25599 at 1,2 +Id : 31740, {_}: multiply (multiply (divide ?138 ?137) (divide ?137 (multiply (divide ?132 ?133) (divide (divide (divide ?133 ?132) (divide ?134 ?135)) ?136)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 136, 135, 134, 133, 132, 137, 138] by Demod 31739 with 25599 at 2,2 +Id : 656, {_}: inverse (divide (divide (divide (inverse ?3361) ?3362) ?3363) (divide (divide ?3364 (multiply ?3362 ?3361)) ?3363)) =>= ?3364 [3364, 3363, 3362, 3361] by Super 202 with 3 at 2,1,2,1,2 +Id : 272, {_}: divide (inverse (divide (divide ?29 ?30) (divide ?31 ?30))) (multiply (divide ?32 ?33) (divide (divide (divide ?33 ?32) ?34) (divide ?29 ?34))) =>= ?31 [34, 33, 32, 31, 30, 29] by Demod 7 with 3 at 2,2 +Id : 661, {_}: inverse (divide (divide (divide (inverse (divide (divide (divide ?3396 ?3397) ?3398) (divide ?3399 ?3398))) (divide ?3397 ?3396)) ?3400) (divide ?3401 ?3400)) =?= inverse (divide (divide ?3399 ?3402) (divide ?3401 ?3402)) [3402, 3401, 3400, 3399, 3398, 3397, 3396] by Super 656 with 272 at 1,2,1,2 +Id : 5809, {_}: inverse (divide (divide ?31363 ?31364) (divide ?31365 ?31364)) =?= inverse (divide (divide ?31363 ?31366) (divide ?31365 ?31366)) [31366, 31365, 31364, 31363] by Demod 661 with 2 at 1,1,1,2 +Id : 5810, {_}: inverse (divide (divide ?31368 ?31369) (divide (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))) ?31369)) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Super 5809 with 2 at 2,1,3 +Id : 25948, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (divide ?31368 (divide ?31371 ?31370)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 5810 with 25599 at 1,2 +Id : 25949, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (divide (divide (divide ?31370 ?31371) ?31372) (divide ?31373 ?31372))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25948 with 25599 at 1,1,3 +Id : 25950, {_}: inverse (multiply (divide ?31368 ?31369) (divide ?31369 (inverse (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373))))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25949 with 25599 at 1,2,2,1,2 +Id : 26071, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= inverse (divide (multiply ?31368 (divide ?31370 ?31371)) ?31373) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 25950 with 3 at 2,1,2 +Id : 26655, {_}: inverse (multiply (divide ?31368 ?31369) (multiply ?31369 (multiply (divide (divide ?31370 ?31371) ?31372) (divide ?31372 ?31373)))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31373, 31372, 31371, 31370, 31369, 31368] by Demod 26071 with 26405 at 3 +Id : 5834, {_}: inverse (divide (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31561 ?31560)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Super 5809 with 2 at 1,1,3 +Id : 25943, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (divide ?31559 (divide ?31561 (divide ?31557 ?31556))) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 5834 with 25599 at 1,2 +Id : 25944, {_}: inverse (multiply (divide (inverse (divide (divide (divide ?31556 ?31557) ?31558) (divide ?31559 ?31558))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25943 with 25599 at 1,3 +Id : 25945, {_}: inverse (multiply (divide (inverse (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) ?31560) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31560, 31559, 31558, 31557, 31556] by Demod 25944 with 25599 at 1,1,1,1,2 +Id : 26832, {_}: inverse (multiply (inverse (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)))) (divide ?31560 ?31561)) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31561, 31559, 31558, 31557, 31556, 31560] by Demod 25945 with 26764 at 1,1,2 +Id : 26966, {_}: multiply (inverse ?135418) ?135419 =<= inverse (multiply (inverse ?135419) ?135418) [135419, 135418] by Super 3 with 26764 at 3 +Id : 27298, {_}: multiply (inverse (divide ?31560 ?31561)) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31561, 31560] by Demod 26832 with 26966 at 2 +Id : 27299, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= inverse (multiply ?31559 (divide (divide ?31557 ?31556) ?31561)) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27298 with 26405 at 1,2 +Id : 27300, {_}: inverse (inverse (multiply ?31373 (divide (divide ?31371 ?31370) ?31368))) =>= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 26655 with 27299 at 1,2 +Id : 27254, {_}: inverse (inverse (multiply ?134958 ?134959)) =>= multiply ?134958 ?134959 [134959, 134958] by Demod 26900 with 3 at 3 +Id : 27506, {_}: multiply ?31373 (divide (divide ?31371 ?31370) ?31368) =<= divide ?31373 (multiply ?31368 (divide ?31370 ?31371)) [31368, 31370, 31371, 31373] by Demod 27300 with 27254 at 2 +Id : 31741, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (divide (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?132 ?133)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31740 with 27506 at 2,1,2 +Id : 31742, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (divide ?136 (divide (divide ?133 ?132) (divide ?134 ?135))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 135, 134, 132, 133, 136, 137, 138] by Demod 31741 with 25599 at 2,2,1,2 +Id : 31743, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (divide (divide ?134 ?135) (divide ?133 ?132))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 132, 133, 135, 134, 136, 137, 138] by Demod 31742 with 25599 at 1,2,2,1,2 +Id : 31744, {_}: multiply (multiply (divide ?138 ?137) (multiply ?137 (multiply (multiply ?136 (multiply (divide ?134 ?135) (divide ?132 ?133))) (divide ?133 ?132)))) (multiply (divide (divide ?135 ?134) ?139) (divide ?139 ?136)) =>= ?138 [139, 133, 132, 135, 134, 136, 137, 138] by Demod 31743 with 25599 at 2,1,2,2,1,2 +Id : 31835, {_}: ?147320 =<= multiply (divide ?147320 (multiply (multiply (divide ?147321 ?147322) (multiply ?147322 (multiply (multiply ?147323 (multiply (divide ?147324 ?147325) (divide ?147326 ?147327))) (divide ?147327 ?147326)))) (multiply (divide (divide ?147325 ?147324) ?147328) (divide ?147328 ?147323)))) ?147321 [147328, 147327, 147326, 147325, 147324, 147323, 147322, 147321, 147320] by Super 27821 with 31744 at 2,3 +Id : 32201, {_}: ?147320 =<= multiply (divide ?147320 ?147321) ?147321 [147321, 147320] by Demod 31835 with 31744 at 2,1,3 +Id : 835, {_}: divide (divide (inverse (divide (divide (divide ?4527 ?4528) ?4529) ?4530)) (divide ?4528 ?4527)) ?4529 =>= ?4530 [4530, 4529, 4528, 4527] by Super 17 with 20 at 1,2 +Id : 25994, {_}: divide (multiply (inverse (divide (divide (divide ?4527 ?4528) ?4529) ?4530)) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4530, 4529, 4528, 4527] by Demod 835 with 25599 at 1,2 +Id : 26651, {_}: divide (multiply (divide ?4530 (divide (divide ?4527 ?4528) ?4529)) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4529, 4528, 4527, 4530] by Demod 25994 with 26405 at 1,1,2 +Id : 26667, {_}: divide (multiply (multiply ?4530 (divide ?4529 (divide ?4527 ?4528))) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4528, 4527, 4529, 4530] by Demod 26651 with 25599 at 1,1,2 +Id : 26668, {_}: divide (multiply (multiply ?4530 (multiply ?4529 (divide ?4528 ?4527))) (divide ?4527 ?4528)) ?4529 =>= ?4530 [4527, 4528, 4529, 4530] by Demod 26667 with 25599 at 2,1,1,2 +Id : 32718, {_}: divide (multiply ?151970 (divide ?151971 ?151972)) ?151973 =?= divide ?151970 (multiply ?151973 (divide ?151972 ?151971)) [151973, 151972, 151971, 151970] by Super 26668 with 32201 at 1,1,2 +Id : 42767, {_}: divide (multiply ?174190 (divide ?174191 ?174192)) ?174193 =>= multiply ?174190 (divide (divide ?174191 ?174192) ?174193) [174193, 174192, 174191, 174190] by Demod 32718 with 27506 at 3 +Id : 25986, {_}: inverse (divide (multiply (divide ?1024 ?1025) ?1026) (multiply (multiply ?1027 (divide ?1024 ?1025)) ?1026)) =>= ?1027 [1027, 1026, 1025, 1024] by Demod 232 with 25599 at 1,2,1,2 +Id : 26619, {_}: divide (multiply (multiply ?1027 (divide ?1024 ?1025)) ?1026) (multiply (divide ?1024 ?1025) ?1026) =>= ?1027 [1026, 1025, 1024, 1027] by Demod 25986 with 26405 at 2 +Id : 42770, {_}: divide (multiply ?174208 ?174209) ?174210 =<= multiply ?174208 (divide (divide (multiply (multiply ?174209 (divide ?174211 ?174212)) ?174213) (multiply (divide ?174211 ?174212) ?174213)) ?174210) [174213, 174212, 174211, 174210, 174209, 174208] by Super 42767 with 26619 at 2,1,2 +Id : 43287, {_}: divide (multiply ?174208 ?174209) ?174210 =>= multiply ?174208 (divide ?174209 ?174210) [174210, 174209, 174208] by Demod 42770 with 26619 at 1,2,3 +Id : 45294, {_}: multiply ?177592 ?177593 =<= multiply (multiply ?177592 (divide ?177593 ?177594)) ?177594 [177594, 177593, 177592] by Super 32201 with 43287 at 1,3 +Id : 25967, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (divide (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?83 ?87)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 20 with 25599 at 2 +Id : 25968, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (divide (divide (divide ?85 ?84) ?86) (divide ?82 ?86))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 25967 with 25599 at 1,3 +Id : 25969, {_}: multiply (inverse (divide (divide (divide ?80 ?81) ?82) ?83)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 83, 82, 81, 80] by Demod 25968 with 25599 at 2,1,1,1,3 +Id : 26616, {_}: multiply (divide ?83 (divide (divide ?80 ?81) ?82)) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 82, 81, 80, 83] by Demod 25969 with 26405 at 1,2 +Id : 26679, {_}: multiply (multiply ?83 (divide ?82 (divide ?80 ?81))) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 81, 80, 82, 83] by Demod 26616 with 25599 at 1,2 +Id : 26680, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= inverse (multiply (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) (divide ?87 ?83)) [87, 86, 85, 84, 80, 81, 82, 83] by Demod 26679 with 25599 at 2,1,2 +Id : 28666, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= divide (divide ?83 ?87) (divide (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82))) ?87) [86, 85, 84, 87, 80, 81, 82, 83] by Demod 26680 with 26724 at 3 +Id : 28715, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (divide ?87 (multiply (divide ?84 ?85) (multiply (divide (divide ?85 ?84) ?86) (divide ?86 ?82)))) [86, 85, 84, 87, 80, 81, 82, 83] by Demod 28666 with 25599 at 3 +Id : 28664, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= divide (divide ?31561 (divide ?31557 ?31556)) ?31559 [31559, 31558, 31557, 31556, 31560, 31561] by Demod 27299 with 26724 at 3 +Id : 28717, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= divide (multiply ?31561 (divide ?31556 ?31557)) ?31559 [31559, 31558, 31557, 31556, 31560, 31561] by Demod 28664 with 25599 at 1,3 +Id : 32902, {_}: divide (multiply ?151970 (divide ?151971 ?151972)) ?151973 =>= multiply ?151970 (divide (divide ?151971 ?151972) ?151973) [151973, 151972, 151971, 151970] by Demod 32718 with 27506 at 3 +Id : 42552, {_}: multiply (divide ?31561 ?31560) (multiply ?31560 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559))) =>= multiply ?31561 (divide (divide ?31556 ?31557) ?31559) [31559, 31558, 31557, 31556, 31560, 31561] by Demod 28717 with 32902 at 3 +Id : 10, {_}: divide (inverse (divide (divide (divide ?43 ?44) (inverse ?45)) (multiply ?46 ?45))) (divide ?44 ?43) =>= ?46 [46, 45, 44, 43] by Super 2 with 3 at 2,1,1,2 +Id : 58, {_}: divide (inverse (divide (multiply (divide ?293 ?294) ?295) (multiply ?296 ?295))) (divide ?294 ?293) =>= ?296 [296, 295, 294, 293] by Demod 10 with 3 at 1,1,1,2 +Id : 66, {_}: divide (inverse (divide (multiply (multiply ?349 ?350) ?351) (multiply ?352 ?351))) (divide (inverse ?350) ?349) =>= ?352 [352, 351, 350, 349] by Super 58 with 3 at 1,1,1,1,2 +Id : 5845, {_}: inverse (divide (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31658 ?31657)) =>= inverse (divide ?31656 (divide ?31658 (divide (inverse ?31654) ?31653))) [31658, 31657, 31656, 31655, 31654, 31653] by Super 5809 with 66 at 1,1,3 +Id : 25939, {_}: inverse (multiply (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31657 ?31658)) =>= inverse (divide ?31656 (divide ?31658 (divide (inverse ?31654) ?31653))) [31658, 31657, 31656, 31655, 31654, 31653] by Demod 5845 with 25599 at 1,2 +Id : 25940, {_}: inverse (multiply (divide (inverse (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (divide (inverse ?31654) ?31653) ?31658)) [31658, 31657, 31656, 31655, 31654, 31653] by Demod 25939 with 25599 at 1,3 +Id : 26656, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (divide (inverse ?31654) ?31653) ?31658)) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 25940 with 26405 at 1,1,1,2 +Id : 26874, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (divide (inverse (multiply ?31653 ?31654)) ?31658)) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26656 with 26764 at 1,2,1,3 +Id : 26875, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (multiply ?31656 (inverse (multiply ?31658 (multiply ?31653 ?31654)))) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26874 with 26764 at 2,1,3 +Id : 11, {_}: divide (inverse (divide (divide (multiply ?48 ?49) ?50) (divide ?51 ?50))) (divide (inverse ?49) ?48) =>= ?51 [51, 50, 49, 48] by Super 2 with 3 at 1,1,1,1,2 +Id : 5813, {_}: inverse (divide (divide ?31391 ?31392) (divide (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))) ?31392)) =>= inverse (divide (divide ?31391 (divide (inverse ?31394) ?31393)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Super 5809 with 11 at 2,1,3 +Id : 26012, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))))) =>= inverse (divide (divide ?31391 (divide (inverse ?31394) ?31393)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 5813 with 25599 at 1,2 +Id : 26013, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (divide (divide (multiply ?31393 ?31394) ?31395) (divide ?31396 ?31395))))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26012 with 25599 at 1,1,3 +Id : 26014, {_}: inverse (multiply (divide ?31391 ?31392) (divide ?31392 (inverse (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396))))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26013 with 25599 at 1,2,2,1,2 +Id : 26060, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= inverse (divide (multiply ?31391 (divide ?31393 (inverse ?31394))) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26014 with 3 at 2,1,2 +Id : 26061, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= inverse (divide (multiply ?31391 (multiply ?31393 ?31394)) ?31396) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26060 with 3 at 2,1,1,3 +Id : 26649, {_}: inverse (multiply (divide ?31391 ?31392) (multiply ?31392 (multiply (divide (multiply ?31393 ?31394) ?31395) (divide ?31395 ?31396)))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31396, 31395, 31394, 31393, 31392, 31391] by Demod 26061 with 26405 at 3 +Id : 5837, {_}: inverse (divide (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31584 ?31583)) =>= inverse (divide ?31582 (divide ?31584 (divide (inverse ?31580) ?31579))) [31584, 31583, 31582, 31581, 31580, 31579] by Super 5809 with 11 at 1,1,3 +Id : 26017, {_}: inverse (multiply (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31583 ?31584)) =>= inverse (divide ?31582 (divide ?31584 (divide (inverse ?31580) ?31579))) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 5837 with 25599 at 1,2 +Id : 26018, {_}: inverse (multiply (divide (inverse (divide (divide (multiply ?31579 ?31580) ?31581) (divide ?31582 ?31581))) ?31583) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 26017 with 25599 at 1,3 +Id : 26019, {_}: inverse (multiply (divide (inverse (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) ?31583) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31583, 31582, 31581, 31580, 31579] by Demod 26018 with 25599 at 1,1,1,1,2 +Id : 26844, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (divide (inverse ?31580) ?31579) ?31584)) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26019 with 26764 at 1,1,2 +Id : 26845, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (divide (inverse (multiply ?31579 ?31580)) ?31584)) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26844 with 26764 at 1,2,1,3 +Id : 26846, {_}: inverse (multiply (inverse (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582)))) (divide ?31583 ?31584)) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31584, 31582, 31581, 31580, 31579, 31583] by Demod 26845 with 26764 at 2,1,3 +Id : 27296, {_}: multiply (inverse (divide ?31583 ?31584)) (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31582, 31581, 31580, 31579, 31584, 31583] by Demod 26846 with 26966 at 2 +Id : 27301, {_}: multiply (divide ?31584 ?31583) (multiply ?31583 (multiply (divide (multiply ?31579 ?31580) ?31581) (divide ?31581 ?31582))) =>= inverse (multiply ?31582 (inverse (multiply ?31584 (multiply ?31579 ?31580)))) [31582, 31581, 31580, 31579, 31583, 31584] by Demod 27296 with 26405 at 1,2 +Id : 27302, {_}: inverse (inverse (multiply ?31396 (inverse (multiply ?31391 (multiply ?31393 ?31394))))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31394, 31393, 31391, 31396] by Demod 26649 with 27301 at 1,2 +Id : 27505, {_}: multiply ?31396 (inverse (multiply ?31391 (multiply ?31393 ?31394))) =>= divide ?31396 (multiply ?31391 (multiply ?31393 ?31394)) [31394, 31393, 31391, 31396] by Demod 27302 with 27254 at 2 +Id : 27520, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= inverse (divide ?31656 (multiply ?31658 (multiply ?31653 ?31654))) [31658, 31657, 31654, 31653, 31655, 31656] by Demod 26875 with 27505 at 1,3 +Id : 27523, {_}: inverse (multiply (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) (divide ?31657 ?31658)) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31658, 31657, 31654, 31653, 31655, 31656] by Demod 27520 with 26405 at 3 +Id : 28682, {_}: divide (divide ?31658 ?31657) (divide (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655)) ?31657) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31654, 31653, 31655, 31656, 31657, 31658] by Demod 27523 with 26724 at 2 +Id : 28683, {_}: multiply (divide ?31658 ?31657) (divide ?31657 (divide (multiply ?31656 ?31655) (multiply (multiply ?31653 ?31654) ?31655))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31654, 31653, 31655, 31656, 31657, 31658] by Demod 28682 with 25599 at 2 +Id : 28684, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (divide (multiply (multiply ?31653 ?31654) ?31655) (multiply ?31656 ?31655))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31656, 31655, 31654, 31653, 31657, 31658] by Demod 28683 with 25599 at 2,2 +Id : 43520, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= divide (multiply ?31658 (multiply ?31653 ?31654)) ?31656 [31656, 31655, 31654, 31653, 31657, 31658] by Demod 28684 with 43287 at 2,2,2 +Id : 43521, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= multiply ?31658 (divide (multiply ?31653 ?31654) ?31656) [31656, 31655, 31654, 31653, 31657, 31658] by Demod 43520 with 43287 at 3 +Id : 43522, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (divide ?31655 (multiply ?31656 ?31655)))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31655, 31654, 31653, 31657, 31658] by Demod 43521 with 43287 at 2,3 +Id : 22472, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (divide (inverse ?116248) ?116247) [116248, 116247, 116246] by Super 22416 with 3 at 2,1,3 +Id : 26848, {_}: ?116246 =<= multiply (multiply ?116246 (multiply ?116247 ?116248)) (inverse (multiply ?116247 ?116248)) [116248, 116247, 116246] by Demod 22472 with 26764 at 2,3 +Id : 27823, {_}: ?116246 =<= divide (multiply ?116246 (multiply ?116247 ?116248)) (multiply ?116247 ?116248) [116248, 116247, 116246] by Demod 26848 with 27734 at 3 +Id : 31832, {_}: ?147291 =<= divide (multiply ?147291 (multiply (multiply (divide ?147292 ?147293) (multiply ?147293 (multiply (multiply ?147294 (multiply (divide ?147295 ?147296) (divide ?147297 ?147298))) (divide ?147298 ?147297)))) (multiply (divide (divide ?147296 ?147295) ?147299) (divide ?147299 ?147294)))) ?147292 [147299, 147298, 147297, 147296, 147295, 147294, 147293, 147292, 147291] by Super 27823 with 31744 at 2,3 +Id : 32203, {_}: ?147291 =<= divide (multiply ?147291 ?147292) ?147292 [147292, 147291] by Demod 31832 with 31744 at 2,1,3 +Id : 33094, {_}: inverse ?153200 =<= divide ?153201 (multiply ?153200 ?153201) [153201, 153200] by Super 26405 with 32203 at 1,2 +Id : 43571, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply (multiply ?31653 ?31654) (inverse ?31656))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43522 with 33094 at 2,2,2,2 +Id : 43572, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (divide (multiply ?31653 ?31654) ?31656)) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43571 with 27734 at 2,2,2 +Id : 43573, {_}: multiply (divide ?31658 ?31657) (multiply ?31657 (multiply ?31653 (divide ?31654 ?31656))) =>= multiply ?31658 (multiply ?31653 (divide ?31654 ?31656)) [31656, 31654, 31653, 31657, 31658] by Demod 43572 with 43287 at 2,2,2 +Id : 43575, {_}: multiply ?31561 (multiply (divide (divide ?31556 ?31557) ?31558) (divide ?31558 ?31559)) =>= multiply ?31561 (divide (divide ?31556 ?31557) ?31559) [31559, 31558, 31557, 31556, 31561] by Demod 42552 with 43573 at 2 +Id : 43578, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (divide ?87 (multiply (divide ?84 ?85) (divide (divide ?85 ?84) ?82))) [85, 84, 87, 80, 81, 82, 83] by Demod 28715 with 43575 at 2,2,3 +Id : 43604, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (divide ?83 ?87) (multiply ?87 (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85))) [84, 85, 87, 80, 81, 82, 83] by Demod 43578 with 27506 at 2,3 +Id : 243, {_}: inverse (divide (multiply (divide ?1104 ?1105) ?1106) (multiply (divide ?1107 (divide ?1105 ?1104)) ?1106)) =>= ?1107 [1107, 1106, 1105, 1104] by Demod 213 with 3 at 1,1,2 +Id : 748, {_}: inverse (divide (multiply (divide (inverse ?3864) ?3865) ?3866) (multiply (divide ?3867 (multiply ?3865 ?3864)) ?3866)) =>= ?3867 [3867, 3866, 3865, 3864] by Super 243 with 3 at 2,1,2,1,2 +Id : 753, {_}: inverse (divide (multiply (divide (inverse (divide (divide (divide ?3899 ?3900) ?3901) (divide ?3902 ?3901))) (divide ?3900 ?3899)) ?3903) (multiply ?3904 ?3903)) =?= inverse (divide (divide ?3902 ?3905) (divide ?3904 ?3905)) [3905, 3904, 3903, 3902, 3901, 3900, 3899] by Super 748 with 272 at 1,2,1,2 +Id : 773, {_}: inverse (divide (multiply ?3902 ?3903) (multiply ?3904 ?3903)) =?= inverse (divide (divide ?3902 ?3905) (divide ?3904 ?3905)) [3905, 3904, 3903, 3902] by Demod 753 with 2 at 1,1,1,2 +Id : 15665, {_}: inverse (divide (multiply (divide ?84988 (divide ?84989 ?84990)) ?84991) (multiply (divide ?84992 ?84993) ?84991)) =>= divide (divide (inverse (divide ?84993 ?84992)) (divide ?84990 ?84989)) ?84988 [84993, 84992, 84991, 84990, 84989, 84988] by Super 773 with 14284 at 3 +Id : 15692, {_}: inverse (divide (multiply (divide ?85261 (divide ?85262 ?85263)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (divide (inverse (divide (inverse ?85266) ?85265)) (divide ?85263 ?85262)) ?85261 [85266, 85265, 85264, 85263, 85262, 85261] by Super 15665 with 3 at 1,2,1,2 +Id : 25923, {_}: inverse (divide (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (divide (inverse (divide (inverse ?85266) ?85265)) (divide ?85263 ?85262)) ?85261 [85266, 85265, 85264, 85262, 85263, 85261] by Demod 15692 with 25599 at 1,1,1,2 +Id : 25924, {_}: inverse (divide (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) (multiply (multiply ?85265 ?85266) ?85264)) =>= divide (multiply (inverse (divide (inverse ?85266) ?85265)) (divide ?85262 ?85263)) ?85261 [85266, 85265, 85264, 85262, 85263, 85261] by Demod 25923 with 25599 at 1,3 +Id : 26606, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (inverse (divide (inverse ?85266) ?85265)) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 25924 with 26405 at 2 +Id : 26607, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (divide ?85265 (inverse ?85266)) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26606 with 26405 at 1,1,3 +Id : 26682, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= divide (multiply (multiply ?85265 ?85266) (divide ?85262 ?85263)) ?85261 [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26607 with 3 at 1,1,3 +Id : 42547, {_}: divide (multiply (multiply ?85265 ?85266) ?85264) (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85264, 85266, 85265] by Demod 26682 with 32902 at 3 +Id : 43537, {_}: multiply (multiply ?85265 ?85266) (divide ?85264 (multiply (multiply ?85261 (divide ?85263 ?85262)) ?85264)) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85264, 85266, 85265] by Demod 42547 with 43287 at 2 +Id : 43538, {_}: multiply (multiply ?85265 ?85266) (inverse (multiply ?85261 (divide ?85263 ?85262))) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43537 with 33094 at 2,2 +Id : 43539, {_}: divide (multiply ?85265 ?85266) (multiply ?85261 (divide ?85263 ?85262)) =>= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43538 with 27734 at 2 +Id : 43540, {_}: multiply ?85265 (divide ?85266 (multiply ?85261 (divide ?85263 ?85262))) =?= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85262, 85263, 85261, 85266, 85265] by Demod 43539 with 43287 at 2 +Id : 43541, {_}: multiply ?85265 (multiply ?85266 (divide (divide ?85262 ?85263) ?85261)) =?= multiply (multiply ?85265 ?85266) (divide (divide ?85262 ?85263) ?85261) [85261, 85263, 85262, 85266, 85265] by Demod 43540 with 27506 at 2,2 +Id : 43605, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply (multiply (divide ?83 ?87) ?87) (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85)) [84, 85, 87, 80, 81, 82, 83] by Demod 43604 with 43541 at 3 +Id : 43606, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply ?83 (divide (divide ?82 (divide ?85 ?84)) (divide ?84 ?85)) [84, 85, 80, 81, 82, 83] by Demod 43605 with 32201 at 1,3 +Id : 43607, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =?= multiply ?83 (multiply (divide ?82 (divide ?85 ?84)) (divide ?85 ?84)) [84, 85, 80, 81, 82, 83] by Demod 43606 with 25599 at 2,3 +Id : 43608, {_}: multiply (multiply ?83 (multiply ?82 (divide ?81 ?80))) (divide ?80 ?81) =>= multiply ?83 ?82 [80, 81, 82, 83] by Demod 43607 with 32201 at 2,3 +Id : 45322, {_}: multiply (multiply ?177731 (multiply ?177732 (divide ?177733 ?177734))) ?177734 =>= multiply (multiply ?177731 ?177732) ?177733 [177734, 177733, 177732, 177731] by Super 45294 with 43608 at 1,3 +Id : 45299, {_}: multiply ?177614 (multiply ?177615 ?177616) =<= multiply (multiply ?177614 (multiply ?177615 (divide ?177616 ?177617))) ?177617 [177617, 177616, 177615, 177614] by Super 45294 with 43287 at 2,1,3 +Id : 64505, {_}: multiply ?177731 (multiply ?177732 ?177733) =?= multiply (multiply ?177731 ?177732) ?177733 [177733, 177732, 177731] by Demod 45322 with 45299 at 2 +Id : 64928, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 64505 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP477-1.p +23952: solved GRP477-1.p in 16.221013 using nrkbo +23952: status Unsatisfiable for GRP477-1.p +NO CLASH, using fixed ground order +23966: Facts: +23966: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23966: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23966: Goal: +23966: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23966: Order: +23966: nrkbo +23966: Leaf order: +23966: a1 2 0 2 1,1,2 +23966: b1 2 0 2 1,1,3 +23966: inverse 4 1 2 0,1,2 +23966: multiply 3 2 2 0,2 +23966: divide 7 2 0 +NO CLASH, using fixed ground order +23967: Facts: +23967: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23967: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23967: Goal: +23967: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23967: Order: +23967: kbo +23967: Leaf order: +23967: a1 2 0 2 1,1,2 +23967: b1 2 0 2 1,1,3 +23967: inverse 4 1 2 0,1,2 +23967: multiply 3 2 2 0,2 +23967: divide 7 2 0 +NO CLASH, using fixed ground order +23968: Facts: +23968: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23968: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23968: Goal: +23968: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +23968: Order: +23968: lpo +23968: Leaf order: +23968: a1 2 0 2 1,1,2 +23968: b1 2 0 2 1,1,3 +23968: inverse 4 1 2 0,1,2 +23968: multiply 3 2 2 0,2 +23968: divide 7 2 0 +% SZS status Timeout for GRP478-1.p +NO CLASH, using fixed ground order +23995: Facts: +23995: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23995: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23995: Goal: +23995: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23995: Order: +23995: nrkbo +23995: Leaf order: +23995: b2 2 0 2 1,1,1,2 +23995: a2 2 0 2 2,2 +23995: inverse 3 1 1 0,1,1,2 +23995: multiply 3 2 2 0,2 +23995: divide 7 2 0 +NO CLASH, using fixed ground order +23996: Facts: +23996: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23996: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23996: Goal: +23996: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23996: Order: +23996: kbo +23996: Leaf order: +23996: b2 2 0 2 1,1,1,2 +23996: a2 2 0 2 2,2 +23996: inverse 3 1 1 0,1,1,2 +23996: multiply 3 2 2 0,2 +23996: divide 7 2 0 +NO CLASH, using fixed ground order +23997: Facts: +23997: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +23997: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +23997: Goal: +23997: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +23997: Order: +23997: lpo +23997: Leaf order: +23997: b2 2 0 2 1,1,1,2 +23997: a2 2 0 2 2,2 +23997: inverse 3 1 1 0,1,1,2 +23997: multiply 3 2 2 0,2 +23997: divide 7 2 0 +Statistics : +Max weight : 78 +Found proof, 37.151334s +% SZS status Unsatisfiable for GRP479-1.p +% SZS output start CNFRefutation for GRP479-1.p +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2 +Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2 +Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2 +Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2 +Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2 +Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2 +Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2 +Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2 +Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2 +Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2 +Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2 +Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2 +Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2 +Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2 +Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2 +Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2 +Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2 +Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2 +Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2 +Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2 +Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2 +Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2 +Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3 +Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2 +Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3 +Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2 +Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3 +Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2 +Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3 +Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3 +Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2 +Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2 +Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2 +Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2 +Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2 +Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2 +Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2 +Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2 +Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2 +Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2 +Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2 +Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2 +Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2 +Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2 +Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3 +Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2 +Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3 +Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3 +Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3 +Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2 +Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3 +Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2 +Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2 +Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2 +Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2 +Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3 +Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2 +Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2 +Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2 +Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2 +Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3 +Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2 +Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3 +Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2 +Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2 +Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2 +Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2 +Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2 +Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2 +Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2 +Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2 +Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2 +Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2 +Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3 +Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2 +Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2 +Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2 +Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2 +Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2 +Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2 +Id : 102470, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2 +Id : 102471, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102470 with 101980 at 2,2 +Id : 102472, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102471 at 2,3 +Id : 102516, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102472 with 101980 at 2,3 +Id : 102787, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102516 with 102471 at 1,2 +Id : 102959, {_}: inverse (divide ?539857 ?539858) =>= divide ?539858 ?539857 [539858, 539857] by Demod 102787 with 102471 at 3 +Id : 102980, {_}: inverse (multiply ?539955 ?539956) =<= divide (inverse ?539956) ?539955 [539956, 539955] by Super 102959 with 3 at 1,2 +Id : 103330, {_}: multiply (inverse ?540510) ?540511 =<= inverse (multiply (inverse ?540511) ?540510) [540511, 540510] by Super 3 with 102980 at 3 +Id : 93587, {_}: multiply (inverse (divide ?504068 ?504070)) ?504068 =>= ?504070 [504070, 504068] by Demod 92186 with 93111 at 2,2 +Id : 96346, {_}: multiply ?522565 (divide ?522566 ?522566) =>= ?522565 [522566, 522565] by Super 93587 with 93886 at 1,2 +Id : 96425, {_}: multiply ?523023 (multiply (inverse ?523024) ?523024) =>= ?523023 [523024, 523023] by Super 96346 with 3 at 2,2 +Id : 103339, {_}: multiply (inverse (multiply (inverse ?540545) ?540545)) ?540546 =>= inverse (inverse ?540546) [540546, 540545] by Super 103330 with 96425 at 1,3 +Id : 103110, {_}: multiply (inverse ?540161) ?540162 =<= inverse (multiply (inverse ?540162) ?540161) [540162, 540161] by Super 3 with 102980 at 3 +Id : 103424, {_}: multiply (multiply (inverse ?540545) ?540545) ?540546 =>= inverse (inverse ?540546) [540546, 540545] by Demod 103339 with 103110 at 1,2 +Id : 103425, {_}: multiply (multiply (inverse ?540545) ?540545) ?540546 =>= ?540546 [540546, 540545] by Demod 103424 with 101328 at 3 +Id : 104863, {_}: a2 === a2 [] by Demod 1 with 103425 at 2 +Id : 1, {_}: multiply (multiply (inverse b2) b2) a2 =>= a2 [] by prove_these_axioms_2 +% SZS output end CNFRefutation for GRP479-1.p +23995: solved GRP479-1.p in 37.162321 using nrkbo +23995: status Unsatisfiable for GRP479-1.p +NO CLASH, using fixed ground order +24007: Facts: +24007: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +24007: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +24007: Goal: +24007: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +24007: Order: +24007: nrkbo +24007: Leaf order: +24007: a3 2 0 2 1,1,2 +24007: b3 2 0 2 2,1,2 +24007: c3 2 0 2 2,2 +24007: inverse 2 1 0 +24007: multiply 5 2 4 0,2 +24007: divide 7 2 0 +NO CLASH, using fixed ground order +24008: Facts: +24008: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +24008: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +24008: Goal: +24008: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +24008: Order: +24008: kbo +24008: Leaf order: +24008: a3 2 0 2 1,1,2 +24008: b3 2 0 2 2,1,2 +24008: c3 2 0 2 2,2 +24008: inverse 2 1 0 +24008: multiply 5 2 4 0,2 +24008: divide 7 2 0 +NO CLASH, using fixed ground order +24009: Facts: +24009: Id : 2, {_}: + divide + (inverse + (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) + ?5 + =>= + ?4 + [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +24009: Id : 3, {_}: + multiply ?7 ?8 =<= divide ?7 (inverse ?8) + [8, 7] by multiply ?7 ?8 +24009: Goal: +24009: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +24009: Order: +24009: lpo +24009: Leaf order: +24009: a3 2 0 2 1,1,2 +24009: b3 2 0 2 2,1,2 +24009: c3 2 0 2 2,2 +24009: inverse 2 1 0 +24009: multiply 5 2 4 0,2 +24009: divide 7 2 0 +Statistics : +Max weight : 78 +Found proof, 40.781292s +% SZS status Unsatisfiable for GRP480-1.p +% SZS output start CNFRefutation for GRP480-1.p +Id : 3, {_}: multiply ?7 ?8 =<= divide ?7 (inverse ?8) [8, 7] by multiply ?7 ?8 +Id : 2, {_}: divide (inverse (divide (divide (divide ?2 ?2) ?3) (divide ?4 (divide ?3 ?5)))) ?5 =>= ?4 [5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 +Id : 4, {_}: divide (inverse (divide (divide (divide ?10 ?10) ?11) (divide ?12 (divide ?11 ?13)))) ?13 =>= ?12 [13, 12, 11, 10] by single_axiom ?10 ?11 ?12 ?13 +Id : 5, {_}: divide (inverse (divide (divide (divide ?15 ?15) (inverse (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19))))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Super 4 with 2 at 2,2,1,1,2 +Id : 22, {_}: divide (inverse (divide (multiply (divide ?87 ?87) (divide (divide (divide ?88 ?88) ?89) (divide ?90 (divide ?89 ?91)))) (divide ?92 ?90))) ?91 =>= ?92 [92, 91, 90, 89, 88, 87] by Demod 5 with 3 at 1,1,1,2 +Id : 23, {_}: divide (inverse (divide (multiply (divide ?94 ?94) (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98)))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95, 94] by Super 22 with 2 at 2,1,1,2 +Id : 18, {_}: divide (inverse (divide (multiply (divide ?15 ?15) (divide (divide (divide ?16 ?16) ?17) (divide ?18 (divide ?17 ?19)))) (divide ?20 ?18))) ?19 =>= ?20 [20, 19, 18, 17, 16, 15] by Demod 5 with 3 at 1,1,1,2 +Id : 1304, {_}: inverse (divide (divide (divide ?6515 ?6515) ?6516) (divide (divide ?6517 ?6518) (divide ?6516 ?6518))) =>= ?6517 [6518, 6517, 6516, 6515] by Super 18 with 23 at 2 +Id : 2998, {_}: inverse (divide (divide (multiply (inverse ?16319) ?16319) ?16320) (divide (divide ?16321 ?16322) (divide ?16320 ?16322))) =>= ?16321 [16322, 16321, 16320, 16319] by Super 1304 with 3 at 1,1,1,2 +Id : 3072, {_}: inverse (divide (multiply (multiply (inverse ?16865) ?16865) ?16866) (divide (divide ?16867 ?16868) (divide (inverse ?16866) ?16868))) =>= ?16867 [16868, 16867, 16866, 16865] by Super 2998 with 3 at 1,1,2 +Id : 1319, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (divide ?6632 (inverse ?6633)) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Super 1304 with 3 at 2,2,1,2 +Id : 1369, {_}: inverse (divide (divide (divide ?6630 ?6630) ?6631) (divide (multiply ?6632 ?6633) (multiply ?6631 ?6633))) =>= ?6632 [6633, 6632, 6631, 6630] by Demod 1319 with 3 at 1,2,1,2 +Id : 1389, {_}: multiply ?6881 (divide (divide (divide ?6882 ?6882) ?6883) (divide (multiply ?6884 ?6885) (multiply ?6883 ?6885))) =>= divide ?6881 ?6884 [6885, 6884, 6883, 6882, 6881] by Super 3 with 1369 at 2,3 +Id : 8, {_}: divide (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) (inverse ?34) =>= ?33 [34, 33, 32, 31] by Super 2 with 3 at 2,2,1,1,2 +Id : 15, {_}: multiply (inverse (divide (divide (divide ?31 ?31) ?32) (divide ?33 (multiply ?32 ?34)))) ?34 =>= ?33 [34, 33, 32, 31] by Demod 8 with 3 at 2 +Id : 6, {_}: divide (inverse (divide (divide (divide ?22 ?22) ?23) ?24)) ?25 =?= inverse (divide (divide (divide ?26 ?26) ?27) (divide ?24 (divide ?27 (divide ?23 ?25)))) [27, 26, 25, 24, 23, 22] by Super 4 with 2 at 2,1,1,2 +Id : 86, {_}: divide (divide (inverse (divide (divide (divide ?404 ?404) ?405) ?406)) ?407) (divide ?405 ?407) =>= ?406 [407, 406, 405, 404] by Super 2 with 6 at 1,2 +Id : 193, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (divide ?904 (inverse (divide (divide (divide ?905 ?905) ?904) ?902))) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Super 15 with 86 at 1,1,1,2 +Id : 223, {_}: multiply (inverse (divide ?902 (divide ?903 (multiply (multiply ?904 (divide (divide (divide ?905 ?905) ?904) ?902)) ?906)))) ?906 =>= ?903 [906, 905, 904, 903, 902] by Demod 193 with 3 at 1,2,2,1,1,2 +Id : 30, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (divide ?161 (inverse (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165)))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Super 22 with 18 at 2,2,1,1,1,2 +Id : 42, {_}: divide (inverse (divide (multiply (divide ?157 ?157) (divide (divide (divide ?158 ?158) ?159) ?160)) (multiply ?161 (divide (multiply (divide ?162 ?162) (divide (divide (divide ?163 ?163) ?164) (divide ?165 (divide ?164 (divide ?159 ?166))))) (divide ?160 ?165))))) ?166 =>= ?161 [166, 165, 164, 163, 162, 161, 160, 159, 158, 157] by Demod 30 with 3 at 2,1,1,2 +Id : 202, {_}: divide (divide (inverse (divide (divide (divide ?974 ?974) ?975) ?976)) ?977) (divide ?975 ?977) =>= ?976 [977, 976, 975, 974] by Super 2 with 6 at 1,2 +Id : 208, {_}: divide (divide (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) (inverse ?1021)) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Super 202 with 3 at 2,2 +Id : 372, {_}: divide (multiply (inverse (divide (divide (divide ?1664 ?1664) ?1665) ?1666)) ?1667) (multiply ?1665 ?1667) =>= ?1666 [1667, 1666, 1665, 1664] by Demod 208 with 3 at 1,2 +Id : 378, {_}: divide (multiply (inverse (divide (multiply (divide ?1702 ?1702) ?1703) ?1704)) ?1705) (multiply (inverse ?1703) ?1705) =>= ?1704 [1705, 1704, 1703, 1702] by Super 372 with 3 at 1,1,1,1,2 +Id : 88082, {_}: divide ?485240 (multiply (inverse ?485241) ?485242) =<= divide ?485240 (multiply (multiply ?485243 (divide (divide (divide ?485244 ?485244) ?485243) (multiply (divide ?485245 ?485245) ?485241))) ?485242) [485245, 485244, 485243, 485242, 485241, 485240] by Super 378 with 223 at 1,2 +Id : 89234, {_}: divide (inverse (divide (multiply (divide ?494319 ?494319) (divide (divide (divide ?494320 ?494320) ?494321) ?494322)) (multiply (inverse ?494323) (divide (multiply (divide ?494324 ?494324) (divide (divide (divide ?494325 ?494325) ?494326) (divide ?494327 (divide ?494326 (divide ?494321 ?494328))))) (divide ?494322 ?494327))))) ?494328 =?= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494328, 494327, 494326, 494325, 494324, 494323, 494322, 494321, 494320, 494319] by Super 42 with 88082 at 1,1,2 +Id : 89554, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (multiply (divide ?494331 ?494331) ?494323)) [494331, 494330, 494329, 494323] by Demod 89234 with 42 at 2 +Id : 90512, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide (divide (divide ?497371 ?497371) (multiply ?497372 (divide (divide (divide ?497373 ?497373) ?497372) ?497368))) (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497373, 497372, 497371, 497370, 497369, 497368] by Super 223 with 89554 at 2,2,1,1,2 +Id : 196, {_}: divide (inverse (divide (divide (divide ?925 ?925) ?926) (divide (inverse (divide (divide (divide ?927 ?927) ?928) ?929)) (divide ?926 ?930)))) ?930 =?= inverse (divide (divide (divide ?931 ?931) ?928) ?929) [931, 930, 929, 928, 927, 926, 925] by Super 6 with 86 at 2,1,3 +Id : 6409, {_}: inverse (divide (divide (divide ?34204 ?34204) ?34205) ?34206) =?= inverse (divide (divide (divide ?34207 ?34207) ?34205) ?34206) [34207, 34206, 34205, 34204] by Demod 196 with 2 at 2 +Id : 6420, {_}: inverse (divide (divide (divide ?34278 ?34278) (divide ?34279 (inverse (divide (divide (divide ?34280 ?34280) ?34279) ?34281)))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Super 6409 with 86 at 1,1,3 +Id : 6497, {_}: inverse (divide (divide (divide ?34278 ?34278) (multiply ?34279 (divide (divide (divide ?34280 ?34280) ?34279) ?34281))) ?34282) =>= inverse (divide ?34281 ?34282) [34282, 34281, 34280, 34279, 34278] by Demod 6420 with 3 at 2,1,1,2 +Id : 28325, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= divide ?153090 (inverse (divide ?153094 ?153095)) [153095, 153094, 153093, 153092, 153091, 153090] by Super 3 with 6497 at 2,3 +Id : 28522, {_}: multiply ?153090 (divide (divide (divide ?153091 ?153091) (multiply ?153092 (divide (divide (divide ?153093 ?153093) ?153092) ?153094))) ?153095) =>= multiply ?153090 (divide ?153094 ?153095) [153095, 153094, 153093, 153092, 153091, 153090] by Demod 28325 with 3 at 3 +Id : 91190, {_}: multiply (inverse (divide ?497368 (divide ?497369 (inverse ?497370)))) (divide ?497368 (multiply (divide ?497374 ?497374) ?497370)) =>= ?497369 [497374, 497370, 497369, 497368] by Demod 90512 with 28522 at 2 +Id : 91665, {_}: multiply (inverse (divide ?503116 (multiply ?503117 ?503118))) (divide ?503116 (multiply (divide ?503119 ?503119) ?503118)) =>= ?503117 [503119, 503118, 503117, 503116] by Demod 91190 with 3 at 2,1,1,2 +Id : 231, {_}: divide (multiply (inverse (divide (divide (divide ?1018 ?1018) ?1019) ?1020)) ?1021) (multiply ?1019 ?1021) =>= ?1020 [1021, 1020, 1019, 1018] by Demod 208 with 3 at 1,2 +Id : 1057, {_}: inverse (divide (divide (divide ?5280 ?5280) ?5281) (divide (divide ?5282 ?5283) (divide ?5281 ?5283))) =>= ?5282 [5283, 5282, 5281, 5280] by Super 18 with 23 at 2 +Id : 1292, {_}: divide (divide ?6440 ?6441) (divide ?6442 ?6441) =?= divide (divide ?6440 ?6443) (divide ?6442 ?6443) [6443, 6442, 6441, 6440] by Super 86 with 1057 at 1,1,2 +Id : 2334, {_}: divide (multiply (inverse (divide (divide (divide ?12626 ?12626) ?12627) (divide ?12628 ?12627))) ?12629) (multiply ?12630 ?12629) =>= divide ?12628 ?12630 [12630, 12629, 12628, 12627, 12626] by Super 231 with 1292 at 1,1,1,2 +Id : 91784, {_}: multiply (inverse (divide (multiply (inverse (divide (divide (divide ?504066 ?504066) ?504067) (divide ?504068 ?504067))) ?504069) (multiply ?504070 ?504069))) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504069, 504068, 504067, 504066] by Super 91665 with 2334 at 2,2 +Id : 92186, {_}: multiply (inverse (divide ?504068 ?504070)) (divide ?504068 (divide ?504071 ?504071)) =>= ?504070 [504071, 504070, 504068] by Demod 91784 with 2334 at 1,1,2 +Id : 92346, {_}: ?505751 =<= divide (inverse (divide (divide (divide ?505752 ?505752) ?505753) ?505751)) ?505753 [505753, 505752, 505751] by Super 1389 with 92186 at 2 +Id : 93111, {_}: divide ?509269 (divide ?509270 ?509270) =>= ?509269 [509270, 509269] by Super 2 with 92346 at 2 +Id : 100321, {_}: inverse (multiply (multiply (inverse ?535124) ?535124) ?535125) =>= inverse ?535125 [535125, 535124] by Super 3072 with 93111 at 1,2 +Id : 100420, {_}: inverse (inverse ?535740) =<= inverse (divide (divide (divide ?535741 ?535741) (multiply (inverse ?535742) ?535742)) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535742, 535741, 535740] by Super 100321 with 89554 at 1,2 +Id : 94282, {_}: divide ?515515 (divide ?515516 ?515516) =>= ?515515 [515516, 515515] by Super 2 with 92346 at 2 +Id : 94361, {_}: divide ?515973 (multiply (inverse ?515974) ?515974) =>= ?515973 [515974, 515973] by Super 94282 with 3 at 2,2 +Id : 100488, {_}: inverse (inverse ?535740) =<= inverse (divide (divide ?535741 ?535741) (multiply (divide ?535743 ?535743) ?535740)) [535743, 535741, 535740] by Demod 100420 with 94361 at 1,1,3 +Id : 93886, {_}: inverse (divide (divide ?513000 ?513000) ?513001) =>= ?513001 [513001, 513000] by Super 1369 with 93111 at 1,2 +Id : 100489, {_}: inverse (inverse ?535740) =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100488 with 93886 at 3 +Id : 100522, {_}: divide (inverse (divide (inverse (inverse (divide (divide (divide ?95 ?95) ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96, 95] by Demod 23 with 100489 at 1,1,1,2 +Id : 1348, {_}: inverse (divide (multiply (divide ?6830 ?6830) ?6831) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831, 6830] by Super 1304 with 3 at 1,1,2 +Id : 3107, {_}: multiply ?16917 (divide (multiply (divide ?16918 ?16918) ?16919) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16918, 16917] by Super 3 with 1348 at 2,3 +Id : 100541, {_}: multiply ?16917 (divide (inverse (inverse ?16919)) (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 3107 with 100489 at 1,2,2 +Id : 100747, {_}: inverse (inverse (divide (inverse (inverse ?536517)) (divide (divide ?536518 ?536519) (divide (inverse ?536517) ?536519)))) =?= divide (divide ?536520 ?536520) ?536518 [536520, 536519, 536518, 536517] by Super 100541 with 100489 at 2 +Id : 100526, {_}: inverse (divide (inverse (inverse ?6831)) (divide (divide ?6832 ?6833) (divide (inverse ?6831) ?6833))) =>= ?6832 [6833, 6832, 6831] by Demod 1348 with 100489 at 1,1,2 +Id : 100849, {_}: inverse ?536518 =<= divide (divide ?536520 ?536520) ?536518 [536520, 536518] by Demod 100747 with 100526 at 1,2 +Id : 101259, {_}: divide (inverse (divide (inverse (inverse (divide (inverse ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (divide (divide ?100 ?100) ?101) (divide ?99 (divide ?101 ?97))) [101, 100, 99, 98, 97, 96] by Demod 100522 with 100849 at 1,1,1,1,1,1,2 +Id : 101260, {_}: divide (inverse (divide (inverse (inverse (divide (inverse ?96) (divide ?97 (divide ?96 ?98))))) ?99)) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 99, 98, 97, 96] by Demod 101259 with 100849 at 1,1,3 +Id : 101328, {_}: inverse (inverse ?513001) =>= ?513001 [513001] by Demod 93886 with 100849 at 1,2 +Id : 101498, {_}: divide (inverse (divide (divide (inverse ?96) (divide ?97 (divide ?96 ?98))) ?99)) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 99, 98, 97, 96] by Demod 101260 with 101328 at 1,1,1,2 +Id : 100491, {_}: inverse ?494323 =<= multiply ?494329 (divide (divide (divide ?494330 ?494330) ?494329) (inverse (inverse ?494323))) [494330, 494329, 494323] by Demod 89554 with 100489 at 2,2,3 +Id : 100612, {_}: inverse ?494323 =<= multiply ?494329 (multiply (divide (divide ?494330 ?494330) ?494329) (inverse ?494323)) [494330, 494329, 494323] by Demod 100491 with 3 at 2,3 +Id : 101341, {_}: inverse ?494323 =<= multiply ?494329 (multiply (inverse ?494329) (inverse ?494323)) [494329, 494323] by Demod 100612 with 100849 at 1,2,3 +Id : 101357, {_}: multiply ?16917 (divide ?16919 (divide (divide ?16920 ?16921) (divide (inverse ?16919) ?16921))) =>= divide ?16917 ?16920 [16921, 16920, 16919, 16917] by Demod 100541 with 101328 at 1,2,2 +Id : 210, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?1032) ?1032) ?1033) ?1034)) ?1035) (divide ?1033 ?1035) =>= ?1034 [1035, 1034, 1033, 1032] by Super 202 with 3 at 1,1,1,1,1,2 +Id : 2224, {_}: divide (divide (inverse (divide (divide (multiply (inverse ?11772) ?11772) ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773, 11772] by Super 210 with 1292 at 1,1,1,2 +Id : 778, {_}: divide (inverse (divide (divide (divide ?3892 ?3892) ?3893) (divide (inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896)) (divide ?3893 ?3897)))) ?3897 =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3897, 3896, 3895, 3894, 3893, 3892] by Super 6 with 210 at 2,1,3 +Id : 811, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =?= inverse (divide (divide (divide ?3898 ?3898) ?3895) ?3896) [3898, 3896, 3895, 3894] by Demod 778 with 2 at 2 +Id : 101312, {_}: inverse (divide (divide (multiply (inverse ?3894) ?3894) ?3895) ?3896) =>= inverse (divide (inverse ?3895) ?3896) [3896, 3895, 3894] by Demod 811 with 100849 at 1,1,3 +Id : 101430, {_}: divide (divide (inverse (divide (inverse ?11773) (divide ?11774 ?11773))) ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774, 11773] by Demod 2224 with 101312 at 1,1,2 +Id : 375, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?1685) ?1685) ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686, 1685] by Super 372 with 3 at 1,1,1,1,1,2 +Id : 2362, {_}: divide (multiply (inverse (divide (divide (multiply (inverse ?12860) ?12860) ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861, 12860] by Super 375 with 1292 at 1,1,1,2 +Id : 101423, {_}: divide (multiply (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12863) (multiply ?12864 ?12863) =>= divide ?12862 ?12864 [12864, 12863, 12862, 12861] by Demod 2362 with 101312 at 1,1,2 +Id : 1298, {_}: divide (multiply ?6472 ?6473) (multiply ?6474 ?6473) =?= divide (divide ?6472 ?6475) (divide ?6474 ?6475) [6475, 6474, 6473, 6472] by Super 231 with 1057 at 1,1,2 +Id : 2653, {_}: divide (multiply (inverse (divide (multiply (divide ?14473 ?14473) ?14474) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474, 14473] by Super 231 with 1298 at 1,1,1,2 +Id : 100505, {_}: divide (multiply (inverse (divide (inverse (inverse ?14474)) (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 2653 with 100489 at 1,1,1,1,2 +Id : 101382, {_}: divide (multiply (inverse (divide ?14474 (multiply ?14475 ?14474))) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475, 14474] by Demod 100505 with 101328 at 1,1,1,1,2 +Id : 101429, {_}: divide (multiply (inverse (divide (inverse ?1686) ?1687)) ?1688) (multiply ?1686 ?1688) =>= ?1687 [1688, 1687, 1686] by Demod 375 with 101312 at 1,1,2 +Id : 101386, {_}: ?535740 =<= multiply (divide ?535743 ?535743) ?535740 [535743, 535740] by Demod 100489 with 101328 at 2 +Id : 101594, {_}: ?537458 =<= multiply (inverse (divide ?537459 ?537459)) ?537458 [537459, 537458] by Super 101386 with 100849 at 1,3 +Id : 101980, {_}: divide ?538112 (multiply ?538113 ?538112) =>= inverse ?538113 [538113, 538112] by Super 101429 with 101594 at 1,2 +Id : 102412, {_}: divide (multiply (inverse (inverse ?14475)) ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 101382 with 101980 at 1,1,1,2 +Id : 102413, {_}: divide (multiply ?14475 ?14476) (multiply ?14477 ?14476) =>= divide ?14475 ?14477 [14477, 14476, 14475] by Demod 102412 with 101328 at 1,1,2 +Id : 102434, {_}: divide (inverse (divide (inverse ?12861) (divide ?12862 ?12861))) ?12864 =>= divide ?12862 ?12864 [12864, 12862, 12861] by Demod 101423 with 102413 at 2 +Id : 102436, {_}: divide (divide ?11774 ?11775) (divide ?11776 ?11775) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 101430 with 102434 at 1,2 +Id : 102441, {_}: multiply ?16917 (divide ?16919 (divide ?16920 (inverse ?16919))) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 101357 with 102436 at 2,2,2 +Id : 102470, {_}: multiply ?16917 (divide ?16919 (multiply ?16920 ?16919)) =>= divide ?16917 ?16920 [16920, 16919, 16917] by Demod 102441 with 3 at 2,2,2 +Id : 102471, {_}: multiply ?16917 (inverse ?16920) =>= divide ?16917 ?16920 [16920, 16917] by Demod 102470 with 101980 at 2,2 +Id : 102472, {_}: inverse ?494323 =<= multiply ?494329 (divide (inverse ?494329) ?494323) [494329, 494323] by Demod 101341 with 102471 at 2,3 +Id : 102516, {_}: inverse (multiply ?538987 (inverse ?538988)) =>= multiply ?538988 (inverse ?538987) [538988, 538987] by Super 102472 with 101980 at 2,3 +Id : 102787, {_}: inverse (divide ?538987 ?538988) =<= multiply ?538988 (inverse ?538987) [538988, 538987] by Demod 102516 with 102471 at 1,2 +Id : 102788, {_}: inverse (divide ?538987 ?538988) =>= divide ?538988 ?538987 [538988, 538987] by Demod 102787 with 102471 at 3 +Id : 102815, {_}: divide (divide ?99 (divide (inverse ?96) (divide ?97 (divide ?96 ?98)))) ?98 =?= inverse (divide (inverse ?101) (divide ?99 (divide ?101 ?97))) [101, 98, 97, 96, 99] by Demod 101498 with 102788 at 1,2 +Id : 102816, {_}: divide (divide ?99 (divide (inverse ?96) (divide ?97 (divide ?96 ?98)))) ?98 =?= divide (divide ?99 (divide ?101 ?97)) (inverse ?101) [101, 98, 97, 96, 99] by Demod 102815 with 102788 at 3 +Id : 2390, {_}: divide (divide ?13180 ?13181) (divide ?13182 ?13181) =?= divide (divide ?13180 ?13183) (divide ?13182 ?13183) [13183, 13182, 13181, 13180] by Super 86 with 1057 at 1,1,2 +Id : 212, {_}: divide (divide (inverse (divide (multiply (divide ?1043 ?1043) ?1044) ?1045)) ?1046) (divide (inverse ?1044) ?1046) =>= ?1045 [1046, 1045, 1044, 1043] by Super 202 with 3 at 1,1,1,1,2 +Id : 2401, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide (multiply (divide ?13275 ?13275) ?13276) ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13275, 13274, 13273] by Super 2390 with 212 at 2,3 +Id : 100530, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide (inverse (inverse ?13276)) ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13274, 13273] by Demod 2401 with 100489 at 1,1,1,1,2,2 +Id : 101375, {_}: divide (divide ?13273 ?13274) (divide (divide (inverse (divide ?13276 ?13277)) ?13278) ?13274) =>= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13274, 13273] by Demod 100530 with 101328 at 1,1,1,1,2,2 +Id : 102446, {_}: divide ?13273 (divide (inverse (divide ?13276 ?13277)) ?13278) =?= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13277, 13276, 13273] by Demod 101375 with 102436 at 2 +Id : 102862, {_}: divide ?13273 (divide (divide ?13277 ?13276) ?13278) =<= divide (divide ?13273 (divide (inverse ?13276) ?13278)) ?13277 [13278, 13276, 13277, 13273] by Demod 102446 with 102788 at 1,2,2 +Id : 102906, {_}: divide ?99 (divide (divide ?98 ?96) (divide ?97 (divide ?96 ?98))) =?= divide (divide ?99 (divide ?101 ?97)) (inverse ?101) [101, 97, 96, 98, 99] by Demod 102816 with 102862 at 2 +Id : 102907, {_}: divide ?99 (divide (divide ?98 ?96) (divide ?97 (divide ?96 ?98))) =?= multiply (divide ?99 (divide ?101 ?97)) ?101 [101, 97, 96, 98, 99] by Demod 102906 with 3 at 3 +Id : 102924, {_}: multiply ?539666 (divide ?539667 ?539668) =<= divide ?539666 (divide ?539668 ?539667) [539668, 539667, 539666] by Super 102471 with 102788 at 2,2 +Id : 103472, {_}: multiply ?99 (divide (divide ?97 (divide ?96 ?98)) (divide ?98 ?96)) =?= multiply (divide ?99 (divide ?101 ?97)) ?101 [101, 98, 96, 97, 99] by Demod 102907 with 102924 at 2 +Id : 103473, {_}: multiply ?99 (divide (divide ?97 (divide ?96 ?98)) (divide ?98 ?96)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 98, 96, 97, 99] by Demod 103472 with 102924 at 1,3 +Id : 103474, {_}: multiply ?99 (multiply (divide ?97 (divide ?96 ?98)) (divide ?96 ?98)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 98, 96, 97, 99] by Demod 103473 with 102924 at 2,2 +Id : 103475, {_}: multiply ?99 (multiply (multiply ?97 (divide ?98 ?96)) (divide ?96 ?98)) =?= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 96, 98, 97, 99] by Demod 103474 with 102924 at 1,2,2 +Id : 9, {_}: divide (inverse (divide (divide (multiply (inverse ?36) ?36) ?37) (divide ?38 (divide ?37 ?39)))) ?39 =>= ?38 [39, 38, 37, 36] by Super 2 with 3 at 1,1,1,1,2 +Id : 101427, {_}: divide (inverse (divide (inverse ?37) (divide ?38 (divide ?37 ?39)))) ?39 =>= ?38 [39, 38, 37] by Demod 9 with 101312 at 1,2 +Id : 102819, {_}: divide (divide (divide ?38 (divide ?37 ?39)) (inverse ?37)) ?39 =>= ?38 [39, 37, 38] by Demod 101427 with 102788 at 1,2 +Id : 102903, {_}: divide (multiply (divide ?38 (divide ?37 ?39)) ?37) ?39 =>= ?38 [39, 37, 38] by Demod 102819 with 3 at 1,2 +Id : 103476, {_}: divide (multiply (multiply ?38 (divide ?39 ?37)) ?37) ?39 =>= ?38 [37, 39, 38] by Demod 102903 with 102924 at 1,1,2 +Id : 2408, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide (multiply (divide ?13324 ?13324) ?13325) ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13324, 13323, 13322] by Super 2390 with 378 at 2,3 +Id : 100531, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide (inverse (inverse ?13325)) ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13323, 13322] by Demod 2408 with 100489 at 1,1,1,1,2,2 +Id : 101355, {_}: divide (divide ?13322 ?13323) (divide (multiply (inverse (divide ?13325 ?13326)) ?13327) ?13323) =>= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13323, 13322] by Demod 100531 with 101328 at 1,1,1,1,2,2 +Id : 102440, {_}: divide ?13322 (multiply (inverse (divide ?13325 ?13326)) ?13327) =?= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13326, 13325, 13322] by Demod 101355 with 102436 at 2 +Id : 102864, {_}: divide ?13322 (multiply (divide ?13326 ?13325) ?13327) =<= divide (divide ?13322 (multiply (inverse ?13325) ?13327)) ?13326 [13327, 13325, 13326, 13322] by Demod 102440 with 102788 at 1,2,2 +Id : 102611, {_}: divide ?539467 (multiply ?539468 ?539467) =>= inverse ?539468 [539468, 539467] by Super 101429 with 101594 at 1,2 +Id : 102625, {_}: divide (inverse ?539525) (divide ?539526 ?539525) =>= inverse ?539526 [539526, 539525] by Super 102611 with 102471 at 2,2 +Id : 103817, {_}: multiply (inverse ?539525) (divide ?539525 ?539526) =>= inverse ?539526 [539526, 539525] by Demod 102625 with 102924 at 2 +Id : 103831, {_}: divide ?541233 (multiply (divide ?541234 ?541235) (divide ?541235 ?541236)) =>= divide (divide ?541233 (inverse ?541236)) ?541234 [541236, 541235, 541234, 541233] by Super 102864 with 103817 at 2,1,3 +Id : 103478, {_}: multiply (divide ?11774 ?11775) (divide ?11775 ?11776) =>= divide ?11774 ?11776 [11776, 11775, 11774] by Demod 102436 with 102924 at 2 +Id : 103925, {_}: divide ?541233 (divide ?541234 ?541236) =<= divide (divide ?541233 (inverse ?541236)) ?541234 [541236, 541234, 541233] by Demod 103831 with 103478 at 2,2 +Id : 103926, {_}: divide ?541233 (divide ?541234 ?541236) =?= divide (multiply ?541233 ?541236) ?541234 [541236, 541234, 541233] by Demod 103925 with 3 at 1,3 +Id : 103927, {_}: multiply ?541233 (divide ?541236 ?541234) =<= divide (multiply ?541233 ?541236) ?541234 [541234, 541236, 541233] by Demod 103926 with 102924 at 2 +Id : 103998, {_}: multiply (multiply ?38 (divide ?39 ?37)) (divide ?37 ?39) =>= ?38 [37, 39, 38] by Demod 103476 with 103927 at 2 +Id : 104001, {_}: multiply ?99 ?97 =<= multiply (multiply ?99 (divide ?97 ?101)) ?101 [101, 97, 99] by Demod 103475 with 103998 at 2,2 +Id : 104034, {_}: multiply ?541526 (multiply ?541527 ?541528) =<= multiply (multiply ?541526 (multiply ?541527 (divide ?541528 ?541529))) ?541529 [541529, 541528, 541527, 541526] by Super 104001 with 103927 at 2,1,3 +Id : 44, {_}: multiply (inverse (divide (divide (divide ?198 ?198) ?199) (divide ?200 (multiply ?199 ?201)))) ?201 =>= ?200 [201, 200, 199, 198] by Demod 8 with 3 at 2 +Id : 46, {_}: multiply (inverse (divide (divide (divide ?210 ?210) ?211) ?212)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 212, 211, 210] by Super 44 with 2 at 2,1,1,2 +Id : 104145, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= inverse (divide (divide (divide ?214 ?214) ?215) (divide ?212 (divide ?215 (multiply ?211 ?213)))) [215, 214, 213, 211, 210, 212] by Demod 46 with 102788 at 1,2 +Id : 104146, {_}: multiply (divide ?212 (divide (divide ?210 ?210) ?211)) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 211, 210, 212] by Demod 104145 with 102788 at 3 +Id : 104147, {_}: multiply (multiply ?212 (divide ?211 (divide ?210 ?210))) ?213 =?= divide (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide (divide ?214 ?214) ?215) [214, 215, 213, 210, 211, 212] by Demod 104146 with 102924 at 1,2 +Id : 104148, {_}: multiply (multiply ?212 (divide ?211 (divide ?210 ?210))) ?213 =?= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104147 with 102924 at 3 +Id : 104149, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (divide ?212 (divide ?215 (multiply ?211 ?213))) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104148 with 102924 at 2,1,2 +Id : 104150, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (divide ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104149 with 102924 at 1,3 +Id : 104151, {_}: multiply (multiply ?212 (multiply ?211 (divide ?210 ?210))) ?213 =?= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 210, 211, 212] by Demod 104150 with 102924 at 2,3 +Id : 93587, {_}: multiply (inverse (divide ?504068 ?504070)) ?504068 =>= ?504070 [504070, 504068] by Demod 92186 with 93111 at 2,2 +Id : 95434, {_}: multiply ?517965 (divide ?517966 ?517966) =>= ?517965 [517966, 517965] by Super 93587 with 93886 at 1,2 +Id : 104152, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (divide (multiply ?211 ?213) ?215)) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 211, 212] by Demod 104151 with 95434 at 2,1,2 +Id : 104153, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (multiply ?211 (divide ?213 ?215))) (multiply ?215 (divide ?214 ?214)) [214, 215, 213, 211, 212] by Demod 104152 with 103927 at 2,1,3 +Id : 104154, {_}: multiply (multiply ?212 ?211) ?213 =<= multiply (multiply ?212 (multiply ?211 (divide ?213 ?215))) ?215 [215, 213, 211, 212] by Demod 104153 with 95434 at 2,3 +Id : 115019, {_}: multiply ?541526 (multiply ?541527 ?541528) =?= multiply (multiply ?541526 ?541527) ?541528 [541528, 541527, 541526] by Demod 104034 with 104154 at 3 +Id : 115288, {_}: multiply a3 (multiply b3 c3) === multiply a3 (multiply b3 c3) [] by Demod 1 with 115019 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP480-1.p +24007: solved GRP480-1.p in 40.758547 using nrkbo +24007: status Unsatisfiable for GRP480-1.p +NO CLASH, using fixed ground order +24021: Facts: +24021: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24021: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24021: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24021: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24021: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24021: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24021: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24021: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24021: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +24021: Goal: +24021: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +24021: Order: +24021: nrkbo +24021: Leaf order: +24021: c 2 0 2 2,2,2 +24021: a 4 0 4 1,2 +24021: b 4 0 4 1,2,2 +24021: meet 17 2 4 0,2 +24021: join 19 2 4 0,2,2 +NO CLASH, using fixed ground order +24022: Facts: +24022: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24022: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24022: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24022: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24022: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24022: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24022: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24022: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24022: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +24022: Goal: +24022: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +24022: Order: +24022: kbo +24022: Leaf order: +24022: c 2 0 2 2,2,2 +24022: a 4 0 4 1,2 +24022: b 4 0 4 1,2,2 +24022: meet 17 2 4 0,2 +24022: join 19 2 4 0,2,2 +NO CLASH, using fixed ground order +24023: Facts: +24023: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +24023: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +24023: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +24023: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +24023: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +24023: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +24023: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +24023: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +24023: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +24023: Goal: +24023: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +24023: Order: +24023: lpo +24023: Leaf order: +24023: c 2 0 2 2,2,2 +24023: a 4 0 4 1,2 +24023: b 4 0 4 1,2,2 +24023: meet 17 2 4 0,2 +24023: join 19 2 4 0,2,2 +% SZS status Timeout for LAT168-1.p +NO CLASH, using fixed ground order +24053: Facts: +24053: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24053: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24053: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24053: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24053: Goal: +24053: Id : 1, {_}: + implies (implies (implies a b) (implies b a)) (implies b a) =>= truth + [] by prove_wajsberg_mv_4 +24053: Order: +24053: kbo +24053: Leaf order: +24053: a 3 0 3 1,1,1,2 +24053: b 3 0 3 2,1,1,2 +24053: truth 4 0 1 3 +24053: not 2 1 0 +24053: implies 18 2 5 0,2 +NO CLASH, using fixed ground order +24054: Facts: +24054: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24054: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24054: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24054: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24054: Goal: +24054: Id : 1, {_}: + implies (implies (implies a b) (implies b a)) (implies b a) =>= truth + [] by prove_wajsberg_mv_4 +24054: Order: +24054: lpo +24054: Leaf order: +24054: a 3 0 3 1,1,1,2 +24054: b 3 0 3 2,1,1,2 +24054: truth 4 0 1 3 +24054: not 2 1 0 +24054: implies 18 2 5 0,2 +NO CLASH, using fixed ground order +24052: Facts: +24052: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24052: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24052: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24052: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24052: Goal: +24052: Id : 1, {_}: + implies (implies (implies a b) (implies b a)) (implies b a) =>= truth + [] by prove_wajsberg_mv_4 +24052: Order: +24052: nrkbo +24052: Leaf order: +24052: a 3 0 3 1,1,1,2 +24052: b 3 0 3 2,1,1,2 +24052: truth 4 0 1 3 +24052: not 2 1 0 +24052: implies 18 2 5 0,2 +% SZS status Timeout for LCL109-2.p +NO CLASH, using fixed ground order +24075: Facts: +24075: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24075: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24075: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24075: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24075: Goal: +24075: Id : 1, {_}: + implies x (implies y z) =<= implies y (implies x z) + [] by prove_wajsberg_lemma +24075: Order: +24075: nrkbo +24075: Leaf order: +24075: x 2 0 2 1,2 +24075: y 2 0 2 1,2,2 +24075: z 2 0 2 2,2,2 +24075: truth 3 0 0 +24075: not 2 1 0 +24075: implies 17 2 4 0,2 +NO CLASH, using fixed ground order +24076: Facts: +24076: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24076: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24076: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24076: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24076: Goal: +24076: Id : 1, {_}: + implies x (implies y z) =<= implies y (implies x z) + [] by prove_wajsberg_lemma +24076: Order: +24076: kbo +24076: Leaf order: +24076: x 2 0 2 1,2 +24076: y 2 0 2 1,2,2 +24076: z 2 0 2 2,2,2 +24076: truth 3 0 0 +24076: not 2 1 0 +24076: implies 17 2 4 0,2 +NO CLASH, using fixed ground order +24077: Facts: +24077: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24077: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24077: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24077: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24077: Goal: +24077: Id : 1, {_}: + implies x (implies y z) =<= implies y (implies x z) + [] by prove_wajsberg_lemma +24077: Order: +24077: lpo +24077: Leaf order: +24077: x 2 0 2 1,2 +24077: y 2 0 2 1,2,2 +24077: z 2 0 2 2,2,2 +24077: truth 3 0 0 +24077: not 2 1 0 +24077: implies 17 2 4 0,2 +% SZS status Timeout for LCL138-1.p +NO CLASH, using fixed ground order +24160: Facts: +24160: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24160: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24160: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24160: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24160: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +24160: Id : 7, {_}: + or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +24160: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +24160: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +24160: Id : 10, {_}: + and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +24160: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +24160: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +24160: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +24160: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +24160: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +24160: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +24160: Id : 17, {_}: not truth =>= falsehood [] by false_definition +24160: Goal: +24160: Id : 1, {_}: + xor x (xor truth y) =<= xor (xor x truth) y + [] by prove_alternative_wajsberg_axiom +24160: Order: +24160: nrkbo +24160: Leaf order: +24160: falsehood 1 0 0 +24160: x 2 0 2 1,2 +24160: y 2 0 2 2,2,2 +24160: truth 6 0 2 1,2,2 +24160: not 12 1 0 +24160: and_star 7 2 0 +24160: xor 7 2 4 0,2 +24160: and 9 2 0 +24160: or 10 2 0 +24160: implies 14 2 0 +NO CLASH, using fixed ground order +24161: Facts: +24161: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24161: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24161: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24161: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24161: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +24161: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +24161: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +24161: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +24161: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +24161: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +24161: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +24161: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +24161: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +24161: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +24161: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +24161: Id : 17, {_}: not truth =>= falsehood [] by false_definition +24161: Goal: +24161: Id : 1, {_}: + xor x (xor truth y) =<= xor (xor x truth) y + [] by prove_alternative_wajsberg_axiom +24161: Order: +24161: kbo +24161: Leaf order: +24161: falsehood 1 0 0 +24161: x 2 0 2 1,2 +24161: y 2 0 2 2,2,2 +24161: truth 6 0 2 1,2,2 +24161: not 12 1 0 +24161: and_star 7 2 0 +24161: xor 7 2 4 0,2 +24161: and 9 2 0 +24161: or 10 2 0 +24161: implies 14 2 0 +NO CLASH, using fixed ground order +24162: Facts: +24162: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +24162: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +24162: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +24162: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +24162: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +24162: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +24162: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +24162: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +24162: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +24162: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +24162: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +24162: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +24162: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +24162: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +24162: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +24162: Id : 17, {_}: not truth =>= falsehood [] by false_definition +24162: Goal: +24162: Id : 1, {_}: + xor x (xor truth y) =<= xor (xor x truth) y + [] by prove_alternative_wajsberg_axiom +24162: Order: +24162: lpo +24162: Leaf order: +24162: falsehood 1 0 0 +24162: x 2 0 2 1,2 +24162: y 2 0 2 2,2,2 +24162: truth 6 0 2 1,2,2 +24162: not 12 1 0 +24162: and_star 7 2 0 +24162: xor 7 2 4 0,2 +24162: and 9 2 0 +24162: or 10 2 0 +24162: implies 14 2 0 +Statistics : +Max weight : 32 +Found proof, 8.845379s +% SZS status Unsatisfiable for LCL159-1.p +% SZS output start CNFRefutation for LCL159-1.p +Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32 +Id : 10, {_}: and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) [29, 28, 27] by and_associativity ?27 ?28 ?29 +Id : 13, {_}: xor ?37 ?38 =?= xor ?38 ?37 [38, 37] by xor_commutativity ?37 ?38 +Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12 +Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19 +Id : 39, {_}: implies (implies ?111 ?112) ?112 =?= implies (implies ?112 ?111) ?111 [112, 111] by wajsberg_3 ?111 ?112 +Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57 +Id : 17, {_}: not truth =>= falsehood [] by false_definition +Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9 +Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15 +Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25 +Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41 +Id : 12, {_}: xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35 +Id : 154, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3 +Id : 162, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 154 at 1,3 +Id : 163, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 162 with 154 at 2,3 +Id : 173, {_}: or truth ?418 =<= implies falsehood ?418 [418] by Super 6 with 17 at 1,3 +Id : 183, {_}: implies (implies ?424 falsehood) falsehood =>= implies (or truth ?424) ?424 [424] by Super 4 with 173 at 1,3 +Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2 +Id : 437, {_}: implies (implies ?923 truth) (implies ?924 (implies ?923 ?924)) =>= truth [924, 923] by Super 20 with 2 at 1,2,2 +Id : 438, {_}: implies (implies truth truth) (implies ?926 ?926) =>= truth [926] by Super 437 with 2 at 2,2,2 +Id : 471, {_}: implies truth (implies ?926 ?926) =>= truth [926] by Demod 438 with 2 at 1,2 +Id : 472, {_}: implies ?926 ?926 =>= truth [926] by Demod 471 with 2 at 2 +Id : 501, {_}: implies (implies (implies ?1003 ?1003) ?1004) (implies (implies ?1004 truth) truth) =>= truth [1004, 1003] by Super 22 with 472 at 2,1,2,2 +Id : 529, {_}: implies (implies truth ?1004) (implies (implies ?1004 truth) truth) =>= truth [1004] by Demod 501 with 472 at 1,1,2 +Id : 40, {_}: implies (implies ?114 truth) truth =>= implies ?114 ?114 [114] by Super 39 with 2 at 1,3 +Id : 495, {_}: implies (implies ?114 truth) truth =>= truth [114] by Demod 40 with 472 at 3 +Id : 530, {_}: implies (implies truth ?1004) truth =>= truth [1004] by Demod 529 with 495 at 2,2 +Id : 531, {_}: implies ?1004 truth =>= truth [1004] by Demod 530 with 2 at 1,2 +Id : 567, {_}: or ?1050 truth =>= truth [1050] by Super 6 with 531 at 3 +Id : 621, {_}: or truth ?1090 =>= truth [1090] by Super 8 with 567 at 3 +Id : 637, {_}: implies (implies ?424 falsehood) falsehood =>= implies truth ?424 [424] by Demod 183 with 621 at 1,3 +Id : 638, {_}: implies (implies ?424 falsehood) falsehood =>= ?424 [424] by Demod 637 with 2 at 3 +Id : 157, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 154 at 2 +Id : 327, {_}: and_star truth ?755 =<= not (or falsehood (not ?755)) [755] by Super 157 with 17 at 1,1,3 +Id : 328, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 327 with 17 at 2,1,3 +Id : 341, {_}: or (or falsehood falsehood) ?773 =<= implies (and_star truth truth) ?773 [773] by Super 6 with 328 at 1,3 +Id : 346, {_}: or falsehood (or falsehood ?773) =<= implies (and_star truth truth) ?773 [773] by Demod 341 with 7 at 2 +Id : 750, {_}: implies (or falsehood (or falsehood falsehood)) falsehood =>= and_star truth truth [] by Super 638 with 346 at 1,2 +Id : 69, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2 +Id : 174, {_}: implies (or ?420 falsehood) (implies truth ?420) =>= truth [420] by Super 69 with 17 at 2,1,2 +Id : 177, {_}: implies (or ?420 falsehood) ?420 =>= truth [420] by Demod 174 with 2 at 2,2 +Id : 777, {_}: implies truth falsehood =>= or falsehood falsehood [] by Super 638 with 177 at 1,2 +Id : 799, {_}: falsehood =<= or falsehood falsehood [] by Demod 777 with 2 at 2 +Id : 805, {_}: and_star truth truth =>= not falsehood [] by Demod 328 with 799 at 1,3 +Id : 809, {_}: or falsehood (or falsehood ?773) =<= implies (not falsehood) ?773 [773] by Demod 346 with 805 at 1,3 +Id : 810, {_}: or falsehood (or falsehood ?773) =>= or falsehood ?773 [773] by Demod 809 with 6 at 3 +Id : 898, {_}: implies (or falsehood falsehood) falsehood =>= and_star truth truth [] by Demod 750 with 810 at 1,2 +Id : 899, {_}: implies (or falsehood falsehood) falsehood =>= not falsehood [] by Demod 898 with 805 at 3 +Id : 900, {_}: truth =<= not falsehood [] by Demod 899 with 177 at 2 +Id : 904, {_}: or falsehood ?1384 =<= implies truth ?1384 [1384] by Super 6 with 900 at 1,3 +Id : 919, {_}: or falsehood ?1384 =>= ?1384 [1384] by Demod 904 with 2 at 3 +Id : 1209, {_}: or ?1836 falsehood =>= ?1836 [1836] by Super 8 with 919 at 3 +Id : 908, {_}: and_star falsehood ?1392 =<= not (or truth (not ?1392)) [1392] by Super 157 with 900 at 1,1,3 +Id : 916, {_}: and_star falsehood ?1392 =>= not truth [1392] by Demod 908 with 621 at 1,3 +Id : 917, {_}: and_star falsehood ?1392 =>= falsehood [1392] by Demod 916 with 17 at 3 +Id : 1175, {_}: xor falsehood ?1822 =<= or falsehood (and_star (not falsehood) ?1822) [1822] by Super 163 with 917 at 1,3 +Id : 1182, {_}: xor falsehood ?1822 =<= or falsehood (and_star truth ?1822) [1822] by Demod 1175 with 900 at 1,2,3 +Id : 907, {_}: and_star ?1390 falsehood =<= not (or (not ?1390) truth) [1390] by Super 157 with 900 at 2,1,3 +Id : 913, {_}: and_star ?1390 falsehood =<= not (or truth (not ?1390)) [1390] by Demod 907 with 8 at 1,3 +Id : 914, {_}: and_star ?1390 falsehood =>= not truth [1390] by Demod 913 with 621 at 1,3 +Id : 915, {_}: and_star ?1390 falsehood =>= falsehood [1390] by Demod 914 with 17 at 3 +Id : 1144, {_}: xor ?1792 falsehood =<= or (and_star ?1792 (not falsehood)) falsehood [1792] by Super 163 with 915 at 2,3 +Id : 1161, {_}: xor ?1792 falsehood =<= or falsehood (and_star ?1792 (not falsehood)) [1792] by Demod 1144 with 8 at 3 +Id : 1162, {_}: xor ?1792 falsehood =<= or falsehood (and_star ?1792 truth) [1792] by Demod 1161 with 900 at 2,2,3 +Id : 1257, {_}: xor ?1792 falsehood =>= and_star ?1792 truth [1792] by Demod 1162 with 919 at 3 +Id : 1258, {_}: xor falsehood ?1880 =>= and_star ?1880 truth [1880] by Super 13 with 1257 at 3 +Id : 1283, {_}: and_star ?1822 truth =<= or falsehood (and_star truth ?1822) [1822] by Demod 1182 with 1258 at 2 +Id : 1284, {_}: and_star ?1822 truth =?= and_star truth ?1822 [1822] by Demod 1283 with 919 at 3 +Id : 170, {_}: and_star truth ?412 =<= not (or falsehood (not ?412)) [412] by Super 157 with 17 at 1,1,3 +Id : 1193, {_}: and_star truth ?412 =>= not (not ?412) [412] by Demod 170 with 919 at 1,3 +Id : 1285, {_}: and_star ?1822 truth =>= not (not ?1822) [1822] by Demod 1284 with 1193 at 3 +Id : 158, {_}: and_star (and ?27 ?28) ?29 =<= and ?27 (and ?28 ?29) [29, 28, 27] by Demod 10 with 154 at 2 +Id : 159, {_}: and_star (and ?27 ?28) ?29 =?= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 158 with 154 at 3 +Id : 160, {_}: and_star (and_star ?27 ?28) ?29 =?= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 159 with 154 at 1,2 +Id : 161, {_}: and_star (and_star ?27 ?28) ?29 =>= and_star ?27 (and_star ?28 ?29) [29, 28, 27] by Demod 160 with 154 at 2,3 +Id : 1290, {_}: and_star (not (not ?1909)) ?1910 =>= and_star ?1909 (and_star truth ?1910) [1910, 1909] by Super 161 with 1285 at 1,2 +Id : 1306, {_}: and_star (not (not ?1909)) ?1910 =>= and_star ?1909 (not (not ?1910)) [1910, 1909] by Demod 1290 with 1193 at 2,3 +Id : 1659, {_}: and_star ?2411 (not (not truth)) =>= not (not (not (not ?2411))) [2411] by Super 1285 with 1306 at 2 +Id : 1669, {_}: and_star ?2411 (not falsehood) =>= not (not (not (not ?2411))) [2411] by Demod 1659 with 17 at 1,2,2 +Id : 1670, {_}: and_star ?2411 truth =>= not (not (not (not ?2411))) [2411] by Demod 1669 with 900 at 2,2 +Id : 1671, {_}: not (not ?2411) =<= not (not (not (not ?2411))) [2411] by Demod 1670 with 1285 at 2 +Id : 1703, {_}: or (not (not (not ?2451))) ?2452 =<= implies (not (not ?2451)) ?2452 [2452, 2451] by Super 6 with 1671 at 1,3 +Id : 1722, {_}: or (not (not (not ?2451))) ?2452 =>= or (not ?2451) ?2452 [2452, 2451] by Demod 1703 with 6 at 3 +Id : 1999, {_}: or (not ?2759) falsehood =>= not (not (not ?2759)) [2759] by Super 1209 with 1722 at 2 +Id : 2014, {_}: or falsehood (not ?2759) =>= not (not (not ?2759)) [2759] by Demod 1999 with 8 at 2 +Id : 2015, {_}: not ?2759 =<= not (not (not ?2759)) [2759] by Demod 2014 with 919 at 2 +Id : 2063, {_}: or (not (not ?2816)) ?2817 =<= implies (not ?2816) ?2817 [2817, 2816] by Super 6 with 2015 at 1,3 +Id : 2088, {_}: or (not (not ?2816)) ?2817 =>= or ?2816 ?2817 [2817, 2816] by Demod 2063 with 6 at 3 +Id : 2169, {_}: or ?2929 falsehood =>= not (not ?2929) [2929] by Super 1209 with 2088 at 2 +Id : 2202, {_}: ?2929 =<= not (not ?2929) [2929] by Demod 2169 with 1209 at 2 +Id : 2232, {_}: and_star ?2997 (not ?2998) =<= not (or (not ?2997) ?2998) [2998, 2997] by Super 157 with 2202 at 2,1,3 +Id : 2716, {_}: or (not ?3623) ?3624 =>= not (and_star ?3623 (not ?3624)) [3624, 3623] by Super 2202 with 2232 at 1,3 +Id : 2722, {_}: or ?3642 ?3643 =>= not (and_star (not ?3642) (not ?3643)) [3643, 3642] by Super 2716 with 2202 at 1,2 +Id : 2787, {_}: xor ?34 ?35 =>= not (and_star (not (and_star ?34 (not ?35))) (not (and_star (not ?34) ?35))) [35, 34] by Demod 163 with 2722 at 3 +Id : 2819, {_}: not (and_star (not (and_star ?37 (not ?38))) (not (and_star (not ?37) ?38))) =<= xor ?38 ?37 [38, 37] by Demod 13 with 2787 at 2 +Id : 2820, {_}: not (and_star (not (and_star ?37 (not ?38))) (not (and_star (not ?37) ?38))) =?= not (and_star (not (and_star ?38 (not ?37))) (not (and_star (not ?38) ?37))) [38, 37] by Demod 2819 with 2787 at 3 +Id : 2785, {_}: not (and_star (not ?21) (not ?22)) =<= or ?22 ?21 [22, 21] by Demod 8 with 2722 at 2 +Id : 2786, {_}: not (and_star (not ?21) (not ?22)) =?= not (and_star (not ?22) (not ?21)) [22, 21] by Demod 2785 with 2722 at 3 +Id : 155, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 154 at 2 +Id : 156, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 155 with 154 at 3 +Id : 2226, {_}: and_star truth ?412 =>= ?412 [412] by Demod 1193 with 2202 at 3 +Id : 2228, {_}: and_star ?1822 truth =>= ?1822 [1822] by Demod 1285 with 2202 at 3 +Id : 2921, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) === not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) [] by Demod 2920 with 156 at 1,1,1,3 +Id : 2920, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y x)) (not (and_star (not x) (not y)))) [] by Demod 2919 with 2786 at 2,1,3 +Id : 2919, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y x)) (not (and_star (not y) (not x)))) [] by Demod 2918 with 2228 at 2,1,1,1,3 +Id : 2918, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x truth))) (not (and_star (not y) (not x)))) [] by Demod 2917 with 2228 at 1,2,1,2,1,3 +Id : 2917, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x truth))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2916 with 900 at 2,2,1,1,1,3 +Id : 2916, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not y)))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2915 with 2228 at 1,2,1,2,1,2 +Id : 2915, {_}: not (and_star (not (and_star x y)) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2914 with 2228 at 2,1,1,1,2 +Id : 2914, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star y (and_star x (not falsehood)))) (not (and_star (not y) (not (and_star x truth))))) [] by Demod 2913 with 2786 at 3 +Id : 2913, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y truth))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2912 with 900 at 2,1,2,1,2,1,2 +Id : 2912, {_}: not (and_star (not (and_star x (and_star y truth))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2911 with 900 at 2,2,1,1,1,2 +Id : 2911, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not falsehood))))) [] by Demod 2910 with 917 at 1,2,2,1,2,1,3 +Id : 2910, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star x (not (and_star falsehood x)))))) [] by Demod 2909 with 2202 at 1,2,1,2,1,3 +Id : 2909, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x truth)))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2908 with 900 at 2,1,2,1,1,1,3 +Id : 2908, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not falsehood)))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2907 with 917 at 1,2,1,2,1,2,1,2 +Id : 2907, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star y (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2906 with 2202 at 1,1,2,1,2,1,2 +Id : 2906, {_}: not (and_star (not (and_star x (and_star y (not falsehood)))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2905 with 917 at 1,2,2,1,1,1,2 +Id : 2905, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (not x)) (not (and_star falsehood x)))))) [] by Demod 2904 with 156 at 2,1,2,1,3 +Id : 2904, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not falsehood))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2903 with 917 at 1,2,1,2,1,1,1,3 +Id : 2903, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star x (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2902 with 2202 at 1,1,2,1,1,1,3 +Id : 2902, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (not y)) (not (and_star falsehood y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2901 with 2786 at 2,1,2,1,2 +Id : 2901, {_}: not (and_star (not (and_star x (and_star y (not (and_star falsehood y))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2900 with 156 at 1,2,2,1,1,1,2 +Id : 2900, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (not x)))))) [] by Demod 2899 with 2226 at 1,2,2,1,2,1,3 +Id : 2899, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star falsehood x)) (not (and_star truth (not x))))))) [] by Demod 2898 with 156 at 1,1,2,1,2,1,3 +Id : 2898, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (not x)) (not (and_star falsehood x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2897 with 2786 at 2,1,1,1,3 +Id : 2897, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (not y))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2896 with 2226 at 1,2,1,2,1,2,1,2 +Id : 2896, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star falsehood y)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2895 with 156 at 1,1,1,2,1,2,1,2 +Id : 2895, {_}: not (and_star (not (and_star x (and_star y (not (and_star y falsehood))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2894 with 17 at 2,1,2,2,1,1,1,2 +Id : 2894, {_}: not (and_star (not (and_star x (and_star y (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2893 with 2202 at 1,2,1,1,1,2 +Id : 2893, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) [] by Demod 2892 with 156 at 1,2,2,1,2,1,3 +Id : 2892, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x falsehood)) (not (and_star (not x) truth)))))) [] by Demod 2891 with 17 at 2,1,1,2,1,2,1,3 +Id : 2891, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (not x)))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2890 with 2226 at 1,2,1,2,1,1,1,3 +Id : 2890, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star falsehood x)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2889 with 156 at 1,1,1,2,1,1,1,3 +Id : 2889, {_}: not (and_star (not (and_star x (and_star (not (not y)) (not (and_star y (not truth)))))) (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y)))))))) =<= not (and_star (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2888 with 2786 at 2 +Id : 2888, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star y (not truth))))))) =>= not (and_star (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x))))))) (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth)))))) [] by Demod 2887 with 2786 at 3 +Id : 2887, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star y (not truth))))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2886 with 156 at 1,2,2,1,2,1,2 +Id : 2886, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (not y)) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2885 with 2226 at 1,1,2,1,2,1,2 +Id : 2885, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star truth (not y))))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2884 with 156 at 1,2,1,2,1,1,1,2 +Id : 2884, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y falsehood)) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2883 with 17 at 2,1,1,1,2,1,1,1,2 +Id : 2883, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star truth (not x)))))))) [] by Demod 2882 with 156 at 1,2,1,2,1,2,1,3 +Id : 2882, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x falsehood)) (not (and_star (not x) truth))))))) [] by Demod 2881 with 17 at 2,1,1,1,2,1,2,1,3 +Id : 2881, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2880 with 2202 at 2,1,1,1,3 +Id : 2880, {_}: not (and_star (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth)))))) (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y)))))) =>= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2879 with 2786 at 2 +Id : 2879, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =>= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) [] by Demod 2878 with 2787 at 2,1,2,1,3 +Id : 2878, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =<= not (and_star (not (and_star y (not (not (and_star (not (and_star x (not truth))) (not (and_star (not x) truth))))))) (not (and_star (not y) (xor x truth)))) [] by Demod 2877 with 2787 at 1,2,1,1,1,3 +Id : 2877, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star y (not truth))) (not (and_star (not y) truth))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2876 with 2820 at 2,1,2,1,2 +Id : 2876, {_}: not (and_star (not (and_star x (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2875 with 2202 at 2,1,1,1,2 +Id : 2875, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star y (not (xor x truth)))) (not (and_star (not y) (xor x truth)))) [] by Demod 2874 with 2820 at 3 +Id : 2874, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) =<= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2873 with 2787 at 2,1,2,1,2 +Id : 2873, {_}: not (and_star (not (and_star x (not (not (and_star (not (and_star truth (not y))) (not (and_star (not truth) y))))))) (not (and_star (not x) (xor truth y)))) =>= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2872 with 2787 at 1,2,1,1,1,2 +Id : 2872, {_}: not (and_star (not (and_star x (not (xor truth y)))) (not (and_star (not x) (xor truth y)))) =>= not (and_star (not (and_star (xor x truth) (not y))) (not (and_star (not (xor x truth)) y))) [] by Demod 2871 with 2787 at 3 +Id : 2871, {_}: not (and_star (not (and_star x (not (xor truth y)))) (not (and_star (not x) (xor truth y)))) =<= xor (xor x truth) y [] by Demod 1 with 2787 at 2 +Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom +% SZS output end CNFRefutation for LCL159-1.p +24162: solved LCL159-1.p in 4.49628 using lpo +24162: status Unsatisfiable for LCL159-1.p +NO CLASH, using fixed ground order +24168: Facts: +24168: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24168: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24168: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24168: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24168: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24168: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24168: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24168: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24168: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24168: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24168: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24168: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +NO CLASH, using fixed ground order +24169: Facts: +24169: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24169: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24169: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24169: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24169: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24169: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24169: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24169: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24169: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24169: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24169: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24169: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24169: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24169: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24169: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24169: Goal: +24169: Id : 1, {_}: + associator x y (add u v) + =>= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +24169: Order: +24169: lpo +24169: Leaf order: +24169: u 2 0 2 1,3,2 +24169: v 2 0 2 2,3,2 +24169: x 3 0 3 1,2 +24169: y 3 0 3 2,2 +24169: additive_identity 8 0 0 +24169: additive_inverse 6 1 0 +24169: commutator 1 2 0 +24169: add 18 2 2 0,3,2 +24169: multiply 22 2 0 +24169: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +24167: Facts: +24167: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24167: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24167: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24167: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24167: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24167: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24167: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24167: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24167: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24167: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24167: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24167: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24167: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24167: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24167: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24167: Goal: +24167: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +24167: Order: +24167: nrkbo +24167: Leaf order: +24167: u 2 0 2 1,3,2 +24167: v 2 0 2 2,3,2 +24167: x 3 0 3 1,2 +24167: y 3 0 3 2,2 +24167: additive_identity 8 0 0 +24167: additive_inverse 6 1 0 +24167: commutator 1 2 0 +24167: add 18 2 2 0,3,2 +24167: multiply 22 2 0 +24167: associator 4 3 3 0,2 +24168: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24168: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24168: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24168: Goal: +24168: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +24168: Order: +24168: kbo +24168: Leaf order: +24168: u 2 0 2 1,3,2 +24168: v 2 0 2 2,3,2 +24168: x 3 0 3 1,2 +24168: y 3 0 3 2,2 +24168: additive_identity 8 0 0 +24168: additive_inverse 6 1 0 +24168: commutator 1 2 0 +24168: add 18 2 2 0,3,2 +24168: multiply 22 2 0 +24168: associator 4 3 3 0,2 +% SZS status Timeout for RNG019-6.p +NO CLASH, using fixed ground order +24186: Facts: +24186: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24186: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24186: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24186: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24186: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24186: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24186: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24186: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24186: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24186: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24186: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24186: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24186: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24186: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24186: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24186: Goal: +24186: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +24186: Order: +24186: kbo +24186: Leaf order: +24186: u 2 0 2 1,1,2 +24186: v 2 0 2 2,1,2 +24186: x 3 0 3 2,2 +24186: y 3 0 3 3,2 +24186: additive_identity 8 0 0 +24186: additive_inverse 6 1 0 +24186: commutator 1 2 0 +24186: add 18 2 2 0,1,2 +24186: multiply 22 2 0 +24186: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +24185: Facts: +24185: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24185: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24185: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24185: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24185: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24185: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24185: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24185: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24185: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24185: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24185: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24185: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24185: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24185: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24185: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24185: Goal: +24185: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +24185: Order: +24185: nrkbo +24185: Leaf order: +24185: u 2 0 2 1,1,2 +24185: v 2 0 2 2,1,2 +24185: x 3 0 3 2,2 +24185: y 3 0 3 3,2 +24185: additive_identity 8 0 0 +24185: additive_inverse 6 1 0 +24185: commutator 1 2 0 +24185: add 18 2 2 0,1,2 +24185: multiply 22 2 0 +24185: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +24187: Facts: +24187: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24187: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24187: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24187: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24187: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24187: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24187: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24187: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24187: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24187: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24187: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24187: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24187: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24187: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24187: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24187: Goal: +24187: Id : 1, {_}: + associator (add u v) x y + =>= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +24187: Order: +24187: lpo +24187: Leaf order: +24187: u 2 0 2 1,1,2 +24187: v 2 0 2 2,1,2 +24187: x 3 0 3 2,2 +24187: y 3 0 3 3,2 +24187: additive_identity 8 0 0 +24187: additive_inverse 6 1 0 +24187: commutator 1 2 0 +24187: add 18 2 2 0,1,2 +24187: multiply 22 2 0 +24187: associator 4 3 3 0,2 +% SZS status Timeout for RNG021-6.p +NO CLASH, using fixed ground order +24214: Facts: +24214: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24214: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24214: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24214: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24214: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24214: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24214: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24214: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24214: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24214: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24214: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24214: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24214: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24214: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24214: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24214: Goal: +24214: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +24214: Order: +24214: nrkbo +24214: Leaf order: +24214: y 1 0 1 2,2 +24214: x 2 0 2 1,2 +24214: additive_identity 9 0 1 3 +24214: additive_inverse 6 1 0 +24214: commutator 1 2 0 +24214: add 16 2 0 +24214: multiply 22 2 0 +24214: associator 2 3 1 0,2 +NO CLASH, using fixed ground order +24215: Facts: +24215: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24215: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24215: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24215: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24215: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24215: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24215: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24215: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24215: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24215: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24215: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24215: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24215: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24215: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24215: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24215: Goal: +24215: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +24215: Order: +24215: kbo +24215: Leaf order: +24215: y 1 0 1 2,2 +24215: x 2 0 2 1,2 +24215: additive_identity 9 0 1 3 +24215: additive_inverse 6 1 0 +24215: commutator 1 2 0 +24215: add 16 2 0 +24215: multiply 22 2 0 +24215: associator 2 3 1 0,2 +NO CLASH, using fixed ground order +24216: Facts: +24216: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24216: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24216: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24216: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24216: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24216: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24216: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24216: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24216: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24216: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24216: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24216: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24216: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24216: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24216: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24216: Goal: +24216: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +24216: Order: +24216: lpo +24216: Leaf order: +24216: y 1 0 1 2,2 +24216: x 2 0 2 1,2 +24216: additive_identity 9 0 1 3 +24216: additive_inverse 6 1 0 +24216: commutator 1 2 0 +24216: add 16 2 0 +24216: multiply 22 2 0 +24216: associator 2 3 1 0,2 +% SZS status Timeout for RNG025-6.p +NO CLASH, using fixed ground order +24240: Facts: +24240: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +24240: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +24240: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +24240: Id : 5, {_}: add c c =>= c [] by idempotence +24240: Goal: +24240: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +24240: Order: +24240: kbo +24240: Leaf order: +24240: a 2 0 2 1,1,1,2 +24240: c 3 0 0 +24240: b 3 0 3 1,2,1,1,2 +24240: negate 9 1 5 0,1,2 +24240: add 13 2 3 0,2 +NO CLASH, using fixed ground order +24239: Facts: +24239: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +24239: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +24239: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +24239: Id : 5, {_}: add c c =>= c [] by idempotence +24239: Goal: +24239: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +24239: Order: +24239: nrkbo +24239: Leaf order: +24239: a 2 0 2 1,1,1,2 +24239: c 3 0 0 +24239: b 3 0 3 1,2,1,1,2 +24239: negate 9 1 5 0,1,2 +24239: add 13 2 3 0,2 +NO CLASH, using fixed ground order +24241: Facts: +24241: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +24241: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +24241: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +24241: Id : 5, {_}: add c c =>= c [] by idempotence +24241: Goal: +24241: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +24241: Order: +24241: lpo +24241: Leaf order: +24241: a 2 0 2 1,1,1,2 +24241: c 3 0 0 +24241: b 3 0 3 1,2,1,1,2 +24241: negate 9 1 5 0,1,2 +24241: add 13 2 3 0,2 +% SZS status Timeout for ROB005-1.p +NO CLASH, using fixed ground order +24337: Facts: +24337: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +24337: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9 +24337: Id : 4, {_}: + multiply (inverse ?11) ?11 ?12 =>= ?12 + [12, 11] by left_inverse ?11 ?12 +24337: Id : 5, {_}: + multiply ?14 ?15 (inverse ?15) =>= ?14 + [15, 14] by right_inverse ?14 ?15 +24337: Goal: +24337: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant +24337: Order: +24337: nrkbo +24337: Leaf order: +24337: y 1 0 1 1,2 +24337: x 3 0 3 2,2 +24337: inverse 2 1 0 +24337: multiply 9 3 1 0,2 +NO CLASH, using fixed ground order +24338: Facts: +24338: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +24338: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9 +24338: Id : 4, {_}: + multiply (inverse ?11) ?11 ?12 =>= ?12 + [12, 11] by left_inverse ?11 ?12 +24338: Id : 5, {_}: + multiply ?14 ?15 (inverse ?15) =>= ?14 + [15, 14] by right_inverse ?14 ?15 +24338: Goal: +24338: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant +24338: Order: +24338: kbo +24338: Leaf order: +24338: y 1 0 1 1,2 +24338: x 3 0 3 2,2 +24338: inverse 2 1 0 +24338: multiply 9 3 1 0,2 +NO CLASH, using fixed ground order +24339: Facts: +24339: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +24339: Id : 3, {_}: multiply ?8 ?8 ?9 =>= ?8 [9, 8] by ternary_multiply_2 ?8 ?9 +24339: Id : 4, {_}: + multiply (inverse ?11) ?11 ?12 =>= ?12 + [12, 11] by left_inverse ?11 ?12 +24339: Id : 5, {_}: + multiply ?14 ?15 (inverse ?15) =>= ?14 + [15, 14] by right_inverse ?14 ?15 +24339: Goal: +24339: Id : 1, {_}: multiply y x x =>= x [] by prove_ternary_multiply_1_independant +24339: Order: +24339: lpo +24339: Leaf order: +24339: y 1 0 1 1,2 +24339: x 3 0 3 2,2 +24339: inverse 2 1 0 +24339: multiply 9 3 1 0,2 +% SZS status Timeout for BOO019-1.p +CLASH, statistics insufficient +25312: Facts: +25312: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +25312: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +25312: Id : 4, {_}: + multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10 + [11, 10] by b1 ?10 ?11 +25312: Id : 5, {_}: + multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13 + [14, 13] by majority1 ?13 ?14 +25312: Id : 6, {_}: + multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16 + [17, 16] by majority2 ?16 ?17 +25312: Id : 7, {_}: + multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20 + [20, 19] by majority3 ?19 ?20 +25312: Goal: +25312: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25312: Order: +25312: nrkbo +25312: Leaf order: +25312: a 2 0 2 1,1,2 +25312: inverse 3 1 2 0,2 +25312: multiply 11 2 0 +25312: add 11 2 0 +CLASH, statistics insufficient +25313: Facts: +25313: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +25313: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +25313: Id : 4, {_}: + multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10 + [11, 10] by b1 ?10 ?11 +25313: Id : 5, {_}: + multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13 + [14, 13] by majority1 ?13 ?14 +25313: Id : 6, {_}: + multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16 + [17, 16] by majority2 ?16 ?17 +25313: Id : 7, {_}: + multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20 + [20, 19] by majority3 ?19 ?20 +25313: Goal: +25313: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25313: Order: +25313: kbo +25313: Leaf order: +25313: a 2 0 2 1,1,2 +25313: inverse 3 1 2 0,2 +25313: multiply 11 2 0 +25313: add 11 2 0 +CLASH, statistics insufficient +25314: Facts: +25314: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +25314: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +25314: Id : 4, {_}: + multiply (add ?10 ?11) (add ?10 (inverse ?11)) =>= ?10 + [11, 10] by b1 ?10 ?11 +25314: Id : 5, {_}: + multiply (add (multiply ?13 ?14) ?13) (add ?13 ?14) =>= ?13 + [14, 13] by majority1 ?13 ?14 +25314: Id : 6, {_}: + multiply (add (multiply ?16 ?16) ?17) (add ?16 ?16) =>= ?16 + [17, 16] by majority2 ?16 ?17 +25314: Id : 7, {_}: + multiply (add (multiply ?19 ?20) ?20) (add ?19 ?20) =>= ?20 + [20, 19] by majority3 ?19 ?20 +25314: Goal: +25314: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25314: Order: +25314: lpo +25314: Leaf order: +25314: a 2 0 2 1,1,2 +25314: inverse 3 1 2 0,2 +25314: multiply 11 2 0 +25314: add 11 2 0 +% SZS status Timeout for BOO030-1.p +CLASH, statistics insufficient +25341: Facts: +25341: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +25341: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +25341: Id : 4, {_}: + multiply (add ?10 (inverse ?10)) ?11 =>= ?11 + [11, 10] by property3 ?10 ?11 +25341: Id : 5, {_}: + multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13 + [15, 14, 13] by l2 ?13 ?14 ?15 +25341: Id : 6, {_}: + multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18 + [19, 18, 17] by l4 ?17 ?18 ?19 +25341: Id : 7, {_}: + add (multiply ?21 (inverse ?21)) ?22 =>= ?22 + [22, 21] by property3_dual ?21 ?22 +25341: Id : 8, {_}: + add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24 + [25, 24] by majority1 ?24 ?25 +25341: Id : 9, {_}: + add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27 + [28, 27] by majority2 ?27 ?28 +25341: Id : 10, {_}: + add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31 + [31, 30] by majority3 ?30 ?31 +25341: Id : 11, {_}: + multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33 + [34, 33] by majority1_dual ?33 ?34 +25341: Id : 12, {_}: + multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36 + [37, 36] by majority2_dual ?36 ?37 +25341: Id : 13, {_}: + multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40 + [40, 39] by majority3_dual ?39 ?40 +25341: Goal: +25341: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25341: Order: +25341: nrkbo +25341: Leaf order: +25341: a 2 0 2 1,1,2 +25341: inverse 4 1 2 0,2 +25341: multiply 21 2 0 +25341: add 21 2 0 +CLASH, statistics insufficient +25342: Facts: +25342: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +25342: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +25342: Id : 4, {_}: + multiply (add ?10 (inverse ?10)) ?11 =>= ?11 + [11, 10] by property3 ?10 ?11 +25342: Id : 5, {_}: + multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13 + [15, 14, 13] by l2 ?13 ?14 ?15 +25342: Id : 6, {_}: + multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18 + [19, 18, 17] by l4 ?17 ?18 ?19 +25342: Id : 7, {_}: + add (multiply ?21 (inverse ?21)) ?22 =>= ?22 + [22, 21] by property3_dual ?21 ?22 +25342: Id : 8, {_}: + add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24 + [25, 24] by majority1 ?24 ?25 +25342: Id : 9, {_}: + add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27 + [28, 27] by majority2 ?27 ?28 +25342: Id : 10, {_}: + add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31 + [31, 30] by majority3 ?30 ?31 +25342: Id : 11, {_}: + multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33 + [34, 33] by majority1_dual ?33 ?34 +25342: Id : 12, {_}: + multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36 + [37, 36] by majority2_dual ?36 ?37 +25342: Id : 13, {_}: + multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40 + [40, 39] by majority3_dual ?39 ?40 +25342: Goal: +25342: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25342: Order: +25342: kbo +25342: Leaf order: +25342: a 2 0 2 1,1,2 +25342: inverse 4 1 2 0,2 +25342: multiply 21 2 0 +25342: add 21 2 0 +CLASH, statistics insufficient +25343: Facts: +25343: Id : 2, {_}: + add ?2 (multiply ?3 (multiply ?2 ?4)) =>= ?2 + [4, 3, 2] by l1 ?2 ?3 ?4 +25343: Id : 3, {_}: + add (add (multiply ?6 ?7) (multiply ?7 ?8)) ?7 =>= ?7 + [8, 7, 6] by l3 ?6 ?7 ?8 +25343: Id : 4, {_}: + multiply (add ?10 (inverse ?10)) ?11 =>= ?11 + [11, 10] by property3 ?10 ?11 +25343: Id : 5, {_}: + multiply ?13 (add ?14 (add ?13 ?15)) =>= ?13 + [15, 14, 13] by l2 ?13 ?14 ?15 +25343: Id : 6, {_}: + multiply (multiply (add ?17 ?18) (add ?18 ?19)) ?18 =>= ?18 + [19, 18, 17] by l4 ?17 ?18 ?19 +25343: Id : 7, {_}: + add (multiply ?21 (inverse ?21)) ?22 =>= ?22 + [22, 21] by property3_dual ?21 ?22 +25343: Id : 8, {_}: + add (multiply (add ?24 ?25) ?24) (multiply ?24 ?25) =>= ?24 + [25, 24] by majority1 ?24 ?25 +25343: Id : 9, {_}: + add (multiply (add ?27 ?27) ?28) (multiply ?27 ?27) =>= ?27 + [28, 27] by majority2 ?27 ?28 +25343: Id : 10, {_}: + add (multiply (add ?30 ?31) ?31) (multiply ?30 ?31) =>= ?31 + [31, 30] by majority3 ?30 ?31 +25343: Id : 11, {_}: + multiply (add (multiply ?33 ?34) ?33) (add ?33 ?34) =>= ?33 + [34, 33] by majority1_dual ?33 ?34 +25343: Id : 12, {_}: + multiply (add (multiply ?36 ?36) ?37) (add ?36 ?36) =>= ?36 + [37, 36] by majority2_dual ?36 ?37 +25343: Id : 13, {_}: + multiply (add (multiply ?39 ?40) ?40) (add ?39 ?40) =>= ?40 + [40, 39] by majority3_dual ?39 ?40 +25343: Goal: +25343: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25343: Order: +25343: lpo +25343: Leaf order: +25343: a 2 0 2 1,1,2 +25343: inverse 4 1 2 0,2 +25343: multiply 21 2 0 +25343: add 21 2 0 +% SZS status Timeout for BOO032-1.p +NO CLASH, using fixed ground order +25370: Facts: +25370: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =<= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +25370: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +25370: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +25370: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +25370: Id : 6, {_}: + multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17 + [18, 17] by majority1 ?17 ?18 +25370: Id : 7, {_}: + multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20 + [21, 20] by majority2 ?20 ?21 +25370: Id : 8, {_}: + multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24 + [24, 23] by majority3 ?23 ?24 +25370: Goal: +25370: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25370: Order: +25370: nrkbo +25370: Leaf order: +25370: a 2 0 2 1,1,2 +25370: inverse 3 1 2 0,2 +25370: add 15 2 0 multiply +25370: multiply 16 2 0 add +NO CLASH, using fixed ground order +25371: Facts: +25371: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =<= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +25371: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +25371: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +25371: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +25371: Id : 6, {_}: + multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17 + [18, 17] by majority1 ?17 ?18 +25371: Id : 7, {_}: + multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20 + [21, 20] by majority2 ?20 ?21 +25371: Id : 8, {_}: + multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24 + [24, 23] by majority3 ?23 ?24 +25371: Goal: +25371: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25371: Order: +25371: kbo +25371: Leaf order: +25371: a 2 0 2 1,1,2 +25371: inverse 3 1 2 0,2 +25371: add 15 2 0 multiply +25371: multiply 16 2 0 add +NO CLASH, using fixed ground order +25372: Facts: +25372: Id : 2, {_}: + add (multiply ?2 ?3) (add (multiply ?3 ?4) (multiply ?4 ?2)) + =<= + multiply (add ?2 ?3) (multiply (add ?3 ?4) (add ?4 ?2)) + [4, 3, 2] by distributivity ?2 ?3 ?4 +25372: Id : 3, {_}: + add ?6 (multiply ?7 (multiply ?6 ?8)) =>= ?6 + [8, 7, 6] by l1 ?6 ?7 ?8 +25372: Id : 4, {_}: + add (add (multiply ?10 ?11) (multiply ?11 ?12)) ?11 =>= ?11 + [12, 11, 10] by l3 ?10 ?11 ?12 +25372: Id : 5, {_}: + multiply (add ?14 (inverse ?14)) ?15 =>= ?15 + [15, 14] by property3 ?14 ?15 +25372: Id : 6, {_}: + multiply (add (multiply ?17 ?18) ?17) (add ?17 ?18) =>= ?17 + [18, 17] by majority1 ?17 ?18 +25372: Id : 7, {_}: + multiply (add (multiply ?20 ?20) ?21) (add ?20 ?20) =>= ?20 + [21, 20] by majority2 ?20 ?21 +25372: Id : 8, {_}: + multiply (add (multiply ?23 ?24) ?24) (add ?23 ?24) =>= ?24 + [24, 23] by majority3 ?23 ?24 +25372: Goal: +25372: Id : 1, {_}: inverse (inverse a) =>= a [] by prove_inverse_involution +25372: Order: +25372: lpo +25372: Leaf order: +25372: a 2 0 2 1,1,2 +25372: inverse 3 1 2 0,2 +25372: add 15 2 0 multiply +25372: multiply 16 2 0 add +% SZS status Timeout for BOO033-1.p +NO CLASH, using fixed ground order +25403: Facts: +25403: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +25403: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +25403: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) + (apply (apply b (apply b w)) (apply (apply b b) b)) + [] by strong_fixed_point +25403: Goal: +25403: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +25403: Order: +25403: nrkbo +25403: Leaf order: +25403: strong_fixed_point 3 0 2 1,2 +25403: fixed_pt 3 0 3 2,2 +25403: w 4 0 0 +25403: b 7 0 0 +25403: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +25404: Facts: +25404: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +25404: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +25404: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) + (apply (apply b (apply b w)) (apply (apply b b) b)) + [] by strong_fixed_point +25404: Goal: +25404: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +25404: Order: +25404: kbo +25404: Leaf order: +25404: strong_fixed_point 3 0 2 1,2 +25404: fixed_pt 3 0 3 2,2 +25404: w 4 0 0 +25404: b 7 0 0 +25404: apply 20 2 3 0,2 +NO CLASH, using fixed ground order +25405: Facts: +25405: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +25405: Id : 3, {_}: + apply (apply w ?6) ?7 =?= apply (apply ?6 ?7) ?7 + [7, 6] by w_definition ?6 ?7 +25405: Id : 4, {_}: + strong_fixed_point + =<= + apply (apply b (apply w w)) + (apply (apply b (apply b w)) (apply (apply b b) b)) + [] by strong_fixed_point +25405: Goal: +25405: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +25405: Order: +25405: lpo +25405: Leaf order: +25405: strong_fixed_point 3 0 2 1,2 +25405: fixed_pt 3 0 3 2,2 +25405: w 4 0 0 +25405: b 7 0 0 +25405: apply 20 2 3 0,2 +% SZS status Timeout for COL003-20.p +NO CLASH, using fixed ground order +25421: Facts: +25421: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +25421: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +25421: Goal: +25421: Id : 1, {_}: + apply + (apply + (apply (apply s (apply k (apply s (apply (apply s k) k)))) + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) + x) y + =>= + apply y (apply (apply x x) y) + [] by prove_u_combinator +25421: Order: +25421: nrkbo +25421: Leaf order: +25421: x 3 0 3 2,1,2 +25421: y 3 0 3 2,2 +25421: s 7 0 6 1,1,1,1,2 +25421: k 8 0 7 1,2,1,1,1,2 +25421: apply 25 2 17 0,2 +NO CLASH, using fixed ground order +25422: Facts: +25422: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +25422: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +25422: Goal: +25422: Id : 1, {_}: + apply + (apply + (apply (apply s (apply k (apply s (apply (apply s k) k)))) + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) + x) y + =>= + apply y (apply (apply x x) y) + [] by prove_u_combinator +25422: Order: +25422: kbo +25422: Leaf order: +25422: x 3 0 3 2,1,2 +25422: y 3 0 3 2,2 +25422: s 7 0 6 1,1,1,1,2 +25422: k 8 0 7 1,2,1,1,1,2 +25422: apply 25 2 17 0,2 +NO CLASH, using fixed ground order +25423: Facts: +25423: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +25423: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +25423: Goal: +25423: Id : 1, {_}: + apply + (apply + (apply (apply s (apply k (apply s (apply (apply s k) k)))) + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) + x) y + =>= + apply y (apply (apply x x) y) + [] by prove_u_combinator +25423: Order: +25423: lpo +25423: Leaf order: +25423: x 3 0 3 2,1,2 +25423: y 3 0 3 2,2 +25423: s 7 0 6 1,1,1,1,2 +25423: k 8 0 7 1,2,1,1,1,2 +25423: apply 25 2 17 0,2 +Statistics : +Max weight : 29 +Found proof, 0.116079s +% SZS status Unsatisfiable for COL004-3.p +% SZS output start CNFRefutation for COL004-3.p +Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +Id : 2, {_}: apply (apply (apply s ?2) ?3) ?4 =?= apply (apply ?2 ?4) (apply ?3 ?4) [4, 3, 2] by s_definition ?2 ?3 ?4 +Id : 35, {_}: apply y (apply (apply x x) y) === apply y (apply (apply x x) y) [] by Demod 34 with 3 at 1,2 +Id : 34, {_}: apply (apply (apply k y) (apply k y)) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 33 with 2 at 1,2 +Id : 33, {_}: apply (apply (apply (apply s k) k) y) (apply (apply x x) y) =>= apply y (apply (apply x x) y) [] by Demod 32 with 2 at 2 +Id : 32, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x x)) y =>= apply y (apply (apply x x) y) [] by Demod 31 with 3 at 2,2,1,2 +Id : 31, {_}: apply (apply (apply s (apply (apply s k) k)) (apply x (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 30 with 3 at 1,2,1,2 +Id : 30, {_}: apply (apply (apply s (apply (apply s k) k)) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 20 with 3 at 1,1,2 +Id : 20, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply k x) (apply k x)))) y =>= apply y (apply (apply x x) y) [] by Demod 19 with 2 at 2,2,1,2 +Id : 19, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply k x) (apply k x)) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 18 with 2 at 1,2,1,2 +Id : 18, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply (apply s k) k) x) (apply (apply (apply s k) k) x))) y =>= apply y (apply (apply x x) y) [] by Demod 17 with 2 at 2,1,2 +Id : 17, {_}: apply (apply (apply (apply k (apply s (apply (apply s k) k))) x) (apply (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)) x)) y =>= apply y (apply (apply x x) y) [] by Demod 1 with 2 at 1,2 +Id : 1, {_}: apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y =>= apply y (apply (apply x x) y) [] by prove_u_combinator +% SZS output end CNFRefutation for COL004-3.p +25423: solved COL004-3.p in 0.020001 using lpo +25423: status Unsatisfiable for COL004-3.p +CLASH, statistics insufficient +25428: Facts: +25428: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25428: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +25428: Goal: +25428: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1 +25428: Order: +25428: nrkbo +25428: Leaf order: +25428: s 1 0 0 +25428: w 1 0 0 +25428: combinator 1 0 1 1,3 +25428: apply 11 2 1 0,3 +CLASH, statistics insufficient +25429: Facts: +25429: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25429: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +25429: Goal: +25429: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1 +25429: Order: +25429: kbo +25429: Leaf order: +25429: s 1 0 0 +25429: w 1 0 0 +25429: combinator 1 0 1 1,3 +25429: apply 11 2 1 0,3 +CLASH, statistics insufficient +25430: Facts: +25430: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25430: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +25430: Goal: +25430: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_model ?1 +25430: Order: +25430: lpo +25430: Leaf order: +25430: s 1 0 0 +25430: w 1 0 0 +25430: combinator 1 0 1 1,3 +25430: apply 11 2 1 0,3 +% SZS status Timeout for COL005-1.p +CLASH, statistics insufficient +25470: Facts: +25470: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25470: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +25470: Id : 4, {_}: + apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 + [11, 10, 9] by v_definition ?9 ?10 ?11 +25470: Goal: +CLASH, statistics insufficient +25471: Facts: +25471: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25471: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +25471: Id : 4, {_}: + apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 + [11, 10, 9] by v_definition ?9 ?10 ?11 +25471: Goal: +25471: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25471: Order: +25471: kbo +25471: Leaf order: +25471: b 1 0 0 +25471: m 1 0 0 +25471: v 1 0 0 +25471: f 3 1 3 0,2,2 +25471: apply 15 2 3 0,2 +25470: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25470: Order: +25470: nrkbo +25470: Leaf order: +25470: b 1 0 0 +25470: m 1 0 0 +25470: v 1 0 0 +25470: f 3 1 3 0,2,2 +25470: apply 15 2 3 0,2 +CLASH, statistics insufficient +25472: Facts: +25472: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25472: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +25472: Id : 4, {_}: + apply (apply (apply v ?9) ?10) ?11 =?= apply (apply ?11 ?9) ?10 + [11, 10, 9] by v_definition ?9 ?10 ?11 +25472: Goal: +25472: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25472: Order: +25472: lpo +25472: Leaf order: +25472: b 1 0 0 +25472: m 1 0 0 +25472: v 1 0 0 +25472: f 3 1 3 0,2,2 +25472: apply 15 2 3 0,2 +Goal subsumed +Statistics : +Max weight : 78 +Found proof, 6.291189s +% SZS status Unsatisfiable for COL038-1.p +% SZS output start CNFRefutation for COL038-1.p +Id : 4, {_}: apply (apply (apply v ?9) ?10) ?11 =>= apply (apply ?11 ?9) ?10 [11, 10, 9] by v_definition ?9 ?10 ?11 +Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by m_definition ?7 +Id : 19, {_}: apply (apply (apply v ?47) ?48) ?49 =>= apply (apply ?49 ?47) ?48 [49, 48, 47] by v_definition ?47 ?48 ?49 +Id : 5, {_}: apply (apply (apply b ?13) ?14) ?15 =>= apply ?13 (apply ?14 ?15) [15, 14, 13] by b_definition ?13 ?14 ?15 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 6, {_}: apply ?17 (apply ?18 ?19) =?= apply ?17 (apply ?18 ?19) [19, 18, 17] by Super 5 with 2 at 2 +Id : 1244, {_}: apply (apply m (apply v ?1596)) ?1597 =?= apply (apply ?1597 ?1596) (apply v ?1596) [1597, 1596] by Super 19 with 3 at 1,2 +Id : 18, {_}: apply m (apply (apply v ?44) ?45) =<= apply (apply (apply (apply v ?44) ?45) ?44) ?45 [45, 44] by Super 3 with 4 at 3 +Id : 224, {_}: apply m (apply (apply v ?485) ?486) =<= apply (apply (apply ?485 ?485) ?486) ?486 [486, 485] by Demod 18 with 4 at 1,3 +Id : 232, {_}: apply m (apply (apply v ?509) ?510) =<= apply (apply (apply m ?509) ?510) ?510 [510, 509] by Super 224 with 3 at 1,1,3 +Id : 7751, {_}: apply (apply m (apply v ?7787)) (apply (apply m ?7788) ?7787) =<= apply (apply m (apply (apply v ?7788) ?7787)) (apply v ?7787) [7788, 7787] by Super 1244 with 232 at 1,3 +Id : 9, {_}: apply (apply (apply m b) ?24) ?25 =>= apply b (apply ?24 ?25) [25, 24] by Super 2 with 3 at 1,1,2 +Id : 236, {_}: apply m (apply (apply v (apply v ?521)) ?522) =<= apply (apply (apply ?522 ?521) (apply v ?521)) ?522 [522, 521] by Super 224 with 4 at 1,3 +Id : 2866, {_}: apply m (apply (apply v (apply v b)) m) =>= apply b (apply (apply v b) m) [] by Super 9 with 236 at 2 +Id : 7790, {_}: apply (apply m (apply v m)) (apply (apply m (apply v b)) m) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Super 7751 with 2866 at 1,3 +Id : 20, {_}: apply (apply m (apply v ?51)) ?52 =?= apply (apply ?52 ?51) (apply v ?51) [52, 51] by Super 19 with 3 at 1,2 +Id : 7860, {_}: apply (apply m (apply v m)) (apply (apply m b) (apply v b)) =>= apply (apply b (apply (apply v b) m)) (apply v m) [] by Demod 7790 with 20 at 2,2 +Id : 11, {_}: apply m (apply (apply b ?30) ?31) =<= apply ?30 (apply ?31 (apply (apply b ?30) ?31)) [31, 30] by Super 2 with 3 at 2 +Id : 9568, {_}: apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) =?= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b)) (apply m (apply (apply b (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) b))) m)) [] by Super 9567 with 11 at 2 +Id : 9567, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m)) [8771] by Demod 9566 with 2 at 2,3 +Id : 9566, {_}: apply m (apply (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) m) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9565 with 2 at 2 +Id : 9565, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m) [8771] by Demod 9564 with 4 at 1,2,3 +Id : 9564, {_}: apply (apply (apply b m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9563 with 4 at 1,2 +Id : 9563, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m) [8771] by Demod 9562 with 4 at 2,3 +Id : 9562, {_}: apply (apply (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) b) m =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9561 with 4 at 2 +Id : 9561, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))))) [8771] by Demod 9560 with 2 at 2,3 +Id : 9560, {_}: apply (apply (apply v b) m) (apply (apply v m) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9559 with 2 at 2 +Id : 9559, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9558 with 7860 at 1,2,3 +Id : 9558, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9557 with 7860 at 2,1,1,1,3 +Id : 9557, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9556 with 7860 at 2,1,1,2,2,2 +Id : 9556, {_}: apply (apply (apply b (apply (apply v b) m)) (apply v m)) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Demod 9078 with 7860 at 1,2 +Id : 9078, {_}: apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771))) =<= apply (f (apply (apply b (apply (apply m (apply v m)) (apply (apply m b) (apply v b)))) ?8771)) (apply (apply (apply m (apply v m)) (apply (apply m b) (apply v b))) (apply ?8771 (f (apply (apply b (apply (apply b (apply (apply v b) m)) (apply v m))) ?8771)))) [8771] by Super 174 with 7860 at 2,1,1,2,2,2,3 +Id : 174, {_}: apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381))) =<= apply (f (apply (apply b (apply ?379 ?380)) ?381)) (apply (apply ?379 ?380) (apply ?381 (f (apply (apply b (apply ?379 ?380)) ?381)))) [381, 380, 379] by Super 8 with 6 at 1,1,2,2,2,3 +Id : 8, {_}: apply ?21 (apply ?22 (f (apply (apply b ?21) ?22))) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Demod 7 with 2 at 2 +Id : 7, {_}: apply (apply (apply b ?21) ?22) (f (apply (apply b ?21) ?22)) =<= apply (f (apply (apply b ?21) ?22)) (apply ?21 (apply ?22 (f (apply (apply b ?21) ?22)))) [22, 21] by Super 1 with 2 at 2,3 +Id : 1, {_}: apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) [1] by prove_fixed_point ?1 +% SZS output end CNFRefutation for COL038-1.p +25471: solved COL038-1.p in 3.192199 using kbo +25471: status Unsatisfiable for COL038-1.p +CLASH, statistics insufficient +25477: Facts: +25477: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25477: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25477: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11 +25477: Goal: +25477: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25477: Order: +25477: nrkbo +25477: Leaf order: +25477: s 1 0 0 +25477: b 1 0 0 +25477: m 1 0 0 +25477: f 3 1 3 0,2,2 +25477: apply 16 2 3 0,2 +CLASH, statistics insufficient +25478: Facts: +25478: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25478: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25478: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11 +25478: Goal: +25478: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25478: Order: +25478: kbo +25478: Leaf order: +25478: s 1 0 0 +25478: b 1 0 0 +25478: m 1 0 0 +25478: f 3 1 3 0,2,2 +25478: apply 16 2 3 0,2 +CLASH, statistics insufficient +25479: Facts: +25479: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25479: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25479: Id : 4, {_}: apply m ?11 =?= apply ?11 ?11 [11] by m_definition ?11 +25479: Goal: +25479: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25479: Order: +25479: lpo +25479: Leaf order: +25479: s 1 0 0 +25479: b 1 0 0 +25479: m 1 0 0 +25479: f 3 1 3 0,2,2 +25479: apply 16 2 3 0,2 +% SZS status Timeout for COL046-1.p +CLASH, statistics insufficient +25500: Facts: +25500: Id : 2, {_}: + apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4) + [4, 3] by l_definition ?3 ?4 +25500: Id : 3, {_}: + apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8) + [8, 7, 6] by q_definition ?6 ?7 ?8 +25500: Goal: +25500: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_model ?1 +25500: Order: +25500: nrkbo +25500: Leaf order: +25500: l 1 0 0 +25500: q 1 0 0 +25500: f 3 1 3 0,2,2 +25500: apply 12 2 3 0,2 +CLASH, statistics insufficient +25501: Facts: +25501: Id : 2, {_}: + apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4) + [4, 3] by l_definition ?3 ?4 +25501: Id : 3, {_}: + apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8) + [8, 7, 6] by q_definition ?6 ?7 ?8 +25501: Goal: +25501: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_model ?1 +25501: Order: +25501: kbo +25501: Leaf order: +25501: l 1 0 0 +25501: q 1 0 0 +25501: f 3 1 3 0,2,2 +25501: apply 12 2 3 0,2 +CLASH, statistics insufficient +25502: Facts: +25502: Id : 2, {_}: + apply (apply l ?3) ?4 =?= apply ?3 (apply ?4 ?4) + [4, 3] by l_definition ?3 ?4 +25502: Id : 3, {_}: + apply (apply (apply q ?6) ?7) ?8 =>= apply ?7 (apply ?6 ?8) + [8, 7, 6] by q_definition ?6 ?7 ?8 +25502: Goal: +25502: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_model ?1 +25502: Order: +25502: lpo +25502: Leaf order: +25502: l 1 0 0 +25502: q 1 0 0 +25502: f 3 1 3 0,2,2 +25502: apply 12 2 3 0,2 +% SZS status Timeout for COL047-1.p +CLASH, statistics insufficient +25526: Facts: +25526: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25526: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25526: Goal: +25526: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (g ?1) (apply (f ?1) (h ?1)) + [1] by prove_q_combinator ?1 +25526: Order: +25526: nrkbo +25526: Leaf order: +25526: b 1 0 0 +25526: t 1 0 0 +25526: f 2 1 2 0,2,1,1,2 +25526: g 2 1 2 0,2,1,2 +25526: h 2 1 2 0,2,2 +25526: apply 13 2 5 0,2 +CLASH, statistics insufficient +25527: Facts: +25527: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25527: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25527: Goal: +25527: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (g ?1) (apply (f ?1) (h ?1)) + [1] by prove_q_combinator ?1 +25527: Order: +25527: kbo +25527: Leaf order: +25527: b 1 0 0 +25527: t 1 0 0 +25527: f 2 1 2 0,2,1,1,2 +25527: g 2 1 2 0,2,1,2 +25527: h 2 1 2 0,2,2 +25527: apply 13 2 5 0,2 +CLASH, statistics insufficient +25528: Facts: +25528: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25528: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25528: Goal: +25528: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (g ?1) (apply (f ?1) (h ?1)) + [1] by prove_q_combinator ?1 +25528: Order: +25528: lpo +25528: Leaf order: +25528: b 1 0 0 +25528: t 1 0 0 +25528: f 2 1 2 0,2,1,1,2 +25528: g 2 1 2 0,2,1,2 +25528: h 2 1 2 0,2,2 +25528: apply 13 2 5 0,2 +Goal subsumed +Statistics : +Max weight : 76 +Found proof, 0.356753s +% SZS status Unsatisfiable for COL060-1.p +% SZS output start CNFRefutation for COL060-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 447, {_}: apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) === apply (g (apply (apply b (apply t b)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t b)) (apply (apply b b) t))) (h (apply (apply b (apply t b)) (apply (apply b b) t)))) [] by Super 445 with 2 at 2 +Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) [1404] by Super 277 with 3 at 1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (g (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (g (apply (apply b ?18) ?19)) (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (g ?1) (apply (f ?1) (h ?1)) [1] by prove_q_combinator ?1 +% SZS output end CNFRefutation for COL060-1.p +25526: solved COL060-1.p in 0.368022 using nrkbo +25526: status Unsatisfiable for COL060-1.p +CLASH, statistics insufficient +25533: Facts: +25533: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25533: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25533: Goal: +25533: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (f ?1) (apply (h ?1) (g ?1)) + [1] by prove_q1_combinator ?1 +25533: Order: +25533: nrkbo +25533: Leaf order: +25533: b 1 0 0 +25533: t 1 0 0 +25533: f 2 1 2 0,2,1,1,2 +25533: g 2 1 2 0,2,1,2 +25533: h 2 1 2 0,2,2 +25533: apply 13 2 5 0,2 +CLASH, statistics insufficient +25534: Facts: +25534: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25534: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25534: Goal: +25534: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (f ?1) (apply (h ?1) (g ?1)) + [1] by prove_q1_combinator ?1 +25534: Order: +25534: kbo +25534: Leaf order: +25534: b 1 0 0 +25534: t 1 0 0 +25534: f 2 1 2 0,2,1,1,2 +25534: g 2 1 2 0,2,1,2 +25534: h 2 1 2 0,2,2 +25534: apply 13 2 5 0,2 +CLASH, statistics insufficient +25535: Facts: +25535: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25535: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25535: Goal: +25535: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (f ?1) (apply (h ?1) (g ?1)) + [1] by prove_q1_combinator ?1 +25535: Order: +25535: lpo +25535: Leaf order: +25535: b 1 0 0 +25535: t 1 0 0 +25535: f 2 1 2 0,2,1,1,2 +25535: g 2 1 2 0,2,1,2 +25535: h 2 1 2 0,2,2 +25535: apply 13 2 5 0,2 +Goal subsumed +Statistics : +Max weight : 76 +Found proof, 0.641348s +% SZS status Unsatisfiable for COL061-1.p +% SZS output start CNFRefutation for COL061-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 447, {_}: apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) === apply (f (apply (apply b (apply t t)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) b))) (g (apply (apply b (apply t t)) (apply (apply b b) b)))) [] by Super 446 with 3 at 2,2 +Id : 446, {_}: apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (apply ?1406 (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) (h (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) =>= apply (f (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (apply (h (apply (apply b (apply t ?1406)) (apply (apply b b) b))) (g (apply (apply b (apply t ?1406)) (apply (apply b b) b)))) [1406] by Super 277 with 2 at 2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (f (apply (apply b ?18) ?19)) (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (f ?1) (apply (h ?1) (g ?1)) [1] by prove_q1_combinator ?1 +% SZS output end CNFRefutation for COL061-1.p +25533: solved COL061-1.p in 0.344021 using nrkbo +25533: status Unsatisfiable for COL061-1.p +CLASH, statistics insufficient +25541: Facts: +25541: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25541: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25541: Goal: +25541: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (h ?1)) (g ?1) + [1] by prove_c_combinator ?1 +25541: Order: +25541: kbo +25541: Leaf order: +25541: b 1 0 0 +25541: t 1 0 0 +25541: f 2 1 2 0,2,1,1,2 +25541: g 2 1 2 0,2,1,2 +25541: h 2 1 2 0,2,2 +25541: apply 13 2 5 0,2 +CLASH, statistics insufficient +25540: Facts: +25540: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25540: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25540: Goal: +25540: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (h ?1)) (g ?1) + [1] by prove_c_combinator ?1 +25540: Order: +25540: nrkbo +25540: Leaf order: +25540: b 1 0 0 +25540: t 1 0 0 +25540: f 2 1 2 0,2,1,1,2 +25540: g 2 1 2 0,2,1,2 +25540: h 2 1 2 0,2,2 +25540: apply 13 2 5 0,2 +CLASH, statistics insufficient +25542: Facts: +25542: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25542: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +25542: Goal: +25542: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (h ?1)) (g ?1) + [1] by prove_c_combinator ?1 +25542: Order: +25542: lpo +25542: Leaf order: +25542: b 1 0 0 +25542: t 1 0 0 +25542: f 2 1 2 0,2,1,1,2 +25542: g 2 1 2 0,2,1,2 +25542: h 2 1 2 0,2,2 +25542: apply 13 2 5 0,2 +Goal subsumed +Statistics : +Max weight : 100 +Found proof, 1.793493s +% SZS status Unsatisfiable for COL062-1.p +% SZS output start CNFRefutation for COL062-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 1574, {_}: apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) === apply (apply (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t))) [] by Super 1573 with 3 at 2 +Id : 1573, {_}: apply (apply ?5215 (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b b) ?5215))) (apply (apply b b) t))) [5215] by Super 447 with 2 at 2 +Id : 447, {_}: apply (apply (apply ?1408 (apply ?1409 (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) (h (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t)))) (g (apply (apply b (apply t (apply (apply b ?1408) ?1409))) (apply (apply b b) t))) [1409, 1408] by Super 445 with 2 at 1,1,2 +Id : 445, {_}: apply (apply (apply ?1404 (g (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (f (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t))) =>= apply (apply (f (apply (apply b (apply t ?1404)) (apply (apply b b) t))) (h (apply (apply b (apply t ?1404)) (apply (apply b b) t)))) (g (apply (apply b (apply t ?1404)) (apply (apply b b) t))) [1404] by Super 277 with 3 at 1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (f (apply (apply b ?33) (apply (apply b ?34) ?35))) (h (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (f (apply (apply b ?18) ?19)) (h (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (f ?1) (h ?1)) (g ?1) [1] by prove_c_combinator ?1 +% SZS output end CNFRefutation for COL062-1.p +25540: solved COL062-1.p in 1.808112 using nrkbo +25540: status Unsatisfiable for COL062-1.p +CLASH, statistics insufficient +25547: Facts: +25547: Id : 2, {_}: + apply (apply (apply n ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?5) ?4) ?5 + [5, 4, 3] by n_definition ?3 ?4 ?5 +25547: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +25547: Goal: +25547: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25547: Order: +25547: nrkbo +25547: Leaf order: +25547: n 1 0 0 +25547: q 1 0 0 +25547: f 3 1 3 0,2,2 +25547: apply 14 2 3 0,2 +CLASH, statistics insufficient +25548: Facts: +25548: Id : 2, {_}: + apply (apply (apply n ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?5) ?4) ?5 + [5, 4, 3] by n_definition ?3 ?4 ?5 +25548: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +25548: Goal: +25548: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25548: Order: +25548: kbo +25548: Leaf order: +25548: n 1 0 0 +25548: q 1 0 0 +25548: f 3 1 3 0,2,2 +25548: apply 14 2 3 0,2 +CLASH, statistics insufficient +25549: Facts: +25549: Id : 2, {_}: + apply (apply (apply n ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?5) ?4) ?5 + [5, 4, 3] by n_definition ?3 ?4 ?5 +25549: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +25549: Goal: +25549: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25549: Order: +25549: lpo +25549: Leaf order: +25549: n 1 0 0 +25549: q 1 0 0 +25549: f 3 1 3 0,2,2 +25549: apply 14 2 3 0,2 +% SZS status Timeout for COL071-1.p +CLASH, statistics insufficient +25572: Facts: +25572: Id : 2, {_}: + apply (apply (apply n1 ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?4) ?4) ?5 + [5, 4, 3] by n1_definition ?3 ?4 ?5 +25572: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25572: Goal: +25572: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +25572: Order: +25572: nrkbo +25572: Leaf order: +25572: n1 1 0 0 +25572: b 1 0 0 +25572: f 3 1 3 0,2,2 +25572: apply 14 2 3 0,2 +CLASH, statistics insufficient +25573: Facts: +25573: Id : 2, {_}: + apply (apply (apply n1 ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?4) ?4) ?5 + [5, 4, 3] by n1_definition ?3 ?4 ?5 +25573: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25573: Goal: +25573: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +25573: Order: +25573: kbo +25573: Leaf order: +25573: n1 1 0 0 +25573: b 1 0 0 +25573: f 3 1 3 0,2,2 +25573: apply 14 2 3 0,2 +CLASH, statistics insufficient +25574: Facts: +25574: Id : 2, {_}: + apply (apply (apply n1 ?3) ?4) ?5 + =?= + apply (apply (apply ?3 ?4) ?4) ?5 + [5, 4, 3] by n1_definition ?3 ?4 ?5 +25574: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25574: Goal: +25574: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +25574: Order: +25574: lpo +25574: Leaf order: +25574: n1 1 0 0 +25574: b 1 0 0 +25574: f 3 1 3 0,2,2 +25574: apply 14 2 3 0,2 +% SZS status Timeout for COL073-1.p +NO CLASH, using fixed ground order +25603: Facts: +25603: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25603: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25603: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25603: Id : 5, {_}: + commutator ?10 ?11 + =<= + multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11)) + [11, 10] by name ?10 ?11 +25603: Id : 6, {_}: + commutator (commutator ?13 ?14) ?15 + =?= + commutator ?13 (commutator ?14 ?15) + [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15 +25603: Goal: +25603: Id : 1, {_}: + multiply a (commutator b c) =<= multiply (commutator b c) a + [] by prove_center +25603: Order: +25603: nrkbo +25603: Leaf order: +25603: identity 2 0 0 +25603: a 2 0 2 1,2 +25603: b 2 0 2 1,2,2 +25603: c 2 0 2 2,2,2 +25603: inverse 3 1 0 +25603: commutator 7 2 2 0,2,2 +25603: multiply 11 2 2 0,2 +NO CLASH, using fixed ground order +25604: Facts: +25604: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25604: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25604: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25604: Id : 5, {_}: + commutator ?10 ?11 + =<= + multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11)) + [11, 10] by name ?10 ?11 +25604: Id : 6, {_}: + commutator (commutator ?13 ?14) ?15 + =>= + commutator ?13 (commutator ?14 ?15) + [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15 +25604: Goal: +25604: Id : 1, {_}: + multiply a (commutator b c) =<= multiply (commutator b c) a + [] by prove_center +25604: Order: +25604: kbo +25604: Leaf order: +25604: identity 2 0 0 +25604: a 2 0 2 1,2 +25604: b 2 0 2 1,2,2 +25604: c 2 0 2 2,2,2 +25604: inverse 3 1 0 +25604: commutator 7 2 2 0,2,2 +25604: multiply 11 2 2 0,2 +NO CLASH, using fixed ground order +25605: Facts: +25605: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25605: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25605: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25605: Id : 5, {_}: + commutator ?10 ?11 + =<= + multiply (inverse ?10) (multiply (inverse ?11) (multiply ?10 ?11)) + [11, 10] by name ?10 ?11 +25605: Id : 6, {_}: + commutator (commutator ?13 ?14) ?15 + =>= + commutator ?13 (commutator ?14 ?15) + [15, 14, 13] by associativity_of_commutator ?13 ?14 ?15 +25605: Goal: +25605: Id : 1, {_}: + multiply a (commutator b c) =<= multiply (commutator b c) a + [] by prove_center +25605: Order: +25605: lpo +25605: Leaf order: +25605: identity 2 0 0 +25605: a 2 0 2 1,2 +25605: b 2 0 2 1,2,2 +25605: c 2 0 2 2,2,2 +25605: inverse 3 1 0 +25605: commutator 7 2 2 0,2,2 +25605: multiply 11 2 2 0,2 +% SZS status Timeout for GRP024-5.p +CLASH, statistics insufficient +25668: Facts: +25668: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25668: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25668: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25668: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +25668: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +25668: Id : 7, {_}: + inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) + [14, 13] by inverse_product_lemma ?13 ?14 +25668: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16 +25668: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18 +25668: Id : 10, {_}: + intersection ?20 ?21 =?= intersection ?21 ?20 + [21, 20] by intersection_commutative ?20 ?21 +25668: Id : 11, {_}: + union ?23 ?24 =?= union ?24 ?23 + [24, 23] by union_commutative ?23 ?24 +25668: Id : 12, {_}: + intersection ?26 (intersection ?27 ?28) + =?= + intersection (intersection ?26 ?27) ?28 + [28, 27, 26] by intersection_associative ?26 ?27 ?28 +25668: Id : 13, {_}: + union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 + [32, 31, 30] by union_associative ?30 ?31 ?32 +25668: Id : 14, {_}: + union (intersection ?34 ?35) ?35 =>= ?35 + [35, 34] by union_intersection_absorbtion ?34 ?35 +25668: Id : 15, {_}: + intersection (union ?37 ?38) ?38 =>= ?38 + [38, 37] by intersection_union_absorbtion ?37 ?38 +25668: Id : 16, {_}: + multiply ?40 (union ?41 ?42) + =<= + union (multiply ?40 ?41) (multiply ?40 ?42) + [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +25668: Id : 17, {_}: + multiply ?44 (intersection ?45 ?46) + =<= + intersection (multiply ?44 ?45) (multiply ?44 ?46) + [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +25668: Id : 18, {_}: + multiply (union ?48 ?49) ?50 + =<= + union (multiply ?48 ?50) (multiply ?49 ?50) + [50, 49, 48] by multiply_union2 ?48 ?49 ?50 +25668: Id : 19, {_}: + multiply (intersection ?52 ?53) ?54 + =<= + intersection (multiply ?52 ?54) (multiply ?53 ?54) + [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54 +25668: Id : 20, {_}: + positive_part ?56 =<= union ?56 identity + [56] by positive_part ?56 +25668: Id : 21, {_}: + negative_part ?58 =<= intersection ?58 identity + [58] by negative_part ?58 +25668: Goal: +25668: Id : 1, {_}: + multiply (positive_part a) (negative_part a) =>= a + [] by prove_product +25668: Order: +25668: nrkbo +25668: Leaf order: +25668: a 3 0 3 1,1,2 +25668: identity 6 0 0 +25668: positive_part 2 1 1 0,1,2 +25668: negative_part 2 1 1 0,2,2 +25668: inverse 7 1 0 +25668: intersection 14 2 0 +25668: union 14 2 0 +25668: multiply 21 2 1 0,2 +CLASH, statistics insufficient +25669: Facts: +25669: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25669: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25669: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25669: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +25669: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +25669: Id : 7, {_}: + inverse (multiply ?13 ?14) =<= multiply (inverse ?14) (inverse ?13) + [14, 13] by inverse_product_lemma ?13 ?14 +25669: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16 +CLASH, statistics insufficient +25670: Facts: +25670: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25670: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25670: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25670: Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +25670: Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +25670: Id : 7, {_}: + inverse (multiply ?13 ?14) =?= multiply (inverse ?14) (inverse ?13) + [14, 13] by inverse_product_lemma ?13 ?14 +25670: Id : 8, {_}: intersection ?16 ?16 =>= ?16 [16] by intersection_idempotent ?16 +25669: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18 +25669: Id : 10, {_}: + intersection ?20 ?21 =?= intersection ?21 ?20 + [21, 20] by intersection_commutative ?20 ?21 +25669: Id : 11, {_}: + union ?23 ?24 =?= union ?24 ?23 + [24, 23] by union_commutative ?23 ?24 +25669: Id : 12, {_}: + intersection ?26 (intersection ?27 ?28) + =<= + intersection (intersection ?26 ?27) ?28 + [28, 27, 26] by intersection_associative ?26 ?27 ?28 +25669: Id : 13, {_}: + union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 + [32, 31, 30] by union_associative ?30 ?31 ?32 +25669: Id : 14, {_}: + union (intersection ?34 ?35) ?35 =>= ?35 + [35, 34] by union_intersection_absorbtion ?34 ?35 +25669: Id : 15, {_}: + intersection (union ?37 ?38) ?38 =>= ?38 + [38, 37] by intersection_union_absorbtion ?37 ?38 +25669: Id : 16, {_}: + multiply ?40 (union ?41 ?42) + =<= + union (multiply ?40 ?41) (multiply ?40 ?42) + [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +25669: Id : 17, {_}: + multiply ?44 (intersection ?45 ?46) + =<= + intersection (multiply ?44 ?45) (multiply ?44 ?46) + [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +25669: Id : 18, {_}: + multiply (union ?48 ?49) ?50 + =<= + union (multiply ?48 ?50) (multiply ?49 ?50) + [50, 49, 48] by multiply_union2 ?48 ?49 ?50 +25669: Id : 19, {_}: + multiply (intersection ?52 ?53) ?54 + =<= + intersection (multiply ?52 ?54) (multiply ?53 ?54) + [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54 +25669: Id : 20, {_}: + positive_part ?56 =<= union ?56 identity + [56] by positive_part ?56 +25669: Id : 21, {_}: + negative_part ?58 =<= intersection ?58 identity + [58] by negative_part ?58 +25669: Goal: +25669: Id : 1, {_}: + multiply (positive_part a) (negative_part a) =>= a + [] by prove_product +25669: Order: +25669: kbo +25669: Leaf order: +25669: a 3 0 3 1,1,2 +25669: identity 6 0 0 +25669: positive_part 2 1 1 0,1,2 +25669: negative_part 2 1 1 0,2,2 +25669: inverse 7 1 0 +25669: intersection 14 2 0 +25669: union 14 2 0 +25669: multiply 21 2 1 0,2 +25670: Id : 9, {_}: union ?18 ?18 =>= ?18 [18] by union_idempotent ?18 +25670: Id : 10, {_}: + intersection ?20 ?21 =?= intersection ?21 ?20 + [21, 20] by intersection_commutative ?20 ?21 +25670: Id : 11, {_}: + union ?23 ?24 =?= union ?24 ?23 + [24, 23] by union_commutative ?23 ?24 +25670: Id : 12, {_}: + intersection ?26 (intersection ?27 ?28) + =<= + intersection (intersection ?26 ?27) ?28 + [28, 27, 26] by intersection_associative ?26 ?27 ?28 +25670: Id : 13, {_}: + union ?30 (union ?31 ?32) =<= union (union ?30 ?31) ?32 + [32, 31, 30] by union_associative ?30 ?31 ?32 +25670: Id : 14, {_}: + union (intersection ?34 ?35) ?35 =>= ?35 + [35, 34] by union_intersection_absorbtion ?34 ?35 +25670: Id : 15, {_}: + intersection (union ?37 ?38) ?38 =>= ?38 + [38, 37] by intersection_union_absorbtion ?37 ?38 +25670: Id : 16, {_}: + multiply ?40 (union ?41 ?42) + =>= + union (multiply ?40 ?41) (multiply ?40 ?42) + [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +25670: Id : 17, {_}: + multiply ?44 (intersection ?45 ?46) + =>= + intersection (multiply ?44 ?45) (multiply ?44 ?46) + [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +25670: Id : 18, {_}: + multiply (union ?48 ?49) ?50 + =>= + union (multiply ?48 ?50) (multiply ?49 ?50) + [50, 49, 48] by multiply_union2 ?48 ?49 ?50 +25670: Id : 19, {_}: + multiply (intersection ?52 ?53) ?54 + =>= + intersection (multiply ?52 ?54) (multiply ?53 ?54) + [54, 53, 52] by multiply_intersection2 ?52 ?53 ?54 +25670: Id : 20, {_}: + positive_part ?56 =>= union ?56 identity + [56] by positive_part ?56 +25670: Id : 21, {_}: + negative_part ?58 =>= intersection ?58 identity + [58] by negative_part ?58 +25670: Goal: +25670: Id : 1, {_}: + multiply (positive_part a) (negative_part a) =>= a + [] by prove_product +25670: Order: +25670: lpo +25670: Leaf order: +25670: a 3 0 3 1,1,2 +25670: identity 6 0 0 +25670: positive_part 2 1 1 0,1,2 +25670: negative_part 2 1 1 0,2,2 +25670: inverse 7 1 0 +25670: intersection 14 2 0 +25670: union 14 2 0 +25670: multiply 21 2 1 0,2 +Statistics : +Max weight : 16 +Found proof, 7.917801s +% SZS status Unsatisfiable for GRP114-1.p +% SZS output start CNFRefutation for GRP114-1.p +Id : 12, {_}: intersection ?26 (intersection ?27 ?28) =?= intersection (intersection ?26 ?27) ?28 [28, 27, 26] by intersection_associative ?26 ?27 ?28 +Id : 17, {_}: multiply ?44 (intersection ?45 ?46) =<= intersection (multiply ?44 ?45) (multiply ?44 ?46) [46, 45, 44] by multiply_intersection1 ?44 ?45 ?46 +Id : 14, {_}: union (intersection ?34 ?35) ?35 =>= ?35 [35, 34] by union_intersection_absorbtion ?34 ?35 +Id : 16, {_}: multiply ?40 (union ?41 ?42) =<= union (multiply ?40 ?41) (multiply ?40 ?42) [42, 41, 40] by multiply_union1 ?40 ?41 ?42 +Id : 13, {_}: union ?30 (union ?31 ?32) =?= union (union ?30 ?31) ?32 [32, 31, 30] by union_associative ?30 ?31 ?32 +Id : 241, {_}: multiply (union ?684 ?685) ?686 =<= union (multiply ?684 ?686) (multiply ?685 ?686) [686, 685, 684] by multiply_union2 ?684 ?685 ?686 +Id : 20, {_}: positive_part ?56 =<= union ?56 identity [56] by positive_part ?56 +Id : 11, {_}: union ?23 ?24 =?= union ?24 ?23 [24, 23] by union_commutative ?23 ?24 +Id : 15, {_}: intersection (union ?37 ?38) ?38 =>= ?38 [38, 37] by intersection_union_absorbtion ?37 ?38 +Id : 205, {_}: multiply ?602 (intersection ?603 ?604) =<= intersection (multiply ?602 ?603) (multiply ?602 ?604) [604, 603, 602] by multiply_intersection1 ?602 ?603 ?604 +Id : 21, {_}: negative_part ?58 =<= intersection ?58 identity [58] by negative_part ?58 +Id : 10, {_}: intersection ?20 ?21 =?= intersection ?21 ?20 [21, 20] by intersection_commutative ?20 ?21 +Id : 276, {_}: multiply (intersection ?769 ?770) ?771 =<= intersection (multiply ?769 ?771) (multiply ?770 ?771) [771, 770, 769] by multiply_intersection2 ?769 ?770 ?771 +Id : 6, {_}: inverse (inverse ?11) =>= ?11 [11] by inverse_involution ?11 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 5, {_}: inverse identity =>= identity [] by inverse_of_identity +Id : 58, {_}: inverse (multiply ?149 ?150) =<= multiply (inverse ?150) (inverse ?149) [150, 149] by inverse_product_lemma ?149 ?150 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 26, {_}: multiply (multiply ?67 ?68) ?69 =?= multiply ?67 (multiply ?68 ?69) [69, 68, 67] by associativity ?67 ?68 ?69 +Id : 28, {_}: multiply (multiply ?74 (inverse ?75)) ?75 =>= multiply ?74 identity [75, 74] by Super 26 with 3 at 2,3 +Id : 59, {_}: inverse (multiply identity ?152) =<= multiply (inverse ?152) identity [152] by Super 58 with 5 at 2,3 +Id : 459, {_}: inverse ?1057 =<= multiply (inverse ?1057) identity [1057] by Demod 59 with 2 at 1,2 +Id : 461, {_}: inverse (inverse ?1060) =<= multiply ?1060 identity [1060] by Super 459 with 6 at 1,3 +Id : 475, {_}: ?1060 =<= multiply ?1060 identity [1060] by Demod 461 with 6 at 2 +Id : 570, {_}: multiply (multiply ?74 (inverse ?75)) ?75 =>= ?74 [75, 74] by Demod 28 with 475 at 3 +Id : 62, {_}: inverse (multiply ?159 (inverse ?160)) =>= multiply ?160 (inverse ?159) [160, 159] by Super 58 with 6 at 1,3 +Id : 283, {_}: multiply (intersection (inverse ?796) ?797) ?796 =>= intersection identity (multiply ?797 ?796) [797, 796] by Super 276 with 3 at 1,3 +Id : 329, {_}: intersection identity ?869 =>= negative_part ?869 [869] by Super 10 with 21 at 3 +Id : 16231, {_}: multiply (intersection (inverse ?20320) ?20321) ?20320 =>= negative_part (multiply ?20321 ?20320) [20321, 20320] by Demod 283 with 329 at 3 +Id : 16259, {_}: multiply (negative_part (inverse ?20413)) ?20413 =>= negative_part (multiply identity ?20413) [20413] by Super 16231 with 21 at 1,2 +Id : 16311, {_}: multiply (negative_part (inverse ?20413)) ?20413 =>= negative_part ?20413 [20413] by Demod 16259 with 2 at 1,3 +Id : 16342, {_}: inverse (negative_part (inverse ?20447)) =<= multiply ?20447 (inverse (negative_part (inverse (inverse ?20447)))) [20447] by Super 62 with 16311 at 1,2 +Id : 16414, {_}: inverse (negative_part (inverse ?20447)) =<= multiply ?20447 (inverse (negative_part ?20447)) [20447] by Demod 16342 with 6 at 1,1,2,3 +Id : 16644, {_}: multiply (inverse (negative_part (inverse ?20815))) (negative_part ?20815) =>= ?20815 [20815] by Super 570 with 16414 at 1,2 +Id : 60, {_}: inverse (multiply (inverse ?154) ?155) =>= multiply (inverse ?155) ?154 [155, 154] by Super 58 with 6 at 2,3 +Id : 207, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= intersection (multiply (inverse ?609) ?610) identity [610, 609] by Super 205 with 3 at 2,3 +Id : 228, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= intersection identity (multiply (inverse ?609) ?610) [610, 609] by Demod 207 with 10 at 3 +Id : 10379, {_}: multiply (inverse ?609) (intersection ?610 ?609) =>= negative_part (multiply (inverse ?609) ?610) [610, 609] by Demod 228 with 329 at 3 +Id : 10396, {_}: inverse (negative_part (multiply (inverse ?14999) ?15000)) =<= multiply (inverse (intersection ?15000 ?14999)) ?14999 [15000, 14999] by Super 60 with 10379 at 1,2 +Id : 309, {_}: union identity ?834 =>= positive_part ?834 [834] by Super 11 with 20 at 3 +Id : 360, {_}: intersection (positive_part ?914) ?914 =>= ?914 [914] by Super 15 with 309 at 1,2 +Id : 686, {_}: intersection ?1353 (positive_part ?1353) =>= ?1353 [1353] by Super 10 with 360 at 3 +Id : 248, {_}: multiply (union (inverse ?711) ?712) ?711 =>= union identity (multiply ?712 ?711) [712, 711] by Super 241 with 3 at 1,3 +Id : 10542, {_}: multiply (union (inverse ?15313) ?15314) ?15313 =>= positive_part (multiply ?15314 ?15313) [15314, 15313] by Demod 248 with 309 at 3 +Id : 359, {_}: union identity (union ?911 ?912) =>= union (positive_part ?911) ?912 [912, 911] by Super 13 with 309 at 1,3 +Id : 367, {_}: positive_part (union ?911 ?912) =>= union (positive_part ?911) ?912 [912, 911] by Demod 359 with 309 at 2 +Id : 312, {_}: union ?841 (union ?842 identity) =>= positive_part (union ?841 ?842) [842, 841] by Super 13 with 20 at 3 +Id : 324, {_}: union ?841 (positive_part ?842) =<= positive_part (union ?841 ?842) [842, 841] by Demod 312 with 20 at 2,2 +Id : 709, {_}: union ?911 (positive_part ?912) =?= union (positive_part ?911) ?912 [912, 911] by Demod 367 with 324 at 2 +Id : 487, {_}: multiply ?1085 (union ?1086 identity) =?= union (multiply ?1085 ?1086) ?1085 [1086, 1085] by Super 16 with 475 at 2,3 +Id : 2720, {_}: multiply ?5029 (positive_part ?5030) =<= union (multiply ?5029 ?5030) ?5029 [5030, 5029] by Demod 487 with 20 at 2,2 +Id : 2722, {_}: multiply (inverse ?5034) (positive_part ?5034) =>= union identity (inverse ?5034) [5034] by Super 2720 with 3 at 1,3 +Id : 2784, {_}: multiply (inverse ?5160) (positive_part ?5160) =>= positive_part (inverse ?5160) [5160] by Demod 2722 with 309 at 3 +Id : 307, {_}: positive_part (intersection ?831 identity) =>= identity [831] by Super 14 with 20 at 2 +Id : 514, {_}: positive_part (negative_part ?831) =>= identity [831] by Demod 307 with 21 at 1,2 +Id : 2786, {_}: multiply (inverse (negative_part ?5163)) identity =>= positive_part (inverse (negative_part ?5163)) [5163] by Super 2784 with 514 at 2,2 +Id : 2807, {_}: inverse (negative_part ?5163) =<= positive_part (inverse (negative_part ?5163)) [5163] by Demod 2786 with 475 at 2 +Id : 2823, {_}: union (inverse (negative_part ?5198)) (positive_part ?5199) =>= union (inverse (negative_part ?5198)) ?5199 [5199, 5198] by Super 709 with 2807 at 1,3 +Id : 10564, {_}: multiply (union (inverse (negative_part ?15386)) ?15387) (negative_part ?15386) =>= positive_part (multiply (positive_part ?15387) (negative_part ?15386)) [15387, 15386] by Super 10542 with 2823 at 1,2 +Id : 10509, {_}: multiply (union (inverse ?711) ?712) ?711 =>= positive_part (multiply ?712 ?711) [712, 711] by Demod 248 with 309 at 3 +Id : 10604, {_}: positive_part (multiply ?15387 (negative_part ?15386)) =<= positive_part (multiply (positive_part ?15387) (negative_part ?15386)) [15386, 15387] by Demod 10564 with 10509 at 2 +Id : 481, {_}: multiply ?1071 (intersection ?1072 identity) =?= intersection (multiply ?1071 ?1072) ?1071 [1072, 1071] by Super 17 with 475 at 2,3 +Id : 505, {_}: multiply ?1071 (negative_part ?1072) =<= intersection (multiply ?1071 ?1072) ?1071 [1072, 1071] by Demod 481 with 21 at 2,2 +Id : 10568, {_}: multiply (positive_part (inverse ?15398)) ?15398 =>= positive_part (multiply identity ?15398) [15398] by Super 10542 with 20 at 1,2 +Id : 10608, {_}: multiply (positive_part (inverse ?15398)) ?15398 =>= positive_part ?15398 [15398] by Demod 10568 with 2 at 1,3 +Id : 10645, {_}: multiply (positive_part (inverse ?15507)) (negative_part ?15507) =>= intersection (positive_part ?15507) (positive_part (inverse ?15507)) [15507] by Super 505 with 10608 at 1,3 +Id : 11493, {_}: positive_part (multiply (inverse ?16415) (negative_part ?16415)) =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Super 10604 with 10645 at 1,3 +Id : 3426, {_}: multiply ?5989 (negative_part ?5990) =<= intersection (multiply ?5989 ?5990) ?5989 [5990, 5989] by Demod 481 with 21 at 2,2 +Id : 3428, {_}: multiply (inverse ?5994) (negative_part ?5994) =>= intersection identity (inverse ?5994) [5994] by Super 3426 with 3 at 1,3 +Id : 3468, {_}: multiply (inverse ?5994) (negative_part ?5994) =>= negative_part (inverse ?5994) [5994] by Demod 3428 with 329 at 3 +Id : 11531, {_}: positive_part (negative_part (inverse ?16415)) =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Demod 11493 with 3468 at 1,2 +Id : 11532, {_}: identity =<= positive_part (intersection (positive_part ?16415) (positive_part (inverse ?16415))) [16415] by Demod 11531 with 514 at 2 +Id : 52635, {_}: intersection (intersection (positive_part ?60922) (positive_part (inverse ?60922))) identity =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Super 686 with 11532 at 2,2 +Id : 52914, {_}: intersection identity (intersection (positive_part ?60922) (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52635 with 10 at 2 +Id : 52915, {_}: negative_part (intersection (positive_part ?60922) (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52914 with 329 at 2 +Id : 332, {_}: intersection ?876 (intersection ?877 identity) =>= negative_part (intersection ?876 ?877) [877, 876] by Super 12 with 21 at 3 +Id : 344, {_}: intersection ?876 (negative_part ?877) =<= negative_part (intersection ?876 ?877) [877, 876] by Demod 332 with 21 at 2,2 +Id : 52916, {_}: intersection (positive_part ?60922) (negative_part (positive_part (inverse ?60922))) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52915 with 344 at 2 +Id : 52917, {_}: intersection (negative_part (positive_part (inverse ?60922))) (positive_part ?60922) =>= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52916 with 10 at 2 +Id : 421, {_}: intersection identity (intersection ?1000 ?1001) =>= intersection (negative_part ?1000) ?1001 [1001, 1000] by Super 12 with 329 at 1,3 +Id : 435, {_}: negative_part (intersection ?1000 ?1001) =>= intersection (negative_part ?1000) ?1001 [1001, 1000] by Demod 421 with 329 at 2 +Id : 903, {_}: intersection ?1965 (negative_part ?1966) =?= intersection (negative_part ?1965) ?1966 [1966, 1965] by Demod 435 with 344 at 2 +Id : 327, {_}: negative_part (union ?866 identity) =>= identity [866] by Super 15 with 21 at 2 +Id : 346, {_}: negative_part (positive_part ?866) =>= identity [866] by Demod 327 with 20 at 1,2 +Id : 914, {_}: intersection (positive_part ?1997) (negative_part ?1998) =>= intersection identity ?1998 [1998, 1997] by Super 903 with 346 at 1,2 +Id : 945, {_}: intersection (negative_part ?1998) (positive_part ?1997) =>= intersection identity ?1998 [1997, 1998] by Demod 914 with 10 at 2 +Id : 946, {_}: intersection (negative_part ?1998) (positive_part ?1997) =>= negative_part ?1998 [1997, 1998] by Demod 945 with 329 at 3 +Id : 52918, {_}: negative_part (positive_part (inverse ?60922)) =<= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52917 with 946 at 2 +Id : 52919, {_}: identity =<= intersection (positive_part ?60922) (positive_part (inverse ?60922)) [60922] by Demod 52918 with 346 at 2 +Id : 53306, {_}: inverse (negative_part (multiply (inverse (positive_part (inverse ?61296))) (positive_part ?61296))) =>= multiply (inverse identity) (positive_part (inverse ?61296)) [61296] by Super 10396 with 52919 at 1,1,3 +Id : 10642, {_}: inverse (positive_part (inverse ?15501)) =<= multiply ?15501 (inverse (positive_part (inverse (inverse ?15501)))) [15501] by Super 62 with 10608 at 1,2 +Id : 10686, {_}: inverse (positive_part (inverse ?15501)) =<= multiply ?15501 (inverse (positive_part ?15501)) [15501] by Demod 10642 with 6 at 1,1,2,3 +Id : 10895, {_}: multiply (inverse (positive_part (inverse ?15767))) (positive_part ?15767) =>= ?15767 [15767] by Super 570 with 10686 at 1,2 +Id : 53366, {_}: inverse (negative_part ?61296) =<= multiply (inverse identity) (positive_part (inverse ?61296)) [61296] by Demod 53306 with 10895 at 1,1,2 +Id : 53367, {_}: inverse (negative_part ?61296) =<= multiply identity (positive_part (inverse ?61296)) [61296] by Demod 53366 with 5 at 1,3 +Id : 53816, {_}: inverse (negative_part ?61700) =<= positive_part (inverse ?61700) [61700] by Demod 53367 with 2 at 3 +Id : 53819, {_}: inverse (negative_part (multiply (inverse ?61705) ?61706)) =>= positive_part (multiply (inverse ?61706) ?61705) [61706, 61705] by Super 53816 with 60 at 1,3 +Id : 62826, {_}: inverse (positive_part (multiply (inverse ?68982) ?68983)) =>= negative_part (multiply (inverse ?68983) ?68982) [68983, 68982] by Super 6 with 53819 at 1,2 +Id : 62827, {_}: inverse (positive_part (multiply identity ?68985)) =<= negative_part (multiply (inverse ?68985) identity) [68985] by Super 62826 with 5 at 1,1,1,2 +Id : 63051, {_}: inverse (positive_part ?68985) =<= negative_part (multiply (inverse ?68985) identity) [68985] by Demod 62827 with 2 at 1,1,2 +Id : 63052, {_}: inverse (positive_part ?68985) =<= negative_part (inverse ?68985) [68985] by Demod 63051 with 475 at 1,3 +Id : 66930, {_}: multiply (inverse (inverse (positive_part ?20815))) (negative_part ?20815) =>= ?20815 [20815] by Demod 16644 with 63052 at 1,1,2 +Id : 66931, {_}: multiply (positive_part ?20815) (negative_part ?20815) =>= ?20815 [20815] by Demod 66930 with 6 at 1,2 +Id : 67152, {_}: a === a [] by Demod 1 with 66931 at 2 +Id : 1, {_}: multiply (positive_part a) (negative_part a) =>= a [] by prove_product +% SZS output end CNFRefutation for GRP114-1.p +25668: solved GRP114-1.p in 7.932495 using nrkbo +25668: status Unsatisfiable for GRP114-1.p +NO CLASH, using fixed ground order +25676: Facts: +25676: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25676: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25676: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25676: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25676: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25676: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25676: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25676: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25676: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25676: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25676: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25676: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25676: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25676: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25676: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25676: Id : 17, {_}: inverse identity =>= identity [] by p19_1 +25676: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51 +25676: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p19_3 ?53 ?54 +25676: Goal: +25676: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +25676: Order: +25676: kbo +25676: Leaf order: +25676: a 3 0 3 2 +25676: identity 6 0 2 2,1,3 +25676: inverse 7 1 0 +25676: least_upper_bound 14 2 1 0,1,3 +25676: greatest_lower_bound 14 2 1 0,2,3 +25676: multiply 21 2 1 0,3 +NO CLASH, using fixed ground order +25675: Facts: +25675: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25675: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25675: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25675: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25675: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25675: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25675: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25675: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25675: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25675: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25675: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25675: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25675: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25675: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25675: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25675: Id : 17, {_}: inverse identity =>= identity [] by p19_1 +25675: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51 +25675: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p19_3 ?53 ?54 +25675: Goal: +25675: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +25675: Order: +25675: nrkbo +25675: Leaf order: +25675: a 3 0 3 2 +25675: identity 6 0 2 2,1,3 +25675: inverse 7 1 0 +25675: least_upper_bound 14 2 1 0,1,3 +25675: greatest_lower_bound 14 2 1 0,2,3 +25675: multiply 21 2 1 0,3 +NO CLASH, using fixed ground order +25677: Facts: +25677: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25677: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25677: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25677: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25677: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25677: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25677: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25677: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25677: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25677: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25677: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25677: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25677: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25677: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25677: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25677: Id : 17, {_}: inverse identity =>= identity [] by p19_1 +25677: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p19_2 ?51 +25677: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p19_3 ?53 ?54 +25677: Goal: +25677: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +25677: Order: +25677: lpo +25677: Leaf order: +25677: a 3 0 3 2 +25677: identity 6 0 2 2,1,3 +25677: inverse 7 1 0 +25677: least_upper_bound 14 2 1 0,1,3 +25677: greatest_lower_bound 14 2 1 0,2,3 +25677: multiply 21 2 1 0,3 +% SZS status Timeout for GRP167-4.p +NO CLASH, using fixed ground order +25699: Facts: +25699: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25699: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25699: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25699: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25699: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25699: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25699: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25699: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25699: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25699: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25699: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25699: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25699: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25699: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25699: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25699: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1 +25699: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2 +25699: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3 +25699: Goal: +25699: Id : 1, {_}: + greatest_lower_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + greatest_lower_bound a (multiply b c) + [] by prove_p08b +25699: Order: +25699: nrkbo +25699: Leaf order: +25699: b 4 0 3 1,2,1,2 +25699: c 4 0 3 2,2,1,2 +25699: a 5 0 4 1,1,2 +25699: identity 8 0 0 +25699: inverse 1 1 0 +25699: least_upper_bound 13 2 0 +25699: multiply 21 2 3 0,2,1,2 +25699: greatest_lower_bound 21 2 5 0,2 +NO CLASH, using fixed ground order +25700: Facts: +25700: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25700: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25700: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25700: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25700: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25700: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25700: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25700: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25700: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25700: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25700: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25700: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25700: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25700: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25700: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25700: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1 +25700: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2 +25700: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3 +25700: Goal: +25700: Id : 1, {_}: + greatest_lower_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + greatest_lower_bound a (multiply b c) + [] by prove_p08b +25700: Order: +25700: kbo +25700: Leaf order: +25700: b 4 0 3 1,2,1,2 +25700: c 4 0 3 2,2,1,2 +25700: a 5 0 4 1,1,2 +25700: identity 8 0 0 +25700: inverse 1 1 0 +25700: least_upper_bound 13 2 0 +25700: multiply 21 2 3 0,2,1,2 +25700: greatest_lower_bound 21 2 5 0,2 +NO CLASH, using fixed ground order +25701: Facts: +25701: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25701: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25701: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25701: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25701: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25701: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25701: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25701: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25701: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25701: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25701: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25701: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25701: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25701: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25701: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25701: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p08b_1 +25701: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p08b_2 +25701: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p08b_3 +25701: Goal: +25701: Id : 1, {_}: + greatest_lower_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + greatest_lower_bound a (multiply b c) + [] by prove_p08b +25701: Order: +25701: lpo +25701: Leaf order: +25701: b 4 0 3 1,2,1,2 +25701: c 4 0 3 2,2,1,2 +25701: a 5 0 4 1,1,2 +25701: identity 8 0 0 +25701: inverse 1 1 0 +25701: least_upper_bound 13 2 0 +25701: multiply 21 2 3 0,2,1,2 +25701: greatest_lower_bound 21 2 5 0,2 +% SZS status Timeout for GRP177-2.p +NO CLASH, using fixed ground order +25723: Facts: +NO CLASH, using fixed ground order +25724: Facts: +25724: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25724: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25724: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25724: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25724: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25724: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25724: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25724: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +NO CLASH, using fixed ground order +25725: Facts: +25725: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25725: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25725: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25725: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25725: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25725: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25725: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25725: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25725: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25725: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25723: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25725: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25723: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25725: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25725: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25725: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25723: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25723: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25725: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25723: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25725: Id : 17, {_}: inverse identity =>= identity [] by p18_1 +25725: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51 +25723: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25725: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p18_3 ?53 ?54 +25725: Goal: +25725: Id : 1, {_}: + least_upper_bound (inverse a) identity + =>= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +25725: Order: +25725: lpo +25725: Leaf order: +25725: a 2 0 2 1,1,2 +25725: identity 6 0 2 2,2 +25725: inverse 9 1 2 0,1,2 +25725: greatest_lower_bound 14 2 1 0,1,3 +25725: least_upper_bound 14 2 1 0,2 +25723: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25723: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25723: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25723: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25723: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25723: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25723: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25723: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25723: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25723: Id : 17, {_}: inverse identity =>= identity [] by p18_1 +25723: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51 +25723: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p18_3 ?53 ?54 +25723: Goal: +25723: Id : 1, {_}: + least_upper_bound (inverse a) identity + =>= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +25723: Order: +25723: nrkbo +25723: Leaf order: +25723: a 2 0 2 1,1,2 +25723: identity 6 0 2 2,2 +25723: inverse 9 1 2 0,1,2 +25723: greatest_lower_bound 14 2 1 0,1,3 +25723: least_upper_bound 14 2 1 0,2 +25723: multiply 20 2 0 +25724: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25725: multiply 20 2 0 +25724: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25724: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25724: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25724: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25724: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25724: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25724: Id : 17, {_}: inverse identity =>= identity [] by p18_1 +25724: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p18_2 ?51 +25724: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p18_3 ?53 ?54 +25724: Goal: +25724: Id : 1, {_}: + least_upper_bound (inverse a) identity + =>= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +25724: Order: +25724: kbo +25724: Leaf order: +25724: a 2 0 2 1,1,2 +25724: identity 6 0 2 2,2 +25724: inverse 9 1 2 0,1,2 +25724: greatest_lower_bound 14 2 1 0,1,3 +25724: least_upper_bound 14 2 1 0,2 +25724: multiply 20 2 0 +% SZS status Timeout for GRP179-3.p +NO CLASH, using fixed ground order +25752: Facts: +25752: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25752: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25752: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25752: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25752: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25752: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25752: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25752: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25752: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25752: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25752: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25752: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25752: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25752: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25752: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25752: Id : 17, {_}: inverse identity =>= identity [] by p11_1 +25752: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51 +25752: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p11_3 ?53 ?54 +25752: Goal: +25752: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +25752: Order: +25752: nrkbo +25752: Leaf order: +25752: a 3 0 3 1,2 +25752: b 3 0 3 2,1,1,2,2 +25752: identity 4 0 0 +25752: inverse 8 1 1 0,1,2,2 +25752: greatest_lower_bound 14 2 1 0,1,1,2,2 +25752: least_upper_bound 14 2 1 0,3 +25752: multiply 22 2 2 0,2 +NO CLASH, using fixed ground order +25753: Facts: +25753: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25753: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25753: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25753: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25753: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25753: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25753: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25753: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25753: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25753: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25753: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25753: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25753: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25753: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25753: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25753: Id : 17, {_}: inverse identity =>= identity [] by p11_1 +25753: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51 +25753: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p11_3 ?53 ?54 +25753: Goal: +25753: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +25753: Order: +25753: kbo +25753: Leaf order: +25753: a 3 0 3 1,2 +25753: b 3 0 3 2,1,1,2,2 +25753: identity 4 0 0 +25753: inverse 8 1 1 0,1,2,2 +25753: greatest_lower_bound 14 2 1 0,1,1,2,2 +25753: least_upper_bound 14 2 1 0,3 +25753: multiply 22 2 2 0,2 +NO CLASH, using fixed ground order +25754: Facts: +25754: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25754: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25754: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25754: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25754: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25754: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25754: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25754: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25754: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25754: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25754: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25754: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25754: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25754: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25754: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25754: Id : 17, {_}: inverse identity =>= identity [] by p11_1 +25754: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p11_2 ?51 +25754: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p11_3 ?53 ?54 +25754: Goal: +25754: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +25754: Order: +25754: lpo +25754: Leaf order: +25754: a 3 0 3 1,2 +25754: b 3 0 3 2,1,1,2,2 +25754: identity 4 0 0 +25754: inverse 8 1 1 0,1,2,2 +25754: greatest_lower_bound 14 2 1 0,1,1,2,2 +25754: least_upper_bound 14 2 1 0,3 +25754: multiply 22 2 2 0,2 +% SZS status Timeout for GRP180-2.p +CLASH, statistics insufficient +25775: Facts: +25775: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25775: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25775: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25775: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25775: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25775: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25775: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25775: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25775: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25775: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25775: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25775: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25775: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25775: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25775: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25775: Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +25775: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +25775: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12x_3 ?53 ?54 +25775: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_4 +25775: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +25775: Id : 22, {_}: + inverse (greatest_lower_bound ?58 ?59) + =<= + least_upper_bound (inverse ?58) (inverse ?59) + [59, 58] by p12x_6 ?58 ?59 +25775: Id : 23, {_}: + inverse (least_upper_bound ?61 ?62) + =<= + greatest_lower_bound (inverse ?61) (inverse ?62) + [62, 61] by p12x_7 ?61 ?62 +25775: Goal: +25775: Id : 1, {_}: a =>= b [] by prove_p12x +25775: Order: +25775: nrkbo +25775: Leaf order: +25775: a 3 0 1 2 +25775: b 3 0 1 3 +25775: identity 4 0 0 +25775: c 4 0 0 +25775: inverse 13 1 0 +25775: greatest_lower_bound 17 2 0 +25775: least_upper_bound 17 2 0 +25775: multiply 20 2 0 +CLASH, statistics insufficient +25776: Facts: +25776: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25776: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25776: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25776: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25776: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25776: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25776: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25776: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25776: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25776: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25776: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25776: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25776: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25776: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25776: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25776: Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +25776: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +25776: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12x_3 ?53 ?54 +25776: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_4 +25776: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +25776: Id : 22, {_}: + inverse (greatest_lower_bound ?58 ?59) + =<= + least_upper_bound (inverse ?58) (inverse ?59) + [59, 58] by p12x_6 ?58 ?59 +25776: Id : 23, {_}: + inverse (least_upper_bound ?61 ?62) + =<= + greatest_lower_bound (inverse ?61) (inverse ?62) + [62, 61] by p12x_7 ?61 ?62 +25776: Goal: +25776: Id : 1, {_}: a =>= b [] by prove_p12x +25776: Order: +25776: kbo +25776: Leaf order: +25776: a 3 0 1 2 +25776: b 3 0 1 3 +25776: identity 4 0 0 +25776: c 4 0 0 +25776: inverse 13 1 0 +25776: greatest_lower_bound 17 2 0 +25776: least_upper_bound 17 2 0 +25776: multiply 20 2 0 +CLASH, statistics insufficient +25777: Facts: +25777: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25777: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25777: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25777: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25777: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25777: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25777: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25777: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25777: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25777: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25777: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25777: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25777: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25777: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25777: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25777: Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +25777: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +25777: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12x_3 ?53 ?54 +25777: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12x_4 +25777: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +25777: Id : 22, {_}: + inverse (greatest_lower_bound ?58 ?59) + =>= + least_upper_bound (inverse ?58) (inverse ?59) + [59, 58] by p12x_6 ?58 ?59 +25777: Id : 23, {_}: + inverse (least_upper_bound ?61 ?62) + =>= + greatest_lower_bound (inverse ?61) (inverse ?62) + [62, 61] by p12x_7 ?61 ?62 +25777: Goal: +25777: Id : 1, {_}: a =>= b [] by prove_p12x +25777: Order: +25777: lpo +25777: Leaf order: +25777: a 3 0 1 2 +25777: b 3 0 1 3 +25777: identity 4 0 0 +25777: c 4 0 0 +25777: inverse 13 1 0 +25777: greatest_lower_bound 17 2 0 +25777: least_upper_bound 17 2 0 +25777: multiply 20 2 0 +Statistics : +Max weight : 16 +Found proof, 8.150042s +% SZS status Unsatisfiable for GRP181-4.p +% SZS output start CNFRefutation for GRP181-4.p +Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11 +Id : 20, {_}: greatest_lower_bound a c =>= greatest_lower_bound b c [] by p12x_4 +Id : 188, {_}: multiply ?586 (greatest_lower_bound ?587 ?588) =<= greatest_lower_bound (multiply ?586 ?587) (multiply ?586 ?588) [588, 587, 586] by monotony_glb1 ?586 ?587 ?588 +Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12x_5 +Id : 364, {_}: inverse (least_upper_bound ?929 ?930) =<= greatest_lower_bound (inverse ?929) (inverse ?930) [930, 929] by p12x_7 ?929 ?930 +Id : 342, {_}: inverse (greatest_lower_bound ?890 ?891) =<= least_upper_bound (inverse ?890) (inverse ?891) [891, 890] by p12x_6 ?890 ?891 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 158, {_}: multiply ?515 (least_upper_bound ?516 ?517) =<= least_upper_bound (multiply ?515 ?516) (multiply ?515 ?517) [517, 516, 515] by monotony_lub1 ?515 ?516 ?517 +Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8 +Id : 19, {_}: inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) [54, 53] by p12x_3 ?53 ?54 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 17, {_}: inverse identity =>= identity [] by p12x_1 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 28, {_}: multiply (multiply ?71 ?72) ?73 =?= multiply ?71 (multiply ?72 ?73) [73, 72, 71] by associativity ?71 ?72 ?73 +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12x_2 ?51 +Id : 302, {_}: inverse (multiply ?845 ?846) =<= multiply (inverse ?846) (inverse ?845) [846, 845] by p12x_3 ?845 ?846 +Id : 803, {_}: inverse (multiply ?1561 (inverse ?1562)) =>= multiply ?1562 (inverse ?1561) [1562, 1561] by Super 302 with 18 at 1,3 +Id : 30, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= multiply ?78 identity [79, 78] by Super 28 with 3 at 2,3 +Id : 303, {_}: inverse (multiply identity ?848) =<= multiply (inverse ?848) identity [848] by Super 302 with 17 at 2,3 +Id : 394, {_}: inverse ?984 =<= multiply (inverse ?984) identity [984] by Demod 303 with 2 at 1,2 +Id : 396, {_}: inverse (inverse ?987) =<= multiply ?987 identity [987] by Super 394 with 18 at 1,3 +Id : 406, {_}: ?987 =<= multiply ?987 identity [987] by Demod 396 with 18 at 2 +Id : 638, {_}: multiply (multiply ?78 (inverse ?79)) ?79 =>= ?78 [79, 78] by Demod 30 with 406 at 3 +Id : 816, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 (inverse (inverse ?1600)))) [1600, 1599] by Super 803 with 638 at 1,2 +Id : 306, {_}: inverse (multiply ?855 (inverse ?856)) =>= multiply ?856 (inverse ?855) [856, 855] by Super 302 with 18 at 1,3 +Id : 837, {_}: inverse ?1599 =<= multiply ?1600 (multiply (inverse ?1600) (inverse ?1599)) [1600, 1599] by Demod 816 with 306 at 2,3 +Id : 838, {_}: inverse ?1599 =<= multiply ?1600 (inverse (multiply ?1599 ?1600)) [1600, 1599] by Demod 837 with 19 at 2,3 +Id : 285, {_}: multiply ?794 (inverse ?794) =>= identity [794] by Super 3 with 18 at 1,2 +Id : 607, {_}: multiply (multiply ?1261 ?1262) (inverse ?1262) =>= multiply ?1261 identity [1262, 1261] by Super 4 with 285 at 2,3 +Id : 19344, {_}: multiply (multiply ?27523 ?27524) (inverse ?27524) =>= ?27523 [27524, 27523] by Demod 607 with 406 at 3 +Id : 160, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound (multiply (inverse ?522) ?523) identity [523, 522] by Super 158 with 3 at 2,3 +Id : 177, {_}: multiply (inverse ?522) (least_upper_bound ?523 ?522) =>= least_upper_bound identity (multiply (inverse ?522) ?523) [523, 522] by Demod 160 with 6 at 3 +Id : 345, {_}: inverse (greatest_lower_bound identity ?898) =>= least_upper_bound identity (inverse ?898) [898] by Super 342 with 17 at 1,3 +Id : 487, {_}: inverse (multiply (greatest_lower_bound identity ?1114) ?1115) =<= multiply (inverse ?1115) (least_upper_bound identity (inverse ?1114)) [1115, 1114] by Super 19 with 345 at 2,3 +Id : 11534, {_}: inverse (multiply (greatest_lower_bound identity ?15482) (inverse ?15482)) =>= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Super 177 with 487 at 2 +Id : 11607, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =?= least_upper_bound identity (multiply (inverse (inverse ?15482)) identity) [15482] by Demod 11534 with 306 at 2 +Id : 11608, {_}: multiply ?15482 (inverse (greatest_lower_bound identity ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11607 with 406 at 2,3 +Id : 11609, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity (inverse (inverse ?15482)) [15482] by Demod 11608 with 345 at 2,2 +Id : 11610, {_}: multiply ?15482 (least_upper_bound identity (inverse ?15482)) =>= least_upper_bound identity ?15482 [15482] by Demod 11609 with 18 at 2,3 +Id : 19409, {_}: multiply (least_upper_bound identity ?27743) (inverse (least_upper_bound identity (inverse ?27743))) =>= ?27743 [27743] by Super 19344 with 11610 at 1,2 +Id : 366, {_}: inverse (least_upper_bound ?934 (inverse ?935)) =>= greatest_lower_bound (inverse ?934) ?935 [935, 934] by Super 364 with 18 at 2,3 +Id : 19451, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound (inverse identity) ?27743) =>= ?27743 [27743] by Demod 19409 with 366 at 2,2 +Id : 44019, {_}: multiply (least_upper_bound identity ?52011) (greatest_lower_bound identity ?52011) =>= ?52011 [52011] by Demod 19451 with 17 at 1,2,2 +Id : 367, {_}: inverse (least_upper_bound identity ?937) =>= greatest_lower_bound identity (inverse ?937) [937] by Super 364 with 17 at 1,3 +Id : 8913, {_}: multiply (inverse ?11632) (least_upper_bound ?11632 ?11633) =>= least_upper_bound identity (multiply (inverse ?11632) ?11633) [11633, 11632] by Super 158 with 3 at 1,3 +Id : 326, {_}: least_upper_bound c a =<= least_upper_bound b c [] by Demod 21 with 6 at 2 +Id : 327, {_}: least_upper_bound c a =>= least_upper_bound c b [] by Demod 326 with 6 at 3 +Id : 8921, {_}: multiply (inverse c) (least_upper_bound c b) =>= least_upper_bound identity (multiply (inverse c) a) [] by Super 8913 with 327 at 2,2 +Id : 164, {_}: multiply (inverse ?538) (least_upper_bound ?538 ?539) =>= least_upper_bound identity (multiply (inverse ?538) ?539) [539, 538] by Super 158 with 3 at 1,3 +Id : 9001, {_}: least_upper_bound identity (multiply (inverse c) b) =<= least_upper_bound identity (multiply (inverse c) a) [] by Demod 8921 with 164 at 2 +Id : 9081, {_}: inverse (least_upper_bound identity (multiply (inverse c) b)) =>= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Super 367 with 9001 at 1,2 +Id : 9110, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =<= greatest_lower_bound identity (inverse (multiply (inverse c) a)) [] by Demod 9081 with 367 at 2 +Id : 304, {_}: inverse (multiply (inverse ?850) ?851) =>= multiply (inverse ?851) ?850 [851, 850] by Super 302 with 18 at 2,3 +Id : 9111, {_}: greatest_lower_bound identity (inverse (multiply (inverse c) b)) =>= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9110 with 304 at 2,3 +Id : 9112, {_}: greatest_lower_bound identity (multiply (inverse b) c) =<= greatest_lower_bound identity (multiply (inverse a) c) [] by Demod 9111 with 304 at 2,2 +Id : 44043, {_}: multiply (least_upper_bound identity (multiply (inverse a) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Super 44019 with 9112 at 2,2 +Id : 10178, {_}: multiply (inverse ?13641) (greatest_lower_bound ?13641 ?13642) =>= greatest_lower_bound identity (multiply (inverse ?13641) ?13642) [13642, 13641] by Super 188 with 3 at 1,3 +Id : 315, {_}: greatest_lower_bound c a =<= greatest_lower_bound b c [] by Demod 20 with 5 at 2 +Id : 316, {_}: greatest_lower_bound c a =>= greatest_lower_bound c b [] by Demod 315 with 5 at 3 +Id : 10190, {_}: multiply (inverse c) (greatest_lower_bound c b) =>= greatest_lower_bound identity (multiply (inverse c) a) [] by Super 10178 with 316 at 2,2 +Id : 194, {_}: multiply (inverse ?609) (greatest_lower_bound ?609 ?610) =>= greatest_lower_bound identity (multiply (inverse ?609) ?610) [610, 609] by Super 188 with 3 at 1,3 +Id : 10270, {_}: greatest_lower_bound identity (multiply (inverse c) b) =<= greatest_lower_bound identity (multiply (inverse c) a) [] by Demod 10190 with 194 at 2 +Id : 10361, {_}: inverse (greatest_lower_bound identity (multiply (inverse c) b)) =>= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Super 345 with 10270 at 1,2 +Id : 10393, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =<= least_upper_bound identity (inverse (multiply (inverse c) a)) [] by Demod 10361 with 345 at 2 +Id : 10394, {_}: least_upper_bound identity (inverse (multiply (inverse c) b)) =>= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10393 with 304 at 2,3 +Id : 10395, {_}: least_upper_bound identity (multiply (inverse b) c) =<= least_upper_bound identity (multiply (inverse a) c) [] by Demod 10394 with 304 at 2,2 +Id : 44130, {_}: multiply (least_upper_bound identity (multiply (inverse b) c)) (greatest_lower_bound identity (multiply (inverse b) c)) =>= multiply (inverse a) c [] by Demod 44043 with 10395 at 1,2 +Id : 19452, {_}: multiply (least_upper_bound identity ?27743) (greatest_lower_bound identity ?27743) =>= ?27743 [27743] by Demod 19451 with 17 at 1,2,2 +Id : 44131, {_}: multiply (inverse b) c =<= multiply (inverse a) c [] by Demod 44130 with 19452 at 2 +Id : 44165, {_}: inverse (inverse a) =<= multiply c (inverse (multiply (inverse b) c)) [] by Super 838 with 44131 at 1,2,3 +Id : 44200, {_}: a =<= multiply c (inverse (multiply (inverse b) c)) [] by Demod 44165 with 18 at 2 +Id : 44201, {_}: a =<= inverse (inverse b) [] by Demod 44200 with 838 at 3 +Id : 44202, {_}: a =>= b [] by Demod 44201 with 18 at 3 +Id : 44399, {_}: b === b [] by Demod 1 with 44202 at 2 +Id : 1, {_}: a =>= b [] by prove_p12x +% SZS output end CNFRefutation for GRP181-4.p +25775: solved GRP181-4.p in 8.112506 using nrkbo +25775: status Unsatisfiable for GRP181-4.p +NO CLASH, using fixed ground order +25788: Facts: +25788: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25788: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25788: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25788: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25788: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25788: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25788: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25788: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25788: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25788: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25788: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25788: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25788: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25788: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25788: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25788: Goal: +25788: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +25788: Order: +25788: nrkbo +25788: Leaf order: +25788: a 2 0 2 1,1,2 +25788: identity 5 0 3 2,1,2 +25788: inverse 2 1 1 0,2,2 +25788: least_upper_bound 14 2 1 0,1,2 +25788: greatest_lower_bound 15 2 2 0,2 +25788: multiply 18 2 0 +NO CLASH, using fixed ground order +25789: Facts: +25789: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25789: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25789: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25789: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25789: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25789: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25789: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25789: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25789: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25789: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25789: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25789: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +NO CLASH, using fixed ground order +25790: Facts: +25790: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25790: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25790: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25790: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25790: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25790: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25790: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25790: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25790: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25790: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25790: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25790: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25790: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25790: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25790: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25790: Goal: +25790: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +25790: Order: +25790: lpo +25790: Leaf order: +25790: a 2 0 2 1,1,2 +25790: identity 5 0 3 2,1,2 +25790: inverse 2 1 1 0,2,2 +25790: least_upper_bound 14 2 1 0,1,2 +25790: greatest_lower_bound 15 2 2 0,2 +25790: multiply 18 2 0 +25789: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25789: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25789: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25789: Goal: +25789: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +25789: Order: +25789: kbo +25789: Leaf order: +25789: a 2 0 2 1,1,2 +25789: identity 5 0 3 2,1,2 +25789: inverse 2 1 1 0,2,2 +25789: least_upper_bound 14 2 1 0,1,2 +25789: greatest_lower_bound 15 2 2 0,2 +25789: multiply 18 2 0 +% SZS status Timeout for GRP183-1.p +NO CLASH, using fixed ground order +25806: Facts: +25806: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25806: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25806: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25806: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25806: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25806: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25806: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25806: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25806: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25806: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25806: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25806: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25806: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25806: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25806: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25806: Goal: +25806: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +25806: Order: +25806: nrkbo +25806: Leaf order: +25806: a 2 0 2 1,1,2 +25806: identity 5 0 3 2,1,2 +25806: inverse 2 1 1 0,1,2,2 +25806: greatest_lower_bound 14 2 1 0,2 +25806: least_upper_bound 15 2 2 0,1,2 +25806: multiply 18 2 0 +NO CLASH, using fixed ground order +25807: Facts: +25807: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25807: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25807: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25807: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25807: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25807: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25807: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25807: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25807: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25807: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25807: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25807: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25807: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25807: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25807: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25807: Goal: +25807: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +25807: Order: +25807: kbo +25807: Leaf order: +25807: a 2 0 2 1,1,2 +25807: identity 5 0 3 2,1,2 +25807: inverse 2 1 1 0,1,2,2 +25807: greatest_lower_bound 14 2 1 0,2 +25807: least_upper_bound 15 2 2 0,1,2 +25807: multiply 18 2 0 +NO CLASH, using fixed ground order +25808: Facts: +25808: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25808: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25808: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25808: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25808: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25808: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25808: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25808: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25808: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25808: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25808: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25808: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25808: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25808: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25808: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25808: Goal: +25808: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +25808: Order: +25808: lpo +25808: Leaf order: +25808: a 2 0 2 1,1,2 +25808: identity 5 0 3 2,1,2 +25808: inverse 2 1 1 0,1,2,2 +25808: greatest_lower_bound 14 2 1 0,2 +25808: least_upper_bound 15 2 2 0,1,2 +25808: multiply 18 2 0 +% SZS status Timeout for GRP183-3.p +NO CLASH, using fixed ground order +25839: Facts: +25839: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25839: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25839: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25839: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25839: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25839: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25839: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25839: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25839: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25839: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25839: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25839: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25839: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25839: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25839: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25839: Id : 17, {_}: inverse identity =>= identity [] by p20x_1 +25839: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51 +25839: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20x_3 ?53 ?54 +25839: Goal: +25839: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +25839: Order: +25839: nrkbo +25839: Leaf order: +25839: a 2 0 2 1,1,2 +25839: identity 7 0 3 2,1,2 +25839: inverse 8 1 1 0,1,2,2 +25839: greatest_lower_bound 14 2 1 0,2 +25839: least_upper_bound 15 2 2 0,1,2 +25839: multiply 20 2 0 +NO CLASH, using fixed ground order +25840: Facts: +25840: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25840: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25840: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25840: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +NO CLASH, using fixed ground order +25841: Facts: +25841: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25841: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25841: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25841: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25841: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25841: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25841: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25841: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25841: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25841: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25841: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25841: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25841: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25841: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25841: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25841: Id : 17, {_}: inverse identity =>= identity [] by p20x_1 +25841: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51 +25841: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20x_3 ?53 ?54 +25841: Goal: +25841: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +25841: Order: +25841: lpo +25841: Leaf order: +25841: a 2 0 2 1,1,2 +25841: identity 7 0 3 2,1,2 +25841: inverse 8 1 1 0,1,2,2 +25841: greatest_lower_bound 14 2 1 0,2 +25841: least_upper_bound 15 2 2 0,1,2 +25841: multiply 20 2 0 +25840: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25840: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25840: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25840: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25840: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25840: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25840: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25840: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25840: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25840: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25840: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25840: Id : 17, {_}: inverse identity =>= identity [] by p20x_1 +25840: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20x_1 ?51 +25840: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20x_3 ?53 ?54 +25840: Goal: +25840: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (least_upper_bound (inverse a) identity) + =>= + identity + [] by prove_20x +25840: Order: +25840: kbo +25840: Leaf order: +25840: a 2 0 2 1,1,2 +25840: identity 7 0 3 2,1,2 +25840: inverse 8 1 1 0,1,2,2 +25840: greatest_lower_bound 14 2 1 0,2 +25840: least_upper_bound 15 2 2 0,1,2 +25840: multiply 20 2 0 +% SZS status Timeout for GRP183-4.p +NO CLASH, using fixed ground order +25861: Facts: +25861: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25861: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25861: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25861: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25861: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25861: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25861: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25861: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25861: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25861: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25861: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25861: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25861: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25861: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25861: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25861: Goal: +25861: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +25861: Order: +25861: nrkbo +25861: Leaf order: +25861: a 4 0 4 1,1,2 +25861: identity 6 0 4 2,1,2 +25861: inverse 3 1 2 0,2,2 +25861: least_upper_bound 15 2 2 0,1,2 +25861: greatest_lower_bound 15 2 2 0,1,2,2 +25861: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +25862: Facts: +25862: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25862: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25862: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25862: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25862: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25862: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25862: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25862: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25862: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25862: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25862: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25862: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25862: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25862: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25862: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25862: Goal: +25862: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +25862: Order: +25862: kbo +25862: Leaf order: +25862: a 4 0 4 1,1,2 +25862: identity 6 0 4 2,1,2 +25862: inverse 3 1 2 0,2,2 +25862: least_upper_bound 15 2 2 0,1,2 +25862: greatest_lower_bound 15 2 2 0,1,2,2 +25862: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +25863: Facts: +25863: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25863: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25863: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25863: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25863: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25863: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25863: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25863: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25863: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25863: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25863: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25863: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25863: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25863: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25863: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25863: Goal: +25863: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21 +25863: Order: +25863: lpo +25863: Leaf order: +25863: a 4 0 4 1,1,2 +25863: identity 6 0 4 2,1,2 +25863: inverse 3 1 2 0,2,2 +25863: least_upper_bound 15 2 2 0,1,2 +25863: greatest_lower_bound 15 2 2 0,1,2,2 +25863: multiply 20 2 2 0,2 +% SZS status Timeout for GRP184-1.p +NO CLASH, using fixed ground order +25898: Facts: +25898: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25898: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25898: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25898: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25898: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25898: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25898: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25898: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25898: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25898: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25898: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25898: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25898: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25898: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25898: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25898: Goal: +25898: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21x +25898: Order: +25898: nrkbo +25898: Leaf order: +25898: a 4 0 4 1,1,2 +25898: identity 6 0 4 2,1,2 +25898: inverse 3 1 2 0,2,2 +25898: least_upper_bound 15 2 2 0,1,2 +25898: greatest_lower_bound 15 2 2 0,1,2,2 +25898: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +25899: Facts: +25899: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25899: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25899: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25899: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25899: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25899: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25899: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25899: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25899: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25899: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25899: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25899: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25899: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25899: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25899: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25899: Goal: +25899: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21x +25899: Order: +25899: kbo +25899: Leaf order: +25899: a 4 0 4 1,1,2 +25899: identity 6 0 4 2,1,2 +25899: inverse 3 1 2 0,2,2 +25899: least_upper_bound 15 2 2 0,1,2 +25899: greatest_lower_bound 15 2 2 0,1,2,2 +25899: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +25900: Facts: +25900: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25900: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25900: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25900: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25900: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25900: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25900: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25900: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25900: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25900: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25900: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25900: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25900: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25900: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25900: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25900: Goal: +25900: Id : 1, {_}: + multiply (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =<= + multiply (inverse (greatest_lower_bound a identity)) + (least_upper_bound a identity) + [] by prove_p21x +25900: Order: +25900: lpo +25900: Leaf order: +25900: a 4 0 4 1,1,2 +25900: identity 6 0 4 2,1,2 +25900: inverse 3 1 2 0,2,2 +25900: least_upper_bound 15 2 2 0,1,2 +25900: greatest_lower_bound 15 2 2 0,1,2,2 +25900: multiply 20 2 2 0,2 +% SZS status Timeout for GRP184-3.p +NO CLASH, using fixed ground order +25933: Facts: +25933: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25933: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25933: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25933: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25933: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25933: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25933: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25933: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25933: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25933: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25933: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25933: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25933: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +NO CLASH, using fixed ground order +25934: Facts: +25934: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25934: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25934: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25934: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25934: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25934: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25934: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25934: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25934: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25934: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25934: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25934: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25934: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25934: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25934: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25934: Goal: +25934: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +25934: Order: +25934: lpo +25934: Leaf order: +25934: a 3 0 3 1,1,1,2 +25934: b 3 0 3 2,1,1,2 +25934: identity 6 0 4 2,1,2 +25934: inverse 1 1 0 +25934: greatest_lower_bound 14 2 1 0,2 +25934: least_upper_bound 17 2 4 0,1,2 +25934: multiply 21 2 3 0,1,1,2 +NO CLASH, using fixed ground order +25932: Facts: +25932: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25932: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25932: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25932: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25932: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25932: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25932: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25932: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25932: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25932: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25932: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25932: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25932: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25932: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25932: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25932: Goal: +25932: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +25932: Order: +25932: nrkbo +25932: Leaf order: +25932: a 3 0 3 1,1,1,2 +25932: b 3 0 3 2,1,1,2 +25932: identity 6 0 4 2,1,2 +25932: inverse 1 1 0 +25932: greatest_lower_bound 14 2 1 0,2 +25932: least_upper_bound 17 2 4 0,1,2 +25932: multiply 21 2 3 0,1,1,2 +25933: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25933: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25933: Goal: +25933: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +25933: Order: +25933: kbo +25933: Leaf order: +25933: a 3 0 3 1,1,1,2 +25933: b 3 0 3 2,1,1,2 +25933: identity 6 0 4 2,1,2 +25933: inverse 1 1 0 +25933: greatest_lower_bound 14 2 1 0,2 +25933: least_upper_bound 17 2 4 0,1,2 +25933: multiply 21 2 3 0,1,1,2 +Statistics : +Max weight : 21 +Found proof, 1.351481s +% SZS status Unsatisfiable for GRP185-3.p +% SZS output start CNFRefutation for GRP185-3.p +Id : 108, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252 +Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2 +Id : 392, {_}: ?594 =<= multiply (inverse ?595) (multiply ?595 ?594) [595, 594] by Demod 23 with 2 at 2 +Id : 394, {_}: ?599 =<= multiply (inverse (inverse ?599)) identity [599] by Super 392 with 3 at 2,3 +Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2 +Id : 400, {_}: multiply ?621 ?622 =<= multiply (inverse (inverse ?621)) ?622 [622, 621] by Super 392 with 27 at 2,3 +Id : 525, {_}: ?599 =<= multiply ?599 identity [599] by Demod 394 with 400 at 3 +Id : 815, {_}: greatest_lower_bound ?1092 (least_upper_bound ?1093 ?1092) =>= ?1092 [1093, 1092] by Super 108 with 6 at 2,2 +Id : 822, {_}: greatest_lower_bound ?1112 (least_upper_bound ?1113 (least_upper_bound ?1114 ?1112)) =>= ?1112 [1114, 1113, 1112] by Super 815 with 8 at 2,2 +Id : 2353, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 2352 with 822 at 2 +Id : 2352, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2351 with 8 at 2,2,2 +Id : 2351, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b))) =>= least_upper_bound identity (multiply a b) [] by Demod 2350 with 8 at 2,2 +Id : 2350, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b)) =>= least_upper_bound identity (multiply a b) [] by Demod 2349 with 6 at 2,2 +Id : 2349, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 2348 with 2 at 2,2,2,2,2 +Id : 2348, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2347 with 525 at 1,2,2,2,2 +Id : 2347, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2346 with 2 at 1,2,2,2 +Id : 2346, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 2345 with 8 at 2,2 +Id : 2345, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 2344 with 15 at 2,2,2 +Id : 2344, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2343 with 15 at 1,2,2 +Id : 2343, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 2342 with 6 at 3 +Id : 2342, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 2341 with 13 at 2,2 +Id : 2341, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2 +Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b +% SZS output end CNFRefutation for GRP185-3.p +25934: solved GRP185-3.p in 0.66004 using lpo +25934: status Unsatisfiable for GRP185-3.p +NO CLASH, using fixed ground order +25939: Facts: +25939: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25939: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25939: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25939: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25939: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25939: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25939: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25939: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25939: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25939: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25939: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25939: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25939: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25939: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25939: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25939: Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +25939: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +25939: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22b_3 ?53 ?54 +25939: Goal: +25939: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +25939: Order: +25939: nrkbo +25939: Leaf order: +25939: a 3 0 3 1,1,1,2 +25939: b 3 0 3 2,1,1,2 +25939: identity 8 0 4 2,1,2 +25939: inverse 7 1 0 +25939: greatest_lower_bound 14 2 1 0,2 +25939: least_upper_bound 17 2 4 0,1,2 +25939: multiply 23 2 3 0,1,1,2 +NO CLASH, using fixed ground order +25940: Facts: +25940: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25940: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25940: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25940: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25940: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25940: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25940: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25940: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25940: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25940: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25940: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25940: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25940: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25940: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25940: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25940: Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +25940: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +25940: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22b_3 ?53 ?54 +25940: Goal: +25940: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +25940: Order: +25940: kbo +25940: Leaf order: +25940: a 3 0 3 1,1,1,2 +25940: b 3 0 3 2,1,1,2 +25940: identity 8 0 4 2,1,2 +25940: inverse 7 1 0 +25940: greatest_lower_bound 14 2 1 0,2 +25940: least_upper_bound 17 2 4 0,1,2 +25940: multiply 23 2 3 0,1,1,2 +NO CLASH, using fixed ground order +25941: Facts: +25941: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25941: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25941: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25941: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25941: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25941: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25941: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25941: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25941: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25941: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25941: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25941: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25941: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25941: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25941: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25941: Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +25941: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +25941: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p22b_3 ?53 ?54 +25941: Goal: +25941: Id : 1, {_}: + greatest_lower_bound (least_upper_bound (multiply a b) identity) + (multiply (least_upper_bound a identity) + (least_upper_bound b identity)) + =>= + least_upper_bound (multiply a b) identity + [] by prove_p22b +25941: Order: +25941: lpo +25941: Leaf order: +25941: a 3 0 3 1,1,1,2 +25941: b 3 0 3 2,1,1,2 +25941: identity 8 0 4 2,1,2 +25941: inverse 7 1 0 +25941: greatest_lower_bound 14 2 1 0,2 +25941: least_upper_bound 17 2 4 0,1,2 +25941: multiply 23 2 3 0,1,1,2 +Statistics : +Max weight : 21 +Found proof, 0.930082s +% SZS status Unsatisfiable for GRP185-4.p +% SZS output start CNFRefutation for GRP185-4.p +Id : 111, {_}: greatest_lower_bound ?257 (least_upper_bound ?257 ?258) =>= ?257 [258, 257] by glb_absorbtion ?257 ?258 +Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p22b_2 ?51 +Id : 17, {_}: inverse identity =>= identity [] by p22b_1 +Id : 338, {_}: inverse (multiply ?520 ?521) =?= multiply (inverse ?521) (inverse ?520) [521, 520] by p22b_3 ?520 ?521 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14 +Id : 339, {_}: inverse (multiply identity ?523) =<= multiply (inverse ?523) identity [523] by Super 338 with 17 at 2,3 +Id : 372, {_}: inverse ?569 =<= multiply (inverse ?569) identity [569] by Demod 339 with 2 at 1,2 +Id : 374, {_}: inverse (inverse ?572) =<= multiply ?572 identity [572] by Super 372 with 18 at 1,3 +Id : 382, {_}: ?572 =<= multiply ?572 identity [572] by Demod 374 with 18 at 2 +Id : 704, {_}: greatest_lower_bound ?881 (least_upper_bound ?882 ?881) =>= ?881 [882, 881] by Super 111 with 6 at 2,2 +Id : 711, {_}: greatest_lower_bound ?901 (least_upper_bound ?902 (least_upper_bound ?903 ?901)) =>= ?901 [903, 902, 901] by Super 704 with 8 at 2,2 +Id : 1908, {_}: least_upper_bound identity (multiply a b) === least_upper_bound identity (multiply a b) [] by Demod 1907 with 711 at 2 +Id : 1907, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound a (least_upper_bound identity (multiply a b)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1906 with 8 at 2,2,2 +Id : 1906, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound b (least_upper_bound (least_upper_bound a identity) (multiply a b))) =>= least_upper_bound identity (multiply a b) [] by Demod 1905 with 8 at 2,2 +Id : 1905, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound b (least_upper_bound a identity)) (multiply a b)) =>= least_upper_bound identity (multiply a b) [] by Demod 1904 with 6 at 2,2 +Id : 1904, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 1903 with 2 at 2,2,2,2,2 +Id : 1903, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound a (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1902 with 382 at 1,2,2,2,2 +Id : 1902, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound b (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1901 with 2 at 1,2,2,2 +Id : 1901, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply a b) (least_upper_bound (multiply identity b) (least_upper_bound (multiply a identity) (multiply identity identity)))) =>= least_upper_bound identity (multiply a b) [] by Demod 1900 with 8 at 2,2 +Id : 1900, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (least_upper_bound (multiply a identity) (multiply identity identity))) =>= least_upper_bound identity (multiply a b) [] by Demod 1899 with 15 at 2,2,2 +Id : 1899, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (least_upper_bound (multiply a b) (multiply identity b)) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 1898 with 15 at 1,2,2 +Id : 1898, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound identity (multiply a b) [] by Demod 1897 with 6 at 3 +Id : 1897, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (least_upper_bound (multiply (least_upper_bound a identity) b) (multiply (least_upper_bound a identity) identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1896 with 13 at 2,2 +Id : 1896, {_}: greatest_lower_bound (least_upper_bound identity (multiply a b)) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by Demod 1 with 6 at 1,2 +Id : 1, {_}: greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) =>= least_upper_bound (multiply a b) identity [] by prove_p22b +% SZS output end CNFRefutation for GRP185-4.p +25941: solved GRP185-4.p in 0.432027 using lpo +25941: status Unsatisfiable for GRP185-4.p +NO CLASH, using fixed ground order +25948: Facts: +25948: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25948: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25948: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25948: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25948: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25948: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25948: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25948: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25948: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25948: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25948: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25948: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25948: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25948: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25948: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25948: Id : 17, {_}: inverse identity =>= identity [] by p23_1 +25948: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51 +25948: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p23_3 ?53 ?54 +25948: Goal: +25948: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +25948: Order: +25948: nrkbo +25948: Leaf order: +25948: b 2 0 2 2,1,2 +25948: a 3 0 3 1,1,2 +25948: identity 5 0 1 2,2 +25948: inverse 9 1 2 0,2,3 +25948: greatest_lower_bound 14 2 1 0,1,2,3 +25948: least_upper_bound 14 2 1 0,2 +25948: multiply 22 2 2 0,1,2 +NO CLASH, using fixed ground order +25950: Facts: +25950: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25950: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25950: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25950: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25950: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25950: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25950: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25950: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25950: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25950: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25950: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25950: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25950: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25950: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25950: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25950: Id : 17, {_}: inverse identity =>= identity [] by p23_1 +25950: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51 +25950: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p23_3 ?53 ?54 +25950: Goal: +25950: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +25950: Order: +25950: lpo +25950: Leaf order: +25950: b 2 0 2 2,1,2 +25950: a 3 0 3 1,1,2 +25950: identity 5 0 1 2,2 +25950: inverse 9 1 2 0,2,3 +25950: greatest_lower_bound 14 2 1 0,1,2,3 +25950: least_upper_bound 14 2 1 0,2 +25950: multiply 22 2 2 0,1,2 +NO CLASH, using fixed ground order +25949: Facts: +25949: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25949: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25949: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25949: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25949: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25949: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25949: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25949: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25949: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25949: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25949: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25949: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25949: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25949: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25949: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25949: Id : 17, {_}: inverse identity =>= identity [] by p23_1 +25949: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p23_2 ?51 +25949: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p23_3 ?53 ?54 +25949: Goal: +25949: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +25949: Order: +25949: kbo +25949: Leaf order: +25949: b 2 0 2 2,1,2 +25949: a 3 0 3 1,1,2 +25949: identity 5 0 1 2,2 +25949: inverse 9 1 2 0,2,3 +25949: greatest_lower_bound 14 2 1 0,1,2,3 +25949: least_upper_bound 14 2 1 0,2 +25949: multiply 22 2 2 0,1,2 +% SZS status Timeout for GRP186-2.p +NO CLASH, using fixed ground order +26073: Facts: +26073: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +26073: Id : 3, {_}: + multiply (left_inverse ?4) ?4 =>= identity + [4] by left_inverse ?4 +26073: Id : 4, {_}: + multiply (multiply ?6 (multiply ?7 ?8)) ?6 + =?= + multiply (multiply ?6 ?7) (multiply ?8 ?6) + [8, 7, 6] by moufang1 ?6 ?7 ?8 +26073: Goal: +26073: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +26073: Order: +26073: nrkbo +26073: Leaf order: +26073: identity 2 0 0 +26073: a 2 0 2 1,1,1,2 +26073: c 2 0 2 2,1,2 +26073: b 4 0 4 2,1,1,2 +26073: left_inverse 1 1 0 +26073: multiply 14 2 6 0,2 +NO CLASH, using fixed ground order +26074: Facts: +26074: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +26074: Id : 3, {_}: + multiply (left_inverse ?4) ?4 =>= identity + [4] by left_inverse ?4 +26074: Id : 4, {_}: + multiply (multiply ?6 (multiply ?7 ?8)) ?6 + =>= + multiply (multiply ?6 ?7) (multiply ?8 ?6) + [8, 7, 6] by moufang1 ?6 ?7 ?8 +26074: Goal: +26074: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +26074: Order: +26074: kbo +26074: Leaf order: +26074: identity 2 0 0 +26074: a 2 0 2 1,1,1,2 +26074: c 2 0 2 2,1,2 +26074: b 4 0 4 2,1,1,2 +26074: left_inverse 1 1 0 +26074: multiply 14 2 6 0,2 +NO CLASH, using fixed ground order +26075: Facts: +26075: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +26075: Id : 3, {_}: + multiply (left_inverse ?4) ?4 =>= identity + [4] by left_inverse ?4 +26075: Id : 4, {_}: + multiply (multiply ?6 (multiply ?7 ?8)) ?6 + =>= + multiply (multiply ?6 ?7) (multiply ?8 ?6) + [8, 7, 6] by moufang1 ?6 ?7 ?8 +26075: Goal: +26075: Id : 1, {_}: + multiply (multiply (multiply a b) c) b + =>= + multiply a (multiply b (multiply c b)) + [] by prove_moufang2 +26075: Order: +26075: lpo +26075: Leaf order: +26075: identity 2 0 0 +26075: a 2 0 2 1,1,1,2 +26075: c 2 0 2 2,1,2 +26075: b 4 0 4 2,1,1,2 +26075: left_inverse 1 1 0 +26075: multiply 14 2 6 0,2 +% SZS status Timeout for GRP204-1.p +CLASH, statistics insufficient +26204: Facts: +26204: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +26204: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +26204: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +26204: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +26204: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +26204: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +26204: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +26204: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +26204: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =?= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +26204: Goal: +26204: Id : 1, {_}: + multiply x (multiply (multiply y z) x) + =<= + multiply (multiply x y) (multiply z x) + [] by prove_moufang4 +26204: Order: +26204: nrkbo +26204: Leaf order: +26204: y 2 0 2 1,1,2,2 +26204: z 2 0 2 2,1,2,2 +26204: identity 4 0 0 +26204: x 4 0 4 1,2 +26204: right_inverse 1 1 0 +26204: left_inverse 1 1 0 +26204: left_division 2 2 0 +26204: right_division 2 2 0 +26204: multiply 20 2 6 0,2 +CLASH, statistics insufficient +26205: Facts: +26205: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +26205: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +26205: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +26205: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +26205: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +26205: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +26205: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +26205: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +26205: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +26205: Goal: +26205: Id : 1, {_}: + multiply x (multiply (multiply y z) x) + =<= + multiply (multiply x y) (multiply z x) + [] by prove_moufang4 +26205: Order: +26205: kbo +26205: Leaf order: +26205: y 2 0 2 1,1,2,2 +26205: z 2 0 2 2,1,2,2 +26205: identity 4 0 0 +26205: x 4 0 4 1,2 +26205: right_inverse 1 1 0 +26205: left_inverse 1 1 0 +26205: left_division 2 2 0 +26205: right_division 2 2 0 +26205: multiply 20 2 6 0,2 +CLASH, statistics insufficient +26206: Facts: +26206: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +26206: Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +26206: Id : 4, {_}: + multiply ?6 (left_division ?6 ?7) =>= ?7 + [7, 6] by multiply_left_division ?6 ?7 +26206: Id : 5, {_}: + left_division ?9 (multiply ?9 ?10) =>= ?10 + [10, 9] by left_division_multiply ?9 ?10 +26206: Id : 6, {_}: + multiply (right_division ?12 ?13) ?13 =>= ?12 + [13, 12] by multiply_right_division ?12 ?13 +26206: Id : 7, {_}: + right_division (multiply ?15 ?16) ?16 =>= ?15 + [16, 15] by right_division_multiply ?15 ?16 +26206: Id : 8, {_}: + multiply ?18 (right_inverse ?18) =>= identity + [18] by right_inverse ?18 +26206: Id : 9, {_}: + multiply (left_inverse ?20) ?20 =>= identity + [20] by left_inverse ?20 +26206: Id : 10, {_}: + multiply (multiply (multiply ?22 ?23) ?22) ?24 + =>= + multiply ?22 (multiply ?23 (multiply ?22 ?24)) + [24, 23, 22] by moufang3 ?22 ?23 ?24 +26206: Goal: +26206: Id : 1, {_}: + multiply x (multiply (multiply y z) x) + =<= + multiply (multiply x y) (multiply z x) + [] by prove_moufang4 +26206: Order: +26206: lpo +26206: Leaf order: +26206: y 2 0 2 1,1,2,2 +26206: z 2 0 2 2,1,2,2 +26206: identity 4 0 0 +26206: x 4 0 4 1,2 +26206: right_inverse 1 1 0 +26206: left_inverse 1 1 0 +26206: left_division 2 2 0 +26206: right_division 2 2 0 +26206: multiply 20 2 6 0,2 +Statistics : +Max weight : 20 +Found proof, 29.317631s +% SZS status Unsatisfiable for GRP205-1.p +% SZS output start CNFRefutation for GRP205-1.p +Id : 56, {_}: multiply (multiply (multiply ?126 ?127) ?126) ?128 =>= multiply ?126 (multiply ?127 (multiply ?126 ?128)) [128, 127, 126] by moufang3 ?126 ?127 ?128 +Id : 4, {_}: multiply ?6 (left_division ?6 ?7) =>= ?7 [7, 6] by multiply_left_division ?6 ?7 +Id : 9, {_}: multiply (left_inverse ?20) ?20 =>= identity [20] by left_inverse ?20 +Id : 22, {_}: left_division ?48 (multiply ?48 ?49) =>= ?49 [49, 48] by left_division_multiply ?48 ?49 +Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +Id : 5, {_}: left_division ?9 (multiply ?9 ?10) =>= ?10 [10, 9] by left_division_multiply ?9 ?10 +Id : 8, {_}: multiply ?18 (right_inverse ?18) =>= identity [18] by right_inverse ?18 +Id : 6, {_}: multiply (right_division ?12 ?13) ?13 =>= ?12 [13, 12] by multiply_right_division ?12 ?13 +Id : 10, {_}: multiply (multiply (multiply ?22 ?23) ?22) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by moufang3 ?22 ?23 ?24 +Id : 3, {_}: multiply ?4 identity =>= ?4 [4] by right_identity ?4 +Id : 7, {_}: right_division (multiply ?15 ?16) ?16 =>= ?15 [16, 15] by right_division_multiply ?15 ?16 +Id : 53, {_}: multiply ?115 (multiply ?116 (multiply ?115 identity)) =>= multiply (multiply ?115 ?116) ?115 [116, 115] by Super 3 with 10 at 2 +Id : 70, {_}: multiply ?115 (multiply ?116 ?115) =<= multiply (multiply ?115 ?116) ?115 [116, 115] by Demod 53 with 3 at 2,2,2 +Id : 889, {_}: right_division (multiply ?1099 (multiply ?1100 ?1099)) ?1099 =>= multiply ?1099 ?1100 [1100, 1099] by Super 7 with 70 at 1,2 +Id : 895, {_}: right_division (multiply ?1115 ?1116) ?1115 =<= multiply ?1115 (right_division ?1116 ?1115) [1116, 1115] by Super 889 with 6 at 2,1,2 +Id : 55, {_}: right_division (multiply ?122 (multiply ?123 (multiply ?122 ?124))) ?124 =>= multiply (multiply ?122 ?123) ?122 [124, 123, 122] by Super 7 with 10 at 1,2 +Id : 2553, {_}: right_division (multiply ?3478 (multiply ?3479 (multiply ?3478 ?3480))) ?3480 =>= multiply ?3478 (multiply ?3479 ?3478) [3480, 3479, 3478] by Demod 55 with 70 at 3 +Id : 647, {_}: multiply ?831 (multiply ?832 ?831) =<= multiply (multiply ?831 ?832) ?831 [832, 831] by Demod 53 with 3 at 2,2,2 +Id : 654, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= multiply identity ?850 [850] by Super 647 with 8 at 1,3 +Id : 677, {_}: multiply ?850 (multiply (right_inverse ?850) ?850) =>= ?850 [850] by Demod 654 with 2 at 3 +Id : 763, {_}: left_division ?991 ?991 =<= multiply (right_inverse ?991) ?991 [991] by Super 5 with 677 at 2,2 +Id : 24, {_}: left_division ?53 ?53 =>= identity [53] by Super 22 with 3 at 2,2 +Id : 789, {_}: identity =<= multiply (right_inverse ?991) ?991 [991] by Demod 763 with 24 at 2 +Id : 816, {_}: right_division identity ?1047 =>= right_inverse ?1047 [1047] by Super 7 with 789 at 1,2 +Id : 45, {_}: right_division identity ?99 =>= left_inverse ?99 [99] by Super 7 with 9 at 1,2 +Id : 843, {_}: left_inverse ?1047 =<= right_inverse ?1047 [1047] by Demod 816 with 45 at 2 +Id : 857, {_}: multiply ?18 (left_inverse ?18) =>= identity [18] by Demod 8 with 843 at 2,2 +Id : 2562, {_}: right_division (multiply ?3513 (multiply ?3514 identity)) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Super 2553 with 857 at 2,2,1,2 +Id : 2621, {_}: right_division (multiply ?3513 ?3514) (left_inverse ?3513) =>= multiply ?3513 (multiply ?3514 ?3513) [3514, 3513] by Demod 2562 with 3 at 2,1,2 +Id : 2806, {_}: right_division (multiply (left_inverse ?3781) (multiply ?3781 ?3782)) (left_inverse ?3781) =>= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Super 895 with 2621 at 2,3 +Id : 52, {_}: multiply ?111 (multiply ?112 (multiply ?111 (left_division (multiply (multiply ?111 ?112) ?111) ?113))) =>= ?113 [113, 112, 111] by Super 4 with 10 at 2 +Id : 963, {_}: multiply ?1216 (multiply ?1217 (multiply ?1216 (left_division (multiply ?1216 (multiply ?1217 ?1216)) ?1218))) =>= ?1218 [1218, 1217, 1216] by Demod 52 with 70 at 1,2,2,2,2 +Id : 970, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division (multiply ?1242 identity) ?1243))) =>= ?1243 [1243, 1242] by Super 963 with 9 at 2,1,2,2,2,2 +Id : 1030, {_}: multiply ?1242 (multiply (left_inverse ?1242) (multiply ?1242 (left_division ?1242 ?1243))) =>= ?1243 [1243, 1242] by Demod 970 with 3 at 1,2,2,2,2 +Id : 1031, {_}: multiply ?1242 (multiply (left_inverse ?1242) ?1243) =>= ?1243 [1243, 1242] by Demod 1030 with 4 at 2,2,2 +Id : 1164, {_}: left_division ?1548 ?1549 =<= multiply (left_inverse ?1548) ?1549 [1549, 1548] by Super 5 with 1031 at 2,2 +Id : 2852, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =<= multiply (left_inverse ?3781) (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2806 with 1164 at 1,2 +Id : 2853, {_}: right_division (left_division ?3781 (multiply ?3781 ?3782)) (left_inverse ?3781) =>= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3782, 3781] by Demod 2852 with 1164 at 3 +Id : 2854, {_}: right_division ?3782 (left_inverse ?3781) =<= left_division ?3781 (multiply ?3781 (multiply ?3782 ?3781)) [3781, 3782] by Demod 2853 with 5 at 1,2 +Id : 2855, {_}: right_division ?3782 (left_inverse ?3781) =>= multiply ?3782 ?3781 [3781, 3782] by Demod 2854 with 5 at 3 +Id : 1378, {_}: right_division (left_division ?1827 ?1828) ?1828 =>= left_inverse ?1827 [1828, 1827] by Super 7 with 1164 at 1,2 +Id : 28, {_}: left_division (right_division ?62 ?63) ?62 =>= ?63 [63, 62] by Super 5 with 6 at 2,2 +Id : 1384, {_}: right_division ?1844 ?1845 =<= left_inverse (right_division ?1845 ?1844) [1845, 1844] by Super 1378 with 28 at 1,2 +Id : 3643, {_}: multiply (multiply ?4879 ?4880) ?4881 =<= multiply ?4880 (multiply (left_division ?4880 ?4879) (multiply ?4880 ?4881)) [4881, 4880, 4879] by Super 56 with 4 at 1,1,2 +Id : 3648, {_}: multiply (multiply ?4897 ?4898) (left_division ?4898 ?4899) =>= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Super 3643 with 4 at 2,2,3 +Id : 2922, {_}: right_division (left_inverse ?3910) ?3911 =>= left_inverse (multiply ?3911 ?3910) [3911, 3910] by Super 1384 with 2855 at 1,3 +Id : 3008, {_}: left_inverse (multiply (left_inverse ?4021) ?4022) =>= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Super 2855 with 2922 at 2 +Id : 3027, {_}: left_inverse (left_division ?4021 ?4022) =<= multiply (left_inverse ?4022) ?4021 [4022, 4021] by Demod 3008 with 1164 at 1,2 +Id : 3028, {_}: left_inverse (left_division ?4021 ?4022) =>= left_division ?4022 ?4021 [4022, 4021] by Demod 3027 with 1164 at 3 +Id : 3191, {_}: right_division ?4224 (left_division ?4225 ?4226) =<= multiply ?4224 (left_division ?4226 ?4225) [4226, 4225, 4224] by Super 2855 with 3028 at 2,2 +Id : 8019, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (multiply (left_division ?4898 ?4897) ?4899) [4899, 4898, 4897] by Demod 3648 with 3191 at 2 +Id : 3187, {_}: left_division (left_division ?4210 ?4211) ?4212 =<= multiply (left_division ?4211 ?4210) ?4212 [4212, 4211, 4210] by Super 1164 with 3028 at 1,3 +Id : 8020, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =<= multiply ?4898 (left_division (left_division ?4897 ?4898) ?4899) [4899, 4898, 4897] by Demod 8019 with 3187 at 2,3 +Id : 8021, {_}: right_division (multiply ?4897 ?4898) (left_division ?4899 ?4898) =>= right_division ?4898 (left_division ?4899 (left_division ?4897 ?4898)) [4899, 4898, 4897] by Demod 8020 with 3191 at 3 +Id : 8034, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= left_inverse (right_division ?9767 (left_division ?9766 (left_division ?9768 ?9767))) [9768, 9767, 9766] by Super 1384 with 8021 at 1,3 +Id : 8099, {_}: right_division (left_division ?9766 ?9767) (multiply ?9768 ?9767) =<= right_division (left_division ?9766 (left_division ?9768 ?9767)) ?9767 [9768, 9767, 9766] by Demod 8034 with 1384 at 3 +Id : 23672, {_}: right_division (left_division ?25246 (left_inverse ?25247)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25247, 25246] by Super 2855 with 8099 at 2 +Id : 2932, {_}: right_division ?3937 (left_inverse ?3938) =>= multiply ?3937 ?3938 [3938, 3937] by Demod 2854 with 5 at 3 +Id : 46, {_}: left_division (left_inverse ?101) identity =>= ?101 [101] by Super 5 with 9 at 2,2 +Id : 40, {_}: left_division ?91 identity =>= right_inverse ?91 [91] by Super 5 with 8 at 2,2 +Id : 426, {_}: right_inverse (left_inverse ?101) =>= ?101 [101] by Demod 46 with 40 at 2 +Id : 860, {_}: left_inverse (left_inverse ?101) =>= ?101 [101] by Demod 426 with 843 at 2 +Id : 2936, {_}: right_division ?3949 ?3950 =<= multiply ?3949 (left_inverse ?3950) [3950, 3949] by Super 2932 with 860 at 2,2 +Id : 3077, {_}: left_division ?4125 (left_inverse ?4126) =>= right_division (left_inverse ?4125) ?4126 [4126, 4125] by Super 1164 with 2936 at 3 +Id : 3115, {_}: left_division ?4125 (left_inverse ?4126) =>= left_inverse (multiply ?4126 ?4125) [4126, 4125] by Demod 3077 with 2922 at 3 +Id : 23819, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (multiply ?25248 (left_inverse ?25247)) =>= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23672 with 3115 at 1,2 +Id : 23820, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= multiply (left_division ?25246 (left_division ?25248 (left_inverse ?25247))) ?25247 [25248, 25246, 25247] by Demod 23819 with 2936 at 2,2 +Id : 23821, {_}: right_division (left_inverse (multiply ?25247 ?25246)) (right_division ?25248 ?25247) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25248, 25246, 25247] by Demod 23820 with 3187 at 3 +Id : 23822, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_division ?25248 (left_inverse ?25247)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23821 with 2922 at 2 +Id : 23823, {_}: left_inverse (multiply (right_division ?25248 ?25247) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25247, 25248] by Demod 23822 with 3115 at 1,1,3 +Id : 1167, {_}: multiply ?1556 (multiply (left_inverse ?1556) ?1557) =>= ?1557 [1557, 1556] by Demod 1030 with 4 at 2,2,2 +Id : 1177, {_}: multiply ?1584 ?1585 =<= left_division (left_inverse ?1584) ?1585 [1585, 1584] by Super 1167 with 4 at 2,2 +Id : 1414, {_}: multiply (right_division ?1873 ?1874) ?1875 =>= left_division (right_division ?1874 ?1873) ?1875 [1875, 1874, 1873] by Super 1177 with 1384 at 1,3 +Id : 23824, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =<= left_division (left_division (left_inverse (multiply ?25247 ?25248)) ?25246) ?25247 [25246, 25248, 25247] by Demod 23823 with 1414 at 1,2 +Id : 23825, {_}: left_inverse (left_division (right_division ?25247 ?25248) (multiply ?25247 ?25246)) =>= left_division (multiply (multiply ?25247 ?25248) ?25246) ?25247 [25246, 25248, 25247] by Demod 23824 with 1177 at 1,3 +Id : 37248, {_}: left_division (multiply ?37773 ?37774) (right_division ?37773 ?37775) =<= left_division (multiply (multiply ?37773 ?37775) ?37774) ?37773 [37775, 37774, 37773] by Demod 23825 with 3028 at 2 +Id : 37265, {_}: left_division (multiply ?37844 ?37845) (right_division ?37844 (left_inverse ?37846)) =>= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Super 37248 with 2936 at 1,1,3 +Id : 37472, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (multiply (right_division ?37844 ?37846) ?37845) ?37844 [37846, 37845, 37844] by Demod 37265 with 2855 at 2,2 +Id : 37473, {_}: left_division (multiply ?37844 ?37845) (multiply ?37844 ?37846) =<= left_division (left_division (right_division ?37846 ?37844) ?37845) ?37844 [37846, 37845, 37844] by Demod 37472 with 1414 at 1,3 +Id : 8041, {_}: right_division (multiply ?9794 ?9795) (left_division ?9796 ?9795) =>= right_division ?9795 (left_division ?9796 (left_division ?9794 ?9795)) [9796, 9795, 9794] by Demod 8020 with 3191 at 3 +Id : 8054, {_}: right_division (multiply ?9845 (left_inverse ?9846)) (left_inverse (multiply ?9846 ?9847)) =>= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Super 8041 with 3115 at 2,2 +Id : 8126, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= right_division (left_inverse ?9846) (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) [9847, 9846, 9845] by Demod 8054 with 2855 at 2 +Id : 8127, {_}: multiply (multiply ?9845 (left_inverse ?9846)) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8126 with 2922 at 3 +Id : 8128, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (multiply (left_division ?9847 (left_division ?9845 (left_inverse ?9846))) ?9846) [9847, 9846, 9845] by Demod 8127 with 2936 at 1,2 +Id : 8129, {_}: multiply (right_division ?9845 ?9846) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9846, 9845] by Demod 8128 with 3187 at 1,3 +Id : 8130, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_inverse (left_division (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) ?9846) [9847, 9845, 9846] by Demod 8129 with 1414 at 2 +Id : 8131, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_division ?9845 (left_inverse ?9846)) ?9847) [9847, 9845, 9846] by Demod 8130 with 3028 at 3 +Id : 8132, {_}: left_division (right_division ?9846 ?9845) (multiply ?9846 ?9847) =<= left_division ?9846 (left_division (left_inverse (multiply ?9846 ?9845)) ?9847) [9847, 9845, 9846] by Demod 8131 with 3115 at 1,2,3 +Id : 24031, {_}: left_division (right_division ?25824 ?25825) (multiply ?25824 ?25826) =>= left_division ?25824 (multiply (multiply ?25824 ?25825) ?25826) [25826, 25825, 25824] by Demod 8132 with 1177 at 2,3 +Id : 24068, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =<= left_division ?25977 (multiply (multiply ?25977 (left_inverse ?25978)) ?25979) [25979, 25978, 25977] by Super 24031 with 2855 at 1,2 +Id : 24287, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (multiply (right_division ?25977 ?25978) ?25979) [25979, 25978, 25977] by Demod 24068 with 2936 at 1,2,3 +Id : 24288, {_}: left_division (multiply ?25977 ?25978) (multiply ?25977 ?25979) =>= left_division ?25977 (left_division (right_division ?25978 ?25977) ?25979) [25979, 25978, 25977] by Demod 24287 with 1414 at 2,3 +Id : 47819, {_}: left_division ?49234 (left_division (right_division ?49235 ?49234) ?49236) =<= left_division (left_division (right_division ?49236 ?49234) ?49235) ?49234 [49236, 49235, 49234] by Demod 37473 with 24288 at 2 +Id : 1246, {_}: multiply (left_inverse ?1641) (multiply ?1642 (left_inverse ?1641)) =>= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Super 70 with 1164 at 1,3 +Id : 1310, {_}: left_division ?1641 (multiply ?1642 (left_inverse ?1641)) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1246 with 1164 at 2 +Id : 3056, {_}: left_division ?1641 (right_division ?1642 ?1641) =<= multiply (left_division ?1641 ?1642) (left_inverse ?1641) [1642, 1641] by Demod 1310 with 2936 at 2,2 +Id : 3057, {_}: left_division ?1641 (right_division ?1642 ?1641) =>= right_division (left_division ?1641 ?1642) ?1641 [1642, 1641] by Demod 3056 with 2936 at 3 +Id : 47887, {_}: left_division ?49524 (left_division (right_division (right_division ?49525 (right_division ?49526 ?49524)) ?49524) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Super 47819 with 3057 at 1,3 +Id : 59, {_}: multiply (multiply ?136 ?137) ?138 =<= multiply ?137 (multiply (left_division ?137 ?136) (multiply ?137 ?138)) [138, 137, 136] by Super 56 with 4 at 1,1,2 +Id : 3632, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= multiply (left_division ?4830 ?4831) (multiply ?4830 ?4832) [4832, 4831, 4830] by Super 5 with 59 at 2,2 +Id : 7833, {_}: left_division ?4830 (multiply (multiply ?4831 ?4830) ?4832) =<= left_division (left_division ?4831 ?4830) (multiply ?4830 ?4832) [4832, 4831, 4830] by Demod 3632 with 3187 at 3 +Id : 7841, {_}: left_inverse (left_division ?9488 (multiply (multiply ?9489 ?9488) ?9490)) =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9489, 9488] by Super 3028 with 7833 at 1,2 +Id : 7910, {_}: left_division (multiply (multiply ?9489 ?9488) ?9490) ?9488 =>= left_division (multiply ?9488 ?9490) (left_division ?9489 ?9488) [9490, 9488, 9489] by Demod 7841 with 3028 at 2 +Id : 22545, {_}: left_division (multiply (left_inverse ?23598) ?23599) (left_division ?23600 (left_inverse ?23598)) =>= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Super 3115 with 7910 at 2 +Id : 22628, {_}: left_division (left_division ?23598 ?23599) (left_division ?23600 (left_inverse ?23598)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22545 with 1164 at 1,2 +Id : 22629, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =<= left_inverse (multiply ?23598 (multiply (multiply ?23600 (left_inverse ?23598)) ?23599)) [23600, 23599, 23598] by Demod 22628 with 3115 at 2,2 +Id : 22630, {_}: left_division (left_division ?23598 ?23599) (left_inverse (multiply ?23598 ?23600)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23600, 23599, 23598] by Demod 22629 with 2936 at 1,2,1,3 +Id : 22631, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (multiply (right_division ?23600 ?23598) ?23599)) [23599, 23600, 23598] by Demod 22630 with 3115 at 2 +Id : 22632, {_}: left_inverse (multiply (multiply ?23598 ?23600) (left_division ?23598 ?23599)) =>= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22631 with 1414 at 2,1,3 +Id : 22633, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =<= left_inverse (multiply ?23598 (left_division (right_division ?23598 ?23600) ?23599)) [23599, 23600, 23598] by Demod 22632 with 3191 at 1,2 +Id : 22634, {_}: left_inverse (right_division (multiply ?23598 ?23600) (left_division ?23599 ?23598)) =>= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23599, 23600, 23598] by Demod 22633 with 3191 at 1,3 +Id : 22635, {_}: right_division (left_division ?23599 ?23598) (multiply ?23598 ?23600) =<= left_inverse (right_division ?23598 (left_division ?23599 (right_division ?23598 ?23600))) [23600, 23598, 23599] by Demod 22634 with 1384 at 2 +Id : 33282, {_}: right_division (left_division ?33402 ?33403) (multiply ?33403 ?33404) =<= right_division (left_division ?33402 (right_division ?33403 ?33404)) ?33403 [33404, 33403, 33402] by Demod 22635 with 1384 at 3 +Id : 33363, {_}: right_division (left_division (left_inverse ?33737) ?33738) (multiply ?33738 ?33739) =>= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Super 33282 with 1177 at 1,3 +Id : 33649, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (multiply ?33737 (right_division ?33738 ?33739)) ?33738 [33739, 33738, 33737] by Demod 33363 with 1177 at 1,2 +Id : 2939, {_}: right_division ?3957 (right_division ?3958 ?3959) =<= multiply ?3957 (right_division ?3959 ?3958) [3959, 3958, 3957] by Super 2932 with 1384 at 2,2 +Id : 33650, {_}: right_division (multiply ?33737 ?33738) (multiply ?33738 ?33739) =<= right_division (right_division ?33737 (right_division ?33739 ?33738)) ?33738 [33739, 33738, 33737] by Demod 33649 with 2939 at 1,3 +Id : 48257, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =<= left_division (right_division (left_division (right_division ?49526 ?49524) ?49525) (right_division ?49526 ?49524)) ?49524 [49526, 49525, 49524] by Demod 47887 with 33650 at 1,2,2 +Id : 640, {_}: multiply (multiply ?22 (multiply ?23 ?22)) ?24 =>= multiply ?22 (multiply ?23 (multiply ?22 ?24)) [24, 23, 22] by Demod 10 with 70 at 1,2 +Id : 1251, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =<= multiply ?1655 (multiply (left_inverse ?1656) (multiply ?1655 ?1657)) [1657, 1656, 1655] by Super 640 with 1164 at 2,1,2 +Id : 1306, {_}: multiply (multiply ?1655 (left_division ?1656 ?1655)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1251 with 1164 at 2,3 +Id : 5008, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= multiply ?1655 (left_division ?1656 (multiply ?1655 ?1657)) [1657, 1656, 1655] by Demod 1306 with 3191 at 1,2 +Id : 5009, {_}: multiply (right_division ?1655 (left_division ?1655 ?1656)) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5008 with 3191 at 3 +Id : 5010, {_}: left_division (right_division (left_division ?1655 ?1656) ?1655) ?1657 =>= right_division ?1655 (left_division (multiply ?1655 ?1657) ?1656) [1657, 1656, 1655] by Demod 5009 with 1414 at 2 +Id : 48258, {_}: left_division ?49524 (left_division (right_division (multiply ?49525 ?49524) (multiply ?49524 ?49526)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49526, 49525, 49524] by Demod 48257 with 5010 at 3 +Id : 3070, {_}: multiply (multiply (left_inverse ?4103) (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Super 640 with 2936 at 2,1,2 +Id : 3126, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= multiply (left_inverse ?4103) (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3070 with 1164 at 1,2 +Id : 3127, {_}: multiply (left_division ?4103 (right_division ?4104 ?4103)) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3126 with 1164 at 3 +Id : 3128, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =<= left_division ?4103 (multiply ?4104 (multiply (left_inverse ?4103) ?4105)) [4105, 4104, 4103] by Demod 3127 with 3057 at 1,2 +Id : 3129, {_}: multiply (right_division (left_division ?4103 ?4104) ?4103) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3128 with 1164 at 2,2,3 +Id : 3130, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (multiply ?4104 (left_division ?4103 ?4105)) [4105, 4104, 4103] by Demod 3129 with 1414 at 2 +Id : 7047, {_}: left_division (right_division ?4103 (left_division ?4103 ?4104)) ?4105 =>= left_division ?4103 (right_division ?4104 (left_division ?4105 ?4103)) [4105, 4104, 4103] by Demod 3130 with 3191 at 2,3 +Id : 7063, {_}: left_division ?8435 (right_division ?8436 (left_division (left_inverse ?8437) ?8435)) =>= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Super 3115 with 7047 at 2 +Id : 7165, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (multiply ?8437 (right_division ?8435 (left_division ?8435 ?8436))) [8437, 8436, 8435] by Demod 7063 with 1177 at 2,2,2 +Id : 7166, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =<= left_inverse (right_division ?8437 (right_division (left_division ?8435 ?8436) ?8435)) [8437, 8436, 8435] by Demod 7165 with 2939 at 1,3 +Id : 7167, {_}: left_division ?8435 (right_division ?8436 (multiply ?8437 ?8435)) =>= right_division (right_division (left_division ?8435 ?8436) ?8435) ?8437 [8437, 8436, 8435] by Demod 7166 with 1384 at 3 +Id : 21426, {_}: left_inverse (right_division (right_division (left_division ?22100 ?22101) ?22100) ?22102) =>= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22102, 22101, 22100] by Super 3028 with 7167 at 1,2 +Id : 21547, {_}: right_division ?22102 (right_division (left_division ?22100 ?22101) ?22100) =<= left_division (right_division ?22101 (multiply ?22102 ?22100)) ?22100 [22101, 22100, 22102] by Demod 21426 with 1384 at 2 +Id : 48259, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (multiply (right_division ?49526 ?49524) ?49524) ?49525) [49525, 49526, 49524] by Demod 48258 with 21547 at 2,2 +Id : 48260, {_}: left_division ?49524 (right_division ?49524 (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526)) =>= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49525, 49526, 49524] by Demod 48259 with 1414 at 1,2,3 +Id : 3073, {_}: left_division ?4114 (right_division ?4114 ?4115) =>= left_inverse ?4115 [4115, 4114] by Super 5 with 2936 at 2,2 +Id : 48261, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =<= right_division (right_division ?49526 ?49524) (left_division (left_division (right_division ?49524 ?49526) ?49524) ?49525) [49524, 49525, 49526] by Demod 48260 with 3073 at 2 +Id : 48262, {_}: left_inverse (right_division (left_division ?49526 (multiply ?49525 ?49524)) ?49526) =>= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48261 with 28 at 1,2,3 +Id : 48263, {_}: right_division ?49526 (left_division ?49526 (multiply ?49525 ?49524)) =<= right_division (right_division ?49526 ?49524) (left_division ?49526 ?49525) [49524, 49525, 49526] by Demod 48262 with 1384 at 2 +Id : 52424, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= left_inverse (right_division ?54688 (left_division ?54688 (multiply ?54689 ?54690))) [54690, 54689, 54688] by Super 1384 with 48263 at 1,3 +Id : 52654, {_}: right_division (left_division ?54688 ?54689) (right_division ?54688 ?54690) =<= right_division (left_division ?54688 (multiply ?54689 ?54690)) ?54688 [54690, 54689, 54688] by Demod 52424 with 1384 at 3 +Id : 54963, {_}: right_division (left_division (left_inverse ?57654) ?57655) (right_division (left_inverse ?57654) ?57656) =>= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Super 2855 with 52654 at 2 +Id : 55156, {_}: right_division (multiply ?57654 ?57655) (right_division (left_inverse ?57654) ?57656) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 54963 with 1177 at 1,2 +Id : 55157, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= multiply (left_division (left_inverse ?57654) (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55156 with 2922 at 2,2 +Id : 55158, {_}: right_division (multiply ?57654 ?57655) (left_inverse (multiply ?57656 ?57654)) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55157 with 3187 at 3 +Id : 55159, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_division (multiply ?57655 ?57656) (left_inverse ?57654)) ?57654 [57656, 57655, 57654] by Demod 55158 with 2855 at 2 +Id : 55160, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= left_division (left_inverse (multiply ?57654 (multiply ?57655 ?57656))) ?57654 [57656, 57655, 57654] by Demod 55159 with 3115 at 1,3 +Id : 55161, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =<= multiply (multiply ?57654 (multiply ?57655 ?57656)) ?57654 [57656, 57655, 57654] by Demod 55160 with 1177 at 3 +Id : 55162, {_}: multiply (multiply ?57654 ?57655) (multiply ?57656 ?57654) =>= multiply ?57654 (multiply (multiply ?57655 ?57656) ?57654) [57656, 57655, 57654] by Demod 55161 with 70 at 3 +Id : 56911, {_}: multiply x (multiply (multiply y z) x) =?= multiply x (multiply (multiply y z) x) [] by Demod 1 with 55162 at 3 +Id : 1, {_}: multiply x (multiply (multiply y z) x) =<= multiply (multiply x y) (multiply z x) [] by prove_moufang4 +% SZS output end CNFRefutation for GRP205-1.p +26205: solved GRP205-1.p in 14.680917 using kbo +26205: status Unsatisfiable for GRP205-1.p +NO CLASH, using fixed ground order +26244: Facts: +26244: Id : 2, {_}: + multiply ?2 + (inverse + (multiply ?3 + (multiply + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?2 ?3))) ?2))) + =>= + ?2 + [4, 3, 2] by single_non_axiom ?2 ?3 ?4 +26244: Goal: +26244: Id : 1, {_}: + multiply x + (inverse + (multiply y + (multiply + (multiply (multiply z (inverse z)) (inverse (multiply u y))) + x))) + =>= + u + [] by try_prove_this_axiom +26244: Order: +26244: nrkbo +26244: Leaf order: +26244: z 2 0 2 1,1,1,2,1,2,2 +26244: u 2 0 2 1,1,2,1,2,1,2,2 +26244: y 2 0 2 1,1,2,2 +26244: x 2 0 2 1,2 +26244: inverse 6 1 3 0,2,2 +26244: multiply 12 2 6 0,2 +NO CLASH, using fixed ground order +26245: Facts: +26245: Id : 2, {_}: + multiply ?2 + (inverse + (multiply ?3 + (multiply + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?2 ?3))) ?2))) + =>= + ?2 + [4, 3, 2] by single_non_axiom ?2 ?3 ?4 +26245: Goal: +26245: Id : 1, {_}: + multiply x + (inverse + (multiply y + (multiply + (multiply (multiply z (inverse z)) (inverse (multiply u y))) + x))) + =>= + u + [] by try_prove_this_axiom +26245: Order: +26245: kbo +26245: Leaf order: +26245: z 2 0 2 1,1,1,2,1,2,2 +26245: u 2 0 2 1,1,2,1,2,1,2,2 +26245: y 2 0 2 1,1,2,2 +26245: x 2 0 2 1,2 +26245: inverse 6 1 3 0,2,2 +26245: multiply 12 2 6 0,2 +NO CLASH, using fixed ground order +26246: Facts: +26246: Id : 2, {_}: + multiply ?2 + (inverse + (multiply ?3 + (multiply + (multiply (multiply ?4 (inverse ?4)) + (inverse (multiply ?2 ?3))) ?2))) + =>= + ?2 + [4, 3, 2] by single_non_axiom ?2 ?3 ?4 +26246: Goal: +26246: Id : 1, {_}: + multiply x + (inverse + (multiply y + (multiply + (multiply (multiply z (inverse z)) (inverse (multiply u y))) + x))) + =>= + u + [] by try_prove_this_axiom +26246: Order: +26246: lpo +26246: Leaf order: +26246: z 2 0 2 1,1,1,2,1,2,2 +26246: u 2 0 2 1,1,2,1,2,1,2,2 +26246: y 2 0 2 1,1,2,2 +26246: x 2 0 2 1,2 +26246: inverse 6 1 3 0,2,2 +26246: multiply 12 2 6 0,2 +% SZS status Timeout for GRP207-1.p +Fatal error: exception Assert_failure("matitaprover.ml", 269, 46) +NO CLASH, using fixed ground order +26289: Facts: +26289: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +26289: Goal: +26289: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +26289: Order: +26289: nrkbo +26289: Leaf order: +26289: a3 2 0 2 1,1,2 +26289: b3 2 0 2 2,1,2 +26289: c3 2 0 2 2,2 +26289: inverse 7 1 0 +26289: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +26290: Facts: +26290: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +26290: Goal: +26290: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +26290: Order: +26290: kbo +26290: Leaf order: +26290: a3 2 0 2 1,1,2 +26290: b3 2 0 2 2,1,2 +26290: c3 2 0 2 2,2 +26290: inverse 7 1 0 +26290: multiply 10 2 4 0,2 +NO CLASH, using fixed ground order +26291: Facts: +26291: Id : 2, {_}: + inverse + (multiply + (inverse + (multiply ?2 + (inverse + (multiply (inverse ?3) + (inverse + (multiply ?4 (inverse (multiply (inverse ?4) ?4)))))))) + (multiply ?2 ?4)) + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +26291: Goal: +26291: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +26291: Order: +26291: lpo +26291: Leaf order: +26291: a3 2 0 2 1,1,2 +26291: b3 2 0 2 2,1,2 +26291: c3 2 0 2 2,2 +26291: inverse 7 1 0 +26291: multiply 10 2 4 0,2 +% SZS status Timeout for GRP420-1.p +NO CLASH, using fixed ground order +26320: Facts: +26320: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +26320: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +26320: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +26320: Goal: +26320: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +26320: Order: +26320: nrkbo +26320: Leaf order: +26320: a3 2 0 2 1,1,2 +26320: b3 2 0 2 2,1,2 +26320: c3 2 0 2 2,2 +26320: inverse 1 1 0 +26320: multiply 5 2 4 0,2 +26320: divide 13 2 0 +NO CLASH, using fixed ground order +26321: Facts: +26321: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +26321: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +26321: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +26321: Goal: +26321: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +26321: Order: +26321: kbo +26321: Leaf order: +26321: a3 2 0 2 1,1,2 +26321: b3 2 0 2 2,1,2 +26321: c3 2 0 2 2,2 +26321: inverse 1 1 0 +26321: multiply 5 2 4 0,2 +26321: divide 13 2 0 +NO CLASH, using fixed ground order +26322: Facts: +26322: Id : 2, {_}: + divide + (divide (divide ?2 ?2) + (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) + ?4 + =>= + ?3 + [4, 3, 2] by single_axiom ?2 ?3 ?4 +26322: Id : 3, {_}: + multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) + [8, 7, 6] by multiply ?6 ?7 ?8 +26322: Id : 4, {_}: + inverse ?10 =<= divide (divide ?11 ?11) ?10 + [11, 10] by inverse ?10 ?11 +26322: Goal: +26322: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +26322: Order: +26322: lpo +26322: Leaf order: +26322: a3 2 0 2 1,1,2 +26322: b3 2 0 2 2,1,2 +26322: c3 2 0 2 2,2 +26322: inverse 1 1 0 +26322: multiply 5 2 4 0,2 +26322: divide 13 2 0 +Statistics : +Max weight : 38 +Found proof, 2.679419s +% SZS status Unsatisfiable for GRP453-1.p +% SZS output start CNFRefutation for GRP453-1.p +Id : 35, {_}: inverse ?90 =<= divide (divide ?91 ?91) ?90 [91, 90] by inverse ?90 ?91 +Id : 2, {_}: divide (divide (divide ?2 ?2) (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by single_axiom ?2 ?3 ?4 +Id : 5, {_}: divide (divide (divide ?13 ?13) (divide ?13 (divide ?14 (divide (divide (divide ?13 ?13) ?13) ?15)))) ?15 =>= ?14 [15, 14, 13] by single_axiom ?13 ?14 ?15 +Id : 4, {_}: inverse ?10 =<= divide (divide ?11 ?11) ?10 [11, 10] by inverse ?10 ?11 +Id : 3, {_}: multiply ?6 ?7 =<= divide ?6 (divide (divide ?8 ?8) ?7) [8, 7, 6] by multiply ?6 ?7 ?8 +Id : 29, {_}: multiply ?6 ?7 =<= divide ?6 (inverse ?7) [7, 6] by Demod 3 with 4 at 2,3 +Id : 6, {_}: divide (divide (divide ?17 ?17) (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Super 5 with 2 at 2,2,1,2 +Id : 142, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= divide (divide ?20 ?20) (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 6 with 4 at 1,2 +Id : 143, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (divide (divide ?20 ?20) ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 142 with 4 at 3 +Id : 144, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (divide (divide ?17 ?17) ?17) ?19)))) [20, 19, 18, 17] by Demod 143 with 4 at 1,2,2,1,3 +Id : 145, {_}: divide (inverse (divide ?17 ?18)) ?19 =<= inverse (divide ?20 (divide ?18 (divide (inverse ?20) (divide (inverse ?17) ?19)))) [20, 19, 18, 17] by Demod 144 with 4 at 1,2,2,2,1,3 +Id : 36, {_}: inverse ?93 =<= divide (inverse (divide ?94 ?94)) ?93 [94, 93] by Super 35 with 4 at 1,3 +Id : 226, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (divide (divide ?529 ?529) (divide ?527 (inverse (divide (inverse ?526) ?528)))) [529, 528, 527, 526] by Super 145 with 36 at 2,2,1,3 +Id : 249, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (divide ?527 (inverse (divide (inverse ?526) ?528)))) [528, 527, 526] by Demod 226 with 4 at 1,3 +Id : 250, {_}: divide (inverse (divide ?526 ?527)) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 527, 526] by Demod 249 with 29 at 1,1,3 +Id : 13, {_}: divide (multiply (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50))) ?50 =>= ?49 [50, 49, 48] by Super 2 with 3 at 1,2 +Id : 32, {_}: multiply (divide ?79 ?79) ?80 =>= inverse (inverse ?80) [80, 79] by Super 29 with 4 at 3 +Id : 479, {_}: divide (inverse (inverse (divide ?49 (divide (divide (divide (divide ?48 ?48) (divide ?48 ?48)) (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 13 with 32 at 1,2 +Id : 480, {_}: divide (inverse (inverse (divide ?49 (divide (inverse (divide ?48 ?48)) ?50)))) ?50 =>= ?49 [50, 48, 49] by Demod 479 with 4 at 1,2,1,1,1,2 +Id : 481, {_}: divide (inverse (inverse (divide ?49 (inverse ?50)))) ?50 =>= ?49 [50, 49] by Demod 480 with 36 at 2,1,1,1,2 +Id : 482, {_}: divide (inverse (inverse (multiply ?49 ?50))) ?50 =>= ?49 [50, 49] by Demod 481 with 29 at 1,1,1,2 +Id : 888, {_}: divide (inverse (divide ?1873 ?1874)) ?1875 =<= inverse (inverse (multiply ?1874 (divide (inverse ?1873) ?1875))) [1875, 1874, 1873] by Demod 249 with 29 at 1,1,3 +Id : 903, {_}: divide (inverse (divide (divide ?1940 ?1940) ?1941)) ?1942 =>= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941, 1940] by Super 888 with 36 at 2,1,1,3 +Id : 936, {_}: divide (inverse (inverse ?1941)) ?1942 =<= inverse (inverse (multiply ?1941 (inverse ?1942))) [1942, 1941] by Demod 903 with 4 at 1,1,2 +Id : 969, {_}: divide (inverse (inverse ?2088)) ?2089 =<= inverse (inverse (multiply ?2088 (inverse ?2089))) [2089, 2088] by Demod 903 with 4 at 1,1,2 +Id : 980, {_}: divide (inverse (inverse (divide ?2127 ?2127))) ?2128 =>= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128, 2127] by Super 969 with 32 at 1,1,3 +Id : 223, {_}: inverse ?515 =<= divide (inverse (inverse (divide ?516 ?516))) ?515 [516, 515] by Super 4 with 36 at 1,3 +Id : 1009, {_}: inverse ?2128 =<= inverse (inverse (inverse (inverse (inverse ?2128)))) [2128] by Demod 980 with 223 at 2 +Id : 1026, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= divide ?2199 (inverse ?2200) [2200, 2199] by Super 29 with 1009 at 2,3 +Id : 1064, {_}: multiply ?2199 (inverse (inverse (inverse (inverse ?2200)))) =>= multiply ?2199 ?2200 [2200, 2199] by Demod 1026 with 29 at 3 +Id : 1096, {_}: divide (inverse (inverse ?2287)) (inverse (inverse (inverse ?2288))) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Super 936 with 1064 at 1,1,3 +Id : 1169, {_}: multiply (inverse (inverse ?2287)) (inverse (inverse ?2288)) =>= inverse (inverse (multiply ?2287 ?2288)) [2288, 2287] by Demod 1096 with 29 at 2 +Id : 1211, {_}: divide (inverse (inverse (inverse (inverse ?2471)))) (inverse ?2472) =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Super 936 with 1169 at 1,1,3 +Id : 1253, {_}: multiply (inverse (inverse (inverse (inverse ?2471)))) ?2472 =>= inverse (inverse (inverse (inverse (multiply ?2471 ?2472)))) [2472, 2471] by Demod 1211 with 29 at 2 +Id : 1506, {_}: divide (inverse (inverse (inverse (inverse (inverse (inverse (multiply ?3181 ?3182))))))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Super 482 with 1253 at 1,1,1,2 +Id : 1558, {_}: divide (inverse (inverse (multiply ?3181 ?3182))) ?3182 =>= inverse (inverse (inverse (inverse ?3181))) [3182, 3181] by Demod 1506 with 1009 at 1,2 +Id : 1559, {_}: ?3181 =<= inverse (inverse (inverse (inverse ?3181))) [3181] by Demod 1558 with 482 at 2 +Id : 1611, {_}: multiply ?3343 (inverse (inverse (inverse ?3344))) =>= divide ?3343 ?3344 [3344, 3343] by Super 29 with 1559 at 2,3 +Id : 1683, {_}: divide (inverse (inverse ?3483)) (inverse (inverse ?3484)) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Super 936 with 1611 at 1,1,3 +Id : 1717, {_}: multiply (inverse (inverse ?3483)) (inverse ?3484) =>= inverse (inverse (divide ?3483 ?3484)) [3484, 3483] by Demod 1683 with 29 at 2 +Id : 1782, {_}: divide (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) (inverse ?3606) =>= inverse (inverse ?3605) [3606, 3605] by Super 482 with 1717 at 1,1,1,2 +Id : 1824, {_}: multiply (inverse (inverse (inverse (inverse (divide ?3605 ?3606))))) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1782 with 29 at 2 +Id : 1825, {_}: multiply (divide ?3605 ?3606) ?3606 =>= inverse (inverse ?3605) [3606, 3605] by Demod 1824 with 1559 at 1,2 +Id : 1854, {_}: inverse (inverse ?3731) =<= divide (divide ?3731 (inverse (inverse (inverse ?3732)))) ?3732 [3732, 3731] by Super 1611 with 1825 at 2 +Id : 2675, {_}: inverse (inverse ?6008) =<= divide (multiply ?6008 (inverse (inverse ?6009))) ?6009 [6009, 6008] by Demod 1854 with 29 at 1,3 +Id : 224, {_}: multiply (inverse (inverse (divide ?518 ?518))) ?519 =>= inverse (inverse ?519) [519, 518] by Super 32 with 36 at 1,2 +Id : 2701, {_}: inverse (inverse (inverse (inverse (divide ?6099 ?6099)))) =?= divide (inverse (inverse (inverse (inverse ?6100)))) ?6100 [6100, 6099] by Super 2675 with 224 at 1,3 +Id : 2754, {_}: divide ?6099 ?6099 =?= divide (inverse (inverse (inverse (inverse ?6100)))) ?6100 [6100, 6099] by Demod 2701 with 1559 at 2 +Id : 2755, {_}: divide ?6099 ?6099 =?= divide ?6100 ?6100 [6100, 6099] by Demod 2754 with 1559 at 1,3 +Id : 2822, {_}: divide (inverse (divide ?6299 (divide (inverse ?6300) (divide (inverse ?6299) ?6301)))) ?6301 =?= inverse (divide ?6300 (divide ?6302 ?6302)) [6302, 6301, 6300, 6299] by Super 145 with 2755 at 2,1,3 +Id : 30, {_}: divide (inverse (divide ?2 (divide ?3 (divide (divide (divide ?2 ?2) ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 2 with 4 at 1,2 +Id : 31, {_}: divide (inverse (divide ?2 (divide ?3 (divide (inverse ?2) ?4)))) ?4 =>= ?3 [4, 3, 2] by Demod 30 with 4 at 1,2,2,1,1,2 +Id : 2899, {_}: inverse ?6300 =<= inverse (divide ?6300 (divide ?6302 ?6302)) [6302, 6300] by Demod 2822 with 31 at 2 +Id : 2957, {_}: divide ?6663 (divide ?6664 ?6664) =>= inverse (inverse (inverse (inverse ?6663))) [6664, 6663] by Super 1559 with 2899 at 1,1,1,3 +Id : 3011, {_}: divide ?6663 (divide ?6664 ?6664) =>= ?6663 [6664, 6663] by Demod 2957 with 1559 at 3 +Id : 3087, {_}: divide (inverse (divide ?6934 ?6935)) (divide ?6936 ?6936) =>= inverse (inverse (multiply ?6935 (inverse ?6934))) [6936, 6935, 6934] by Super 250 with 3011 at 2,1,1,3 +Id : 3149, {_}: inverse (divide ?6934 ?6935) =<= inverse (inverse (multiply ?6935 (inverse ?6934))) [6935, 6934] by Demod 3087 with 3011 at 2 +Id : 3445, {_}: inverse (divide ?7675 ?7676) =<= divide (inverse (inverse ?7676)) ?7675 [7676, 7675] by Demod 3149 with 936 at 3 +Id : 1622, {_}: ?3381 =<= inverse (inverse (inverse (inverse ?3381))) [3381] by Demod 1558 with 482 at 2 +Id : 1636, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (divide (inverse (inverse ?3417)) ?3418)) [3418, 3417] by Super 1622 with 936 at 1,1,3 +Id : 3150, {_}: inverse (divide ?6934 ?6935) =<= divide (inverse (inverse ?6935)) ?6934 [6935, 6934] by Demod 3149 with 936 at 3 +Id : 3402, {_}: multiply ?3417 (inverse ?3418) =<= inverse (inverse (inverse (divide ?3418 ?3417))) [3418, 3417] by Demod 1636 with 3150 at 1,1,3 +Id : 3466, {_}: inverse (divide ?7752 (inverse (divide ?7753 ?7754))) =>= divide (multiply ?7754 (inverse ?7753)) ?7752 [7754, 7753, 7752] by Super 3445 with 3402 at 1,3 +Id : 3559, {_}: inverse (multiply ?7752 (divide ?7753 ?7754)) =<= divide (multiply ?7754 (inverse ?7753)) ?7752 [7754, 7753, 7752] by Demod 3466 with 29 at 1,2 +Id : 229, {_}: inverse ?541 =<= divide (inverse (divide ?542 ?542)) ?541 [542, 541] by Super 35 with 4 at 1,3 +Id : 236, {_}: inverse ?562 =<= divide (inverse (inverse (inverse (divide ?563 ?563)))) ?562 [563, 562] by Super 229 with 36 at 1,1,3 +Id : 3400, {_}: inverse ?562 =<= inverse (divide ?562 (inverse (divide ?563 ?563))) [563, 562] by Demod 236 with 3150 at 3 +Id : 3405, {_}: inverse ?562 =<= inverse (multiply ?562 (divide ?563 ?563)) [563, 562] by Demod 3400 with 29 at 1,3 +Id : 3088, {_}: multiply ?6938 (divide ?6939 ?6939) =>= inverse (inverse ?6938) [6939, 6938] by Super 1825 with 3011 at 1,2 +Id : 3773, {_}: inverse ?562 =<= inverse (inverse (inverse ?562)) [562] by Demod 3405 with 3088 at 1,3 +Id : 3776, {_}: multiply ?3343 (inverse ?3344) =>= divide ?3343 ?3344 [3344, 3343] by Demod 1611 with 3773 at 2,2 +Id : 4266, {_}: inverse (multiply ?8883 (divide ?8884 ?8885)) =>= divide (divide ?8885 ?8884) ?8883 [8885, 8884, 8883] by Demod 3559 with 3776 at 1,3 +Id : 3463, {_}: inverse (divide ?7741 (inverse (inverse ?7742))) =>= divide ?7742 ?7741 [7742, 7741] by Super 3445 with 1559 at 1,3 +Id : 3558, {_}: inverse (multiply ?7741 (inverse ?7742)) =>= divide ?7742 ?7741 [7742, 7741] by Demod 3463 with 29 at 1,2 +Id : 3777, {_}: inverse (divide ?7741 ?7742) =>= divide ?7742 ?7741 [7742, 7741] by Demod 3558 with 3776 at 1,2 +Id : 3787, {_}: divide (divide ?527 ?526) ?528 =<= inverse (inverse (multiply ?527 (divide (inverse ?526) ?528))) [528, 526, 527] by Demod 250 with 3777 at 1,2 +Id : 3399, {_}: inverse (divide ?50 (multiply ?49 ?50)) =>= ?49 [49, 50] by Demod 482 with 3150 at 2 +Id : 3783, {_}: divide (multiply ?49 ?50) ?50 =>= ?49 [50, 49] by Demod 3399 with 3777 at 2 +Id : 1860, {_}: multiply (divide ?3752 ?3753) ?3753 =>= inverse (inverse ?3752) [3753, 3752] by Demod 1824 with 1559 at 1,2 +Id : 1869, {_}: multiply (multiply ?3781 ?3782) (inverse ?3782) =>= inverse (inverse ?3781) [3782, 3781] by Super 1860 with 29 at 1,2 +Id : 3779, {_}: divide (multiply ?3781 ?3782) ?3782 =>= inverse (inverse ?3781) [3782, 3781] by Demod 1869 with 3776 at 2 +Id : 3799, {_}: inverse (inverse ?49) =>= ?49 [49] by Demod 3783 with 3779 at 2 +Id : 3800, {_}: divide (divide ?527 ?526) ?528 =<= multiply ?527 (divide (inverse ?526) ?528) [528, 526, 527] by Demod 3787 with 3799 at 3 +Id : 4296, {_}: inverse (divide (divide ?9013 ?9014) ?9015) =<= divide (divide ?9015 (inverse ?9014)) ?9013 [9015, 9014, 9013] by Super 4266 with 3800 at 1,2 +Id : 4346, {_}: divide ?9015 (divide ?9013 ?9014) =<= divide (divide ?9015 (inverse ?9014)) ?9013 [9014, 9013, 9015] by Demod 4296 with 3777 at 2 +Id : 4347, {_}: divide ?9015 (divide ?9013 ?9014) =<= divide (multiply ?9015 ?9014) ?9013 [9014, 9013, 9015] by Demod 4346 with 29 at 1,3 +Id : 4244, {_}: inverse (multiply ?7752 (divide ?7753 ?7754)) =>= divide (divide ?7754 ?7753) ?7752 [7754, 7753, 7752] by Demod 3559 with 3776 at 1,3 +Id : 4262, {_}: inverse (divide (divide ?8865 ?8866) ?8867) =>= multiply ?8867 (divide ?8866 ?8865) [8867, 8866, 8865] by Super 3799 with 4244 at 1,2 +Id : 4303, {_}: divide ?8867 (divide ?8865 ?8866) =>= multiply ?8867 (divide ?8866 ?8865) [8866, 8865, 8867] by Demod 4262 with 3777 at 2 +Id : 4889, {_}: multiply ?9015 (divide ?9014 ?9013) =<= divide (multiply ?9015 ?9014) ?9013 [9013, 9014, 9015] by Demod 4347 with 4303 at 2 +Id : 4905, {_}: multiply (multiply ?10384 ?10385) ?10386 =<= multiply ?10384 (divide ?10385 (inverse ?10386)) [10386, 10385, 10384] by Super 29 with 4889 at 3 +Id : 4955, {_}: multiply (multiply ?10384 ?10385) ?10386 =>= multiply ?10384 (multiply ?10385 ?10386) [10386, 10385, 10384] by Demod 4905 with 29 at 2,3 +Id : 5096, {_}: multiply a3 (multiply b3 c3) =?= multiply a3 (multiply b3 c3) [] by Demod 1 with 4955 at 2 +Id : 1, {_}: multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) [] by prove_these_axioms_3 +% SZS output end CNFRefutation for GRP453-1.p +26321: solved GRP453-1.p in 1.372085 using kbo +26321: status Unsatisfiable for GRP453-1.p +Fatal error: exception Assert_failure("matitaprover.ml", 269, 46) +NO CLASH, using fixed ground order +26331: Facts: +26331: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +26331: Id : 3, {_}: + meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) + [7, 6, 5] by distribution ?5 ?6 ?7 +26331: Goal: +26331: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_associativity_of_join +26331: Order: +26331: nrkbo +26331: Leaf order: +26331: a 2 0 2 1,1,2 +26331: b 2 0 2 2,1,2 +26331: c 2 0 2 2,2 +26331: meet 4 2 0 +26331: join 7 2 4 0,2 +NO CLASH, using fixed ground order +26332: Facts: +26332: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +26332: Id : 3, {_}: + meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) + [7, 6, 5] by distribution ?5 ?6 ?7 +26332: Goal: +26332: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_associativity_of_join +26332: Order: +26332: kbo +26332: Leaf order: +26332: a 2 0 2 1,1,2 +26332: b 2 0 2 2,1,2 +26332: c 2 0 2 2,2 +26332: meet 4 2 0 +26332: join 7 2 4 0,2 +NO CLASH, using fixed ground order +26333: Facts: +26333: Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +26333: Id : 3, {_}: + meet ?5 (join ?6 ?7) =?= join (meet ?7 ?5) (meet ?6 ?5) + [7, 6, 5] by distribution ?5 ?6 ?7 +26333: Goal: +26333: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_associativity_of_join +26333: Order: +26333: lpo +26333: Leaf order: +26333: a 2 0 2 1,1,2 +26333: b 2 0 2 2,1,2 +26333: c 2 0 2 2,2 +26333: meet 4 2 0 +26333: join 7 2 4 0,2 +Statistics : +Max weight : 31 +Found proof, 28.344880s +% SZS status Unsatisfiable for LAT007-1.p +% SZS output start CNFRefutation for LAT007-1.p +Id : 3, {_}: meet ?5 (join ?6 ?7) =<= join (meet ?7 ?5) (meet ?6 ?5) [7, 6, 5] by distribution ?5 ?6 ?7 +Id : 2, {_}: meet ?2 (join ?2 ?3) =>= ?2 [3, 2] by absorption ?2 ?3 +Id : 7, {_}: meet ?18 (join ?19 ?20) =<= join (meet ?20 ?18) (meet ?19 ?18) [20, 19, 18] by distribution ?18 ?19 ?20 +Id : 8, {_}: meet (join ?22 ?23) (join ?22 ?24) =<= join (meet ?24 (join ?22 ?23)) ?22 [24, 23, 22] by Super 7 with 2 at 2,3 +Id : 13, {_}: meet (meet ?44 ?45) (meet ?45 (join ?46 ?44)) =>= meet ?44 ?45 [46, 45, 44] by Super 2 with 3 at 2,2 +Id : 15, {_}: meet (meet ?53 ?54) ?54 =>= meet ?53 ?54 [54, 53] by Super 13 with 2 at 2,2 +Id : 21, {_}: meet ?68 (join (meet ?69 ?68) ?70) =<= join (meet ?70 ?68) (meet ?69 ?68) [70, 69, 68] by Super 3 with 15 at 2,3 +Id : 69, {_}: meet ?209 (join (meet ?210 ?209) ?211) =>= meet ?209 (join ?210 ?211) [211, 210, 209] by Demod 21 with 3 at 3 +Id : 74, {_}: meet ?231 (meet ?231 (join ?232 ?233)) =<= meet ?231 (join ?233 (meet ?232 ?231)) [233, 232, 231] by Super 69 with 3 at 2,2 +Id : 22, {_}: meet ?72 (join ?73 (meet ?74 ?72)) =<= join (meet ?74 ?72) (meet ?73 ?72) [74, 73, 72] by Super 3 with 15 at 1,3 +Id : 33, {_}: meet ?72 (join ?73 (meet ?74 ?72)) =>= meet ?72 (join ?73 ?74) [74, 73, 72] by Demod 22 with 3 at 3 +Id : 219, {_}: meet ?572 (meet ?572 (join ?573 ?574)) =>= meet ?572 (join ?574 ?573) [574, 573, 572] by Demod 74 with 33 at 3 +Id : 224, {_}: meet ?597 ?597 =<= meet ?597 (join ?598 ?597) [598, 597] by Super 219 with 2 at 2,2 +Id : 244, {_}: meet (join ?635 ?636) (join ?635 ?636) =>= join (meet ?636 ?636) ?635 [636, 635] by Super 8 with 224 at 1,3 +Id : 247, {_}: meet ?644 ?644 =>= ?644 [644] by Super 2 with 224 at 2 +Id : 1803, {_}: join ?635 ?636 =<= join (meet ?636 ?636) ?635 [636, 635] by Demod 244 with 247 at 2 +Id : 1804, {_}: join ?635 ?636 =?= join ?636 ?635 [636, 635] by Demod 1803 with 247 at 1,3 +Id : 9, {_}: meet (join ?26 ?27) (join ?28 ?26) =<= join ?26 (meet ?28 (join ?26 ?27)) [28, 27, 26] by Super 7 with 2 at 1,3 +Id : 6, {_}: meet (meet ?14 ?15) (meet ?15 (join ?16 ?14)) =>= meet ?14 ?15 [16, 15, 14] by Super 2 with 3 at 2,2 +Id : 11, {_}: meet (meet ?34 (join ?35 ?36)) (join (meet ?36 ?34) ?37) =<= join (meet ?37 (meet ?34 (join ?35 ?36))) (meet ?36 ?34) [37, 36, 35, 34] by Super 3 with 6 at 2,3 +Id : 364, {_}: meet (meet ?919 (join ?920 ?919)) (join (meet ?919 ?919) ?921) =>= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [921, 920, 919] by Super 11 with 247 at 2,3 +Id : 349, {_}: ?597 =<= meet ?597 (join ?598 ?597) [598, 597] by Demod 224 with 247 at 2 +Id : 370, {_}: meet ?919 (join (meet ?919 ?919) ?921) =<= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [920, 921, 919] by Demod 364 with 349 at 1,2 +Id : 371, {_}: meet ?919 (join ?919 ?921) =<= join (meet ?921 (meet ?919 (join ?920 ?919))) ?919 [920, 921, 919] by Demod 370 with 247 at 1,2,2 +Id : 372, {_}: meet ?919 (join ?919 ?921) =<= join (meet ?921 ?919) ?919 [921, 919] by Demod 371 with 349 at 2,1,3 +Id : 411, {_}: ?977 =<= join (meet ?978 ?977) ?977 [978, 977] by Demod 372 with 2 at 2 +Id : 420, {_}: join ?1006 ?1007 =<= join ?1007 (join ?1006 ?1007) [1007, 1006] by Super 411 with 349 at 1,3 +Id : 703, {_}: meet (join ?1582 (join ?1583 ?1582)) (join ?1584 ?1582) =>= join ?1582 (meet ?1584 (join ?1583 ?1582)) [1584, 1583, 1582] by Super 9 with 420 at 2,2,3 +Id : 2541, {_}: meet (join ?5116 ?5117) (join ?5118 ?5117) =<= join ?5117 (meet ?5118 (join ?5116 ?5117)) [5118, 5117, 5116] by Demod 703 with 420 at 1,2 +Id : 419, {_}: ?1004 =<= join ?1004 ?1004 [1004] by Super 411 with 247 at 1,3 +Id : 446, {_}: meet ?1028 (join ?1029 ?1029) =>= meet ?1029 ?1028 [1029, 1028] by Super 3 with 419 at 3 +Id : 462, {_}: meet ?1028 ?1029 =?= meet ?1029 ?1028 [1029, 1028] by Demod 446 with 419 at 2,2 +Id : 2566, {_}: meet (join ?5222 ?5223) (join ?5224 ?5223) =<= join ?5223 (meet (join ?5222 ?5223) ?5224) [5224, 5223, 5222] by Super 2541 with 462 at 2,3 +Id : 1841, {_}: meet (join ?3986 ?3987) (join ?3988 ?3986) =<= join ?3986 (meet ?3988 (join ?3987 ?3986)) [3988, 3987, 3986] by Super 9 with 1804 at 2,2,3 +Id : 731, {_}: meet (join ?1583 ?1582) (join ?1584 ?1582) =<= join ?1582 (meet ?1584 (join ?1583 ?1582)) [1584, 1582, 1583] by Demod 703 with 420 at 1,2 +Id : 6413, {_}: meet (join ?3986 ?3987) (join ?3988 ?3986) =?= meet (join ?3987 ?3986) (join ?3988 ?3986) [3988, 3987, 3986] by Demod 1841 with 731 at 3 +Id : 210, {_}: meet ?231 (meet ?231 (join ?232 ?233)) =>= meet ?231 (join ?233 ?232) [233, 232, 231] by Demod 74 with 33 at 3 +Id : 449, {_}: meet ?1037 (meet ?1037 ?1038) =?= meet ?1037 (join ?1038 ?1038) [1038, 1037] by Super 210 with 419 at 2,2,2 +Id : 457, {_}: meet ?1037 (meet ?1037 ?1038) =>= meet ?1037 ?1038 [1038, 1037] by Demod 449 with 419 at 2,3 +Id : 754, {_}: meet ?231 (join ?232 ?233) =?= meet ?231 (join ?233 ?232) [233, 232, 231] by Demod 210 with 457 at 2 +Id : 32, {_}: meet ?68 (join (meet ?69 ?68) ?70) =>= meet ?68 (join ?69 ?70) [70, 69, 68] by Demod 21 with 3 at 3 +Id : 763, {_}: meet (meet ?1697 ?1698) (join (meet ?1697 ?1698) ?1699) =>= meet (meet ?1697 ?1698) (join ?1697 ?1699) [1699, 1698, 1697] by Super 32 with 457 at 1,2,2 +Id : 793, {_}: meet ?1697 ?1698 =<= meet (meet ?1697 ?1698) (join ?1697 ?1699) [1699, 1698, 1697] by Demod 763 with 2 at 2 +Id : 2682, {_}: meet (join ?5359 ?5360) (join ?5361 (meet ?5359 ?5362)) =<= join (meet ?5359 ?5362) (meet ?5361 (join ?5359 ?5360)) [5362, 5361, 5360, 5359] by Super 3 with 793 at 1,3 +Id : 1421, {_}: meet ?2943 (join ?2944 (meet ?2943 ?2945)) =>= meet ?2943 (join ?2944 ?2945) [2945, 2944, 2943] by Super 33 with 462 at 2,2,2 +Id : 4338, {_}: meet (join ?8616 (meet ?8617 ?8618)) (join ?8616 ?8617) =>= join (meet ?8617 (join ?8616 ?8618)) ?8616 [8618, 8617, 8616] by Super 8 with 1421 at 1,3 +Id : 4448, {_}: meet (join ?8616 (meet ?8617 ?8618)) (join ?8616 ?8617) =>= meet (join ?8616 ?8618) (join ?8616 ?8617) [8618, 8617, 8616] by Demod 4338 with 8 at 3 +Id : 62692, {_}: meet (join ?135834 ?135835) (join (join ?135834 (meet ?135835 ?135836)) (meet ?135834 ?135837)) =>= join (meet ?135834 ?135837) (meet (join ?135834 ?135836) (join ?135834 ?135835)) [135837, 135836, 135835, 135834] by Super 2682 with 4448 at 2,3 +Id : 62942, {_}: meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 (meet ?135835 ?135836))) =>= join (meet ?135834 ?135837) (meet (join ?135834 ?135836) (join ?135834 ?135835)) [135836, 135837, 135835, 135834] by Demod 62692 with 754 at 2 +Id : 62943, {_}: meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 (meet ?135835 ?135836))) =>= meet (join ?135834 ?135835) (join (join ?135834 ?135836) (meet ?135834 ?135837)) [135836, 135837, 135835, 135834] by Demod 62942 with 2682 at 3 +Id : 373, {_}: ?919 =<= join (meet ?921 ?919) ?919 [921, 919] by Demod 372 with 2 at 2 +Id : 2674, {_}: join ?5321 ?5322 =<= join (meet ?5321 ?5323) (join ?5321 ?5322) [5323, 5322, 5321] by Super 373 with 793 at 1,3 +Id : 62944, {_}: meet (join ?135834 ?135835) (join ?135834 (meet ?135835 ?135836)) =?= meet (join ?135834 ?135835) (join (join ?135834 ?135836) (meet ?135834 ?135837)) [135837, 135836, 135835, 135834] by Demod 62943 with 2674 at 2,2 +Id : 62945, {_}: meet (join ?135834 ?135835) (join ?135834 (meet ?135835 ?135836)) =?= meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 ?135836)) [135837, 135836, 135835, 135834] by Demod 62944 with 754 at 3 +Id : 762, {_}: meet (meet ?1693 ?1694) (meet (meet ?1693 ?1694) (join ?1695 ?1693)) =>= meet ?1693 (meet ?1693 ?1694) [1695, 1694, 1693] by Super 6 with 457 at 1,2 +Id : 794, {_}: meet (meet ?1693 ?1694) (join ?1695 ?1693) =>= meet ?1693 (meet ?1693 ?1694) [1695, 1694, 1693] by Demod 762 with 457 at 2 +Id : 795, {_}: meet (meet ?1693 ?1694) (join ?1695 ?1693) =>= meet ?1693 ?1694 [1695, 1694, 1693] by Demod 794 with 457 at 3 +Id : 2860, {_}: meet (join ?5717 ?5718) (join ?5717 (meet ?5718 ?5719)) =>= join (meet ?5718 ?5719) ?5717 [5719, 5718, 5717] by Super 8 with 795 at 1,3 +Id : 62946, {_}: join (meet ?135835 ?135836) ?135834 =<= meet (join ?135834 ?135835) (join (meet ?135834 ?135837) (join ?135834 ?135836)) [135837, 135834, 135836, 135835] by Demod 62945 with 2860 at 2 +Id : 62947, {_}: join (meet ?135835 ?135836) ?135834 =<= meet (join ?135834 ?135835) (join ?135834 ?135836) [135834, 135836, 135835] by Demod 62946 with 2674 at 2,3 +Id : 63610, {_}: meet (join ?137323 ?137324) (join ?137325 ?137323) =>= join (meet ?137324 ?137325) ?137323 [137325, 137324, 137323] by Super 754 with 62947 at 3 +Id : 64209, {_}: join (meet ?3987 ?3988) ?3986 =<= meet (join ?3987 ?3986) (join ?3988 ?3986) [3986, 3988, 3987] by Demod 6413 with 63610 at 2 +Id : 64222, {_}: join (meet ?5222 ?5224) ?5223 =<= join ?5223 (meet (join ?5222 ?5223) ?5224) [5223, 5224, 5222] by Demod 2566 with 64209 at 2 +Id : 64386, {_}: join (meet ?139191 (join ?139192 ?139191)) ?139193 =?= join ?139193 (join (meet ?139193 ?139192) ?139191) [139193, 139192, 139191] by Super 64222 with 63610 at 2,3 +Id : 66054, {_}: join ?143110 ?143111 =<= join ?143111 (join (meet ?143111 ?143112) ?143110) [143112, 143111, 143110] by Demod 64386 with 349 at 1,2 +Id : 36, {_}: meet (join ?109 ?110) (join ?109 ?111) =<= join (meet ?111 (join ?109 ?110)) ?109 [111, 110, 109] by Super 7 with 2 at 2,3 +Id : 39, {_}: meet (join ?123 ?124) (join ?123 ?123) =>= join ?123 ?123 [124, 123] by Super 36 with 2 at 1,3 +Id : 438, {_}: meet (join ?123 ?124) ?123 =>= join ?123 ?123 [124, 123] by Demod 39 with 419 at 2,2 +Id : 439, {_}: meet (join ?123 ?124) ?123 =>= ?123 [124, 123] by Demod 438 with 419 at 3 +Id : 66061, {_}: join ?143140 (join ?143141 ?143142) =<= join (join ?143141 ?143142) (join ?143141 ?143140) [143142, 143141, 143140] by Super 66054 with 439 at 1,2,3 +Id : 706, {_}: meet (join ?1593 (join ?1594 ?1593)) (join ?1593 ?1595) =>= join (meet ?1595 (join ?1594 ?1593)) ?1593 [1595, 1594, 1593] by Super 8 with 420 at 2,1,3 +Id : 2402, {_}: meet (join ?4835 ?4836) (join ?4836 ?4837) =<= join (meet ?4837 (join ?4835 ?4836)) ?4836 [4837, 4836, 4835] by Demod 706 with 420 at 1,2 +Id : 2426, {_}: meet (join ?4936 ?4937) (join ?4937 ?4938) =<= join (meet (join ?4936 ?4937) ?4938) ?4937 [4938, 4937, 4936] by Super 2402 with 462 at 1,3 +Id : 1831, {_}: meet (join ?3948 ?3949) (join ?3948 ?3950) =<= join (meet ?3950 (join ?3949 ?3948)) ?3948 [3950, 3949, 3948] by Super 8 with 1804 at 2,1,3 +Id : 729, {_}: meet (join ?1594 ?1593) (join ?1593 ?1595) =<= join (meet ?1595 (join ?1594 ?1593)) ?1593 [1595, 1593, 1594] by Demod 706 with 420 at 1,2 +Id : 5899, {_}: meet (join ?3948 ?3949) (join ?3948 ?3950) =?= meet (join ?3949 ?3948) (join ?3948 ?3950) [3950, 3949, 3948] by Demod 1831 with 729 at 3 +Id : 63510, {_}: join (meet ?3949 ?3950) ?3948 =<= meet (join ?3949 ?3948) (join ?3948 ?3950) [3948, 3950, 3949] by Demod 5899 with 62947 at 2 +Id : 63518, {_}: join (meet ?4936 ?4938) ?4937 =<= join (meet (join ?4936 ?4937) ?4938) ?4937 [4937, 4938, 4936] by Demod 2426 with 63510 at 2 +Id : 63690, {_}: join (meet ?137703 (join ?137703 ?137704)) ?137705 =?= join (join (meet ?137705 ?137704) ?137703) ?137705 [137705, 137704, 137703] by Super 63518 with 62947 at 1,3 +Id : 65015, {_}: join ?140539 ?140540 =<= join (join (meet ?140540 ?140541) ?140539) ?140540 [140541, 140540, 140539] by Demod 63690 with 2 at 1,2 +Id : 65022, {_}: join ?140569 (join ?140570 ?140571) =<= join (join ?140570 ?140569) (join ?140570 ?140571) [140571, 140570, 140569] by Super 65015 with 439 at 1,1,3 +Id : 71034, {_}: join ?143140 (join ?143141 ?143142) =?= join ?143142 (join ?143141 ?143140) [143142, 143141, 143140] by Demod 66061 with 65022 at 3 +Id : 709, {_}: meet (join ?1606 ?1607) ?1607 =>= ?1607 [1607, 1606] by Super 439 with 420 at 1,2 +Id : 1049, {_}: meet ?2275 (join ?2275 ?2276) =<= meet ?2275 (join (join ?2277 ?2275) ?2276) [2277, 2276, 2275] by Super 32 with 709 at 1,2,2 +Id : 1082, {_}: ?2275 =<= meet ?2275 (join (join ?2277 ?2275) ?2276) [2276, 2277, 2275] by Demod 1049 with 2 at 2 +Id : 10434, {_}: join (join ?21238 ?21239) ?21240 =<= join ?21239 (join (join ?21238 ?21239) ?21240) [21240, 21239, 21238] by Super 373 with 1082 at 1,3 +Id : 10435, {_}: join (join ?21242 ?21243) ?21244 =<= join ?21243 (join (join ?21243 ?21242) ?21244) [21244, 21243, 21242] by Super 10434 with 1804 at 1,2,3 +Id : 7878, {_}: join ?15712 ?15713 =<= join (meet ?15712 ?15714) (join ?15712 ?15713) [15714, 15713, 15712] by Super 373 with 793 at 1,3 +Id : 7917, {_}: join (join ?15885 ?15886) ?15887 =<= join ?15885 (join (join ?15885 ?15886) ?15887) [15887, 15886, 15885] by Super 7878 with 439 at 1,3 +Id : 21540, {_}: join (join ?21242 ?21243) ?21244 =?= join (join ?21243 ?21242) ?21244 [21244, 21243, 21242] by Demod 10435 with 7917 at 3 +Id : 63854, {_}: join ?137703 ?137705 =<= join (join (meet ?137705 ?137704) ?137703) ?137705 [137704, 137705, 137703] by Demod 63690 with 2 at 1,2 +Id : 67172, {_}: join (join ?145721 (meet ?145722 ?145723)) ?145722 =>= join ?145721 ?145722 [145723, 145722, 145721] by Super 21540 with 63854 at 3 +Id : 67179, {_}: join (join ?145751 ?145752) (join ?145752 ?145753) =>= join ?145751 (join ?145752 ?145753) [145753, 145752, 145751] by Super 67172 with 439 at 2,1,2 +Id : 66065, {_}: join ?143156 (join ?143157 ?143158) =<= join (join ?143157 ?143158) (join ?143158 ?143156) [143158, 143157, 143156] by Super 66054 with 709 at 1,2,3 +Id : 73159, {_}: join ?145753 (join ?145751 ?145752) =?= join ?145751 (join ?145752 ?145753) [145752, 145751, 145753] by Demod 67179 with 66065 at 2 +Id : 359, {_}: meet ?904 (join ?905 ?904) =<= join ?904 (meet ?905 ?904) [905, 904] by Super 3 with 247 at 1,3 +Id : 386, {_}: ?904 =<= join ?904 (meet ?905 ?904) [905, 904] by Demod 359 with 349 at 2 +Id : 1047, {_}: meet ?2267 (meet ?2267 (join ?2268 (join ?2269 ?2267))) =>= meet (join ?2269 ?2267) ?2267 [2269, 2268, 2267] by Super 6 with 709 at 1,2 +Id : 1084, {_}: meet ?2267 (join ?2268 (join ?2269 ?2267)) =>= meet (join ?2269 ?2267) ?2267 [2269, 2268, 2267] by Demod 1047 with 457 at 2 +Id : 1085, {_}: meet ?2267 (join ?2268 (join ?2269 ?2267)) =>= ?2267 [2269, 2268, 2267] by Demod 1084 with 709 at 3 +Id : 11489, {_}: join ?23526 (join ?23527 ?23528) =<= join (join ?23526 (join ?23527 ?23528)) ?23528 [23528, 23527, 23526] by Super 386 with 1085 at 2,3 +Id : 11490, {_}: join ?23530 (join ?23531 ?23532) =<= join (join ?23530 (join ?23532 ?23531)) ?23532 [23532, 23531, 23530] by Super 11489 with 1804 at 2,1,3 +Id : 2878, {_}: meet (meet ?5800 ?5801) (join ?5802 ?5800) =>= meet ?5800 ?5801 [5802, 5801, 5800] by Demod 794 with 457 at 3 +Id : 2907, {_}: meet ?5929 (join ?5930 (join ?5929 ?5931)) =>= meet (join ?5929 ?5931) ?5929 [5931, 5930, 5929] by Super 2878 with 439 at 1,2 +Id : 3014, {_}: meet ?5929 (join ?5930 (join ?5929 ?5931)) =>= ?5929 [5931, 5930, 5929] by Demod 2907 with 439 at 3 +Id : 10163, {_}: join ?20474 (join ?20475 ?20476) =<= join (join ?20474 (join ?20475 ?20476)) ?20475 [20476, 20475, 20474] by Super 386 with 3014 at 2,3 +Id : 22205, {_}: join ?23530 (join ?23531 ?23532) =?= join ?23530 (join ?23532 ?23531) [23532, 23531, 23530] by Demod 11490 with 10163 at 3 +Id : 73995, {_}: join a (join b c) === join a (join b c) [] by Demod 73994 with 22205 at 2 +Id : 73994, {_}: join a (join c b) =>= join a (join b c) [] by Demod 73993 with 73159 at 2 +Id : 73993, {_}: join b (join a c) =>= join a (join b c) [] by Demod 73992 with 71034 at 2 +Id : 73992, {_}: join c (join a b) =>= join a (join b c) [] by Demod 1 with 1804 at 2 +Id : 1, {_}: join (join a b) c =>= join a (join b c) [] by prove_associativity_of_join +% SZS output end CNFRefutation for LAT007-1.p +26331: solved LAT007-1.p in 28.241764 using nrkbo +26331: status Unsatisfiable for LAT007-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +26339: Facts: +26339: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +26339: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +26339: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +26339: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +26339: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +26339: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +26339: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +26339: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +26339: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +26339: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +26339: Goal: +NO CLASH, using fixed ground order +26340: Facts: +26340: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +26340: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +26340: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +26340: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +26340: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +26340: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +26340: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +26340: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +26340: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +26340: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +26340: Goal: +26338: Facts: +26340: Id : 1, {_}: + join (complement (join (meet a (complement b)) (complement a))) + (join (meet a (complement b)) + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (complement (meet (join a (complement b)) (join a b)))))) + =>= + n1 + [] by prove_e1 +26340: Order: +26340: lpo +26340: Leaf order: +26340: n0 1 0 0 +26340: n1 2 0 1 3 +26340: b 6 0 6 1,2,1,1,1,2 +26340: a 9 0 9 1,1,1,1,2 +26340: complement 18 1 9 0,1,2 +26340: meet 15 2 6 0,1,1,1,2 +26340: join 20 2 8 0,2 +26339: Id : 1, {_}: + join (complement (join (meet a (complement b)) (complement a))) + (join (meet a (complement b)) + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (complement (meet (join a (complement b)) (join a b)))))) + =>= + n1 + [] by prove_e1 +26339: Order: +26339: kbo +26339: Leaf order: +26339: n0 1 0 0 +26339: n1 2 0 1 3 +26339: b 6 0 6 1,2,1,1,1,2 +26339: a 9 0 9 1,1,1,1,2 +26339: complement 18 1 9 0,1,2 +26339: meet 15 2 6 0,1,1,1,2 +26339: join 20 2 8 0,2 +26338: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +26338: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +26338: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +26338: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +26338: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +26338: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +26338: Id : 8, {_}: + join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +26338: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +26338: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +26338: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +26338: Goal: +26338: Id : 1, {_}: + join (complement (join (meet a (complement b)) (complement a))) + (join (meet a (complement b)) + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (complement (meet (join a (complement b)) (join a b)))))) + =>= + n1 + [] by prove_e1 +26338: Order: +26338: nrkbo +26338: Leaf order: +26338: n0 1 0 0 +26338: n1 2 0 1 3 +26338: b 6 0 6 1,2,1,1,1,2 +26338: a 9 0 9 1,1,1,1,2 +26338: complement 18 1 9 0,1,2 +26338: meet 15 2 6 0,1,1,1,2 +26338: join 20 2 8 0,2 +% SZS status Timeout for LAT016-1.p +NO CLASH, using fixed ground order +26368: Facts: +26368: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26368: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26368: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +26368: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +26368: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +26368: Id : 7, {_}: + join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +26368: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +26368: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +26368: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28 +26368: Id : 11, {_}: + meet2 ?30 ?31 =?= meet2 ?31 ?30 + [31, 30] by commutativity_of_meet2 ?30 ?31 +26368: Id : 12, {_}: + meet2 (meet2 ?33 ?34) ?35 =?= meet2 ?33 (meet2 ?34 ?35) + [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35 +26368: Id : 13, {_}: + join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38) + =>= + meet2 ?37 (join ?38 ?39) + [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39 +26368: Id : 14, {_}: + meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42) + =>= + join ?41 (meet2 ?42 ?43) + [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43 +26368: Goal: +26368: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal +26368: Order: +26368: nrkbo +26368: Leaf order: +26368: a 2 0 2 1,2 +26368: b 2 0 2 2,2 +26368: meet 14 2 1 0,2 +26368: meet2 14 2 1 0,3 +26368: join 19 2 0 +NO CLASH, using fixed ground order +26369: Facts: +26369: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26369: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26369: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +26369: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +26369: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +26369: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +26369: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +26369: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +26369: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28 +26369: Id : 11, {_}: + meet2 ?30 ?31 =?= meet2 ?31 ?30 + [31, 30] by commutativity_of_meet2 ?30 ?31 +26369: Id : 12, {_}: + meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35) + [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35 +26369: Id : 13, {_}: + join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38) + =>= + meet2 ?37 (join ?38 ?39) + [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39 +26369: Id : 14, {_}: + meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42) + =>= + join ?41 (meet2 ?42 ?43) + [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43 +26369: Goal: +26369: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal +26369: Order: +26369: kbo +26369: Leaf order: +26369: a 2 0 2 1,2 +26369: b 2 0 2 2,2 +26369: meet 14 2 1 0,2 +26369: meet2 14 2 1 0,3 +26369: join 19 2 0 +NO CLASH, using fixed ground order +26370: Facts: +26370: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26370: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26370: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +26370: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +26370: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +26370: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +26370: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +26370: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +26370: Id : 10, {_}: meet2 ?28 ?28 =>= ?28 [28] by idempotence_of_meet2 ?28 +26370: Id : 11, {_}: + meet2 ?30 ?31 =?= meet2 ?31 ?30 + [31, 30] by commutativity_of_meet2 ?30 ?31 +26370: Id : 12, {_}: + meet2 (meet2 ?33 ?34) ?35 =>= meet2 ?33 (meet2 ?34 ?35) + [35, 34, 33] by associativity_of_meet2 ?33 ?34 ?35 +26370: Id : 13, {_}: + join (meet2 ?37 (join ?38 ?39)) (meet2 ?37 ?38) + =>= + meet2 ?37 (join ?38 ?39) + [39, 38, 37] by quasi_lattice1_2 ?37 ?38 ?39 +26370: Id : 14, {_}: + meet2 (join ?41 (meet2 ?42 ?43)) (join ?41 ?42) + =>= + join ?41 (meet2 ?42 ?43) + [43, 42, 41] by quasi_lattice2_2 ?41 ?42 ?43 +26370: Goal: +26370: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal +26370: Order: +26370: lpo +26370: Leaf order: +26370: a 2 0 2 1,2 +26370: b 2 0 2 2,2 +26370: meet 14 2 1 0,2 +26370: meet2 14 2 1 0,3 +26370: join 19 2 0 +% SZS status Timeout for LAT024-1.p +NO CLASH, using fixed ground order +26386: Facts: +26386: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26386: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26386: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26386: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26386: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26386: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26386: Id : 8, {_}: + join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18 + [20, 19, 18] by tnl_1 ?18 ?19 ?20 +26386: Id : 9, {_}: + meet ?22 (join ?23 (join ?22 ?24)) =>= ?22 + [24, 23, 22] by tnl_2 ?22 ?23 ?24 +26386: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26 +26386: Id : 11, {_}: + meet2 ?28 (join ?28 ?29) =>= ?28 + [29, 28] by absorption1_2 ?28 ?29 +26386: Id : 12, {_}: + join ?31 (meet2 ?31 ?32) =>= ?31 + [32, 31] by absorption2_2 ?31 ?32 +26386: Id : 13, {_}: + meet2 ?34 ?35 =?= meet2 ?35 ?34 + [35, 34] by commutativity_of_meet2 ?34 ?35 +26386: Id : 14, {_}: + join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37 + [39, 38, 37] by tnl_1_2 ?37 ?38 ?39 +26386: Id : 15, {_}: + meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41 + [43, 42, 41] by tnl_2_2 ?41 ?42 ?43 +26386: Goal: +26386: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal +26386: Order: +26386: nrkbo +26386: Leaf order: +26386: a 2 0 2 1,2 +26386: b 2 0 2 2,2 +26386: meet 9 2 1 0,2 +26386: meet2 9 2 1 0,3 +26386: join 13 2 0 +NO CLASH, using fixed ground order +26387: Facts: +26387: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26387: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26387: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26387: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26387: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26387: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26387: Id : 8, {_}: + join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18 + [20, 19, 18] by tnl_1 ?18 ?19 ?20 +26387: Id : 9, {_}: + meet ?22 (join ?23 (join ?22 ?24)) =>= ?22 + [24, 23, 22] by tnl_2 ?22 ?23 ?24 +26387: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26 +26387: Id : 11, {_}: + meet2 ?28 (join ?28 ?29) =>= ?28 + [29, 28] by absorption1_2 ?28 ?29 +26387: Id : 12, {_}: + join ?31 (meet2 ?31 ?32) =>= ?31 + [32, 31] by absorption2_2 ?31 ?32 +26387: Id : 13, {_}: + meet2 ?34 ?35 =?= meet2 ?35 ?34 + [35, 34] by commutativity_of_meet2 ?34 ?35 +26387: Id : 14, {_}: + join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37 + [39, 38, 37] by tnl_1_2 ?37 ?38 ?39 +NO CLASH, using fixed ground order +26388: Facts: +26388: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26388: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26388: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26388: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26388: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26388: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26388: Id : 8, {_}: + join ?18 (meet ?19 (meet ?18 ?20)) =>= ?18 + [20, 19, 18] by tnl_1 ?18 ?19 ?20 +26388: Id : 9, {_}: + meet ?22 (join ?23 (join ?22 ?24)) =>= ?22 + [24, 23, 22] by tnl_2 ?22 ?23 ?24 +26388: Id : 10, {_}: meet2 ?26 ?26 =>= ?26 [26] by idempotence_of_meet2 ?26 +26388: Id : 11, {_}: + meet2 ?28 (join ?28 ?29) =>= ?28 + [29, 28] by absorption1_2 ?28 ?29 +26388: Id : 12, {_}: + join ?31 (meet2 ?31 ?32) =>= ?31 + [32, 31] by absorption2_2 ?31 ?32 +26388: Id : 13, {_}: + meet2 ?34 ?35 =?= meet2 ?35 ?34 + [35, 34] by commutativity_of_meet2 ?34 ?35 +26388: Id : 14, {_}: + join ?37 (meet2 ?38 (meet2 ?37 ?39)) =>= ?37 + [39, 38, 37] by tnl_1_2 ?37 ?38 ?39 +26388: Id : 15, {_}: + meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41 + [43, 42, 41] by tnl_2_2 ?41 ?42 ?43 +26388: Goal: +26388: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal +26388: Order: +26388: lpo +26388: Leaf order: +26388: a 2 0 2 1,2 +26388: b 2 0 2 2,2 +26388: meet 9 2 1 0,2 +26388: meet2 9 2 1 0,3 +26388: join 13 2 0 +26387: Id : 15, {_}: + meet2 ?41 (join ?42 (join ?41 ?43)) =>= ?41 + [43, 42, 41] by tnl_2_2 ?41 ?42 ?43 +26387: Goal: +26387: Id : 1, {_}: meet a b =<= meet2 a b [] by prove_meets_equal +26387: Order: +26387: kbo +26387: Leaf order: +26387: a 2 0 2 1,2 +26387: b 2 0 2 2,2 +26387: meet 9 2 1 0,2 +26387: meet2 9 2 1 0,3 +26387: join 13 2 0 +% SZS status Timeout for LAT025-1.p +CLASH, statistics insufficient +26417: Facts: +26417: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26417: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26417: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26417: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26417: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26417: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26417: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26417: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26417: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26417: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26417: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26417: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26417: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26417: Id : 15, {_}: + join ?38 (meet ?39 (join ?38 ?40)) + =>= + meet (join ?38 ?39) (join ?38 ?40) + [40, 39, 38] by modular_law ?38 ?39 ?40 +26417: Goal: +26417: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +26417: Order: +26417: nrkbo +26417: Leaf order: +26417: n1 1 0 0 +26417: n0 1 0 0 +26417: b 2 0 2 1,2,2 +26417: c 2 0 2 2,2,2 +26417: a 3 0 3 1,2 +26417: complement 10 1 0 +26417: meet 17 2 3 0,2 +26417: join 18 2 2 0,2,2 +CLASH, statistics insufficient +26418: Facts: +26418: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26418: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26418: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26418: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26418: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26418: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26418: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26418: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26418: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26418: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26418: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26418: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26418: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26418: Id : 15, {_}: + join ?38 (meet ?39 (join ?38 ?40)) + =>= + meet (join ?38 ?39) (join ?38 ?40) + [40, 39, 38] by modular_law ?38 ?39 ?40 +26418: Goal: +26418: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +26418: Order: +26418: kbo +26418: Leaf order: +26418: n1 1 0 0 +26418: n0 1 0 0 +26418: b 2 0 2 1,2,2 +26418: c 2 0 2 2,2,2 +26418: a 3 0 3 1,2 +26418: complement 10 1 0 +26418: meet 17 2 3 0,2 +26418: join 18 2 2 0,2,2 +CLASH, statistics insufficient +26419: Facts: +26419: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26419: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26419: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26419: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26419: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26419: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26419: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26419: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26419: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26419: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26419: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26419: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26419: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26419: Id : 15, {_}: + join ?38 (meet ?39 (join ?38 ?40)) + =>= + meet (join ?38 ?39) (join ?38 ?40) + [40, 39, 38] by modular_law ?38 ?39 ?40 +26419: Goal: +26419: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +26419: Order: +26419: lpo +26419: Leaf order: +26419: n1 1 0 0 +26419: n0 1 0 0 +26419: b 2 0 2 1,2,2 +26419: c 2 0 2 2,2,2 +26419: a 3 0 3 1,2 +26419: complement 10 1 0 +26419: meet 17 2 3 0,2 +26419: join 18 2 2 0,2,2 +% SZS status Timeout for LAT046-1.p +NO CLASH, using fixed ground order +26436: Facts: +26436: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26436: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26436: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26436: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26436: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26436: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26436: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26436: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26436: Goal: +26436: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modularity +26436: Order: +26436: nrkbo +26436: Leaf order: +26436: b 2 0 2 1,2,2 +26436: c 2 0 2 2,2,2,2 +26436: a 4 0 4 1,2 +26436: meet 11 2 2 0,2,2 +26436: join 13 2 4 0,2 +NO CLASH, using fixed ground order +26437: Facts: +26437: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26437: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26437: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26437: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26437: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26437: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26437: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26437: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26437: Goal: +26437: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modularity +26437: Order: +26437: kbo +26437: Leaf order: +26437: b 2 0 2 1,2,2 +26437: c 2 0 2 2,2,2,2 +26437: a 4 0 4 1,2 +26437: meet 11 2 2 0,2,2 +26437: join 13 2 4 0,2 +NO CLASH, using fixed ground order +26438: Facts: +26438: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26438: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26438: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26438: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26438: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26438: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26438: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26438: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26438: Goal: +26438: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modularity +26438: Order: +26438: lpo +26438: Leaf order: +26438: b 2 0 2 1,2,2 +26438: c 2 0 2 2,2,2,2 +26438: a 4 0 4 1,2 +26438: meet 11 2 2 0,2,2 +26438: join 13 2 4 0,2 +% SZS status Timeout for LAT047-1.p +NO CLASH, using fixed ground order +26479: Facts: +26479: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26479: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26479: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26479: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26479: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26479: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26479: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26479: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26479: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26479: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26479: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26479: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26479: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26479: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by weak_orthomodular_law ?38 ?39 +26479: Goal: +26479: Id : 1, {_}: + join a (meet (complement a) (join a b)) =>= join a b + [] by prove_orthomodular_law +26479: Order: +26479: nrkbo +26479: Leaf order: +26479: n0 1 0 0 +26479: n1 2 0 0 +26479: b 2 0 2 2,2,2,2 +26479: a 4 0 4 1,2 +26479: complement 13 1 1 0,1,2,2 +26479: meet 15 2 1 0,2,2 +26479: join 18 2 3 0,2 +NO CLASH, using fixed ground order +26480: Facts: +26480: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26480: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26480: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26480: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26480: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26480: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26480: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26480: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26480: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26480: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26480: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26480: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26480: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +NO CLASH, using fixed ground order +26481: Facts: +26481: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26481: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26481: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26481: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26481: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26481: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26481: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26481: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26481: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26481: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26481: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26481: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26481: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26481: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by weak_orthomodular_law ?38 ?39 +26481: Goal: +26481: Id : 1, {_}: + join a (meet (complement a) (join a b)) =>= join a b + [] by prove_orthomodular_law +26481: Order: +26481: lpo +26481: Leaf order: +26481: n0 1 0 0 +26481: n1 2 0 0 +26481: b 2 0 2 2,2,2,2 +26481: a 4 0 4 1,2 +26481: complement 13 1 1 0,1,2,2 +26481: meet 15 2 1 0,2,2 +26481: join 18 2 3 0,2 +26480: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by weak_orthomodular_law ?38 ?39 +26480: Goal: +26480: Id : 1, {_}: + join a (meet (complement a) (join a b)) =>= join a b + [] by prove_orthomodular_law +26480: Order: +26480: kbo +26480: Leaf order: +26480: n0 1 0 0 +26480: n1 2 0 0 +26480: b 2 0 2 2,2,2,2 +26480: a 4 0 4 1,2 +26480: complement 13 1 1 0,1,2,2 +26480: meet 15 2 1 0,2,2 +26480: join 18 2 3 0,2 +% SZS status Timeout for LAT048-1.p +NO CLASH, using fixed ground order +26500: Facts: +26500: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26500: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26500: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26500: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26500: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26500: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26500: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26500: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26500: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26500: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26500: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26500: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26500: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26500: Goal: +26500: Id : 1, {_}: + join (meet (complement a) (join a b)) + (join (complement b) (meet a b)) + =>= + n1 + [] by prove_weak_orthomodular_law +26500: Order: +26500: nrkbo +26500: Leaf order: +26500: n0 1 0 0 +26500: n1 2 0 1 3 +26500: a 3 0 3 1,1,1,2 +26500: b 3 0 3 2,2,1,2 +26500: complement 12 1 2 0,1,1,2 +26500: meet 14 2 2 0,1,2 +26500: join 15 2 3 0,2 +NO CLASH, using fixed ground order +26501: Facts: +26501: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26501: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26501: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26501: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26501: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26501: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26501: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26501: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26501: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26501: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26501: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26501: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26501: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26501: Goal: +26501: Id : 1, {_}: + join (meet (complement a) (join a b)) + (join (complement b) (meet a b)) + =>= + n1 + [] by prove_weak_orthomodular_law +26501: Order: +26501: kbo +26501: Leaf order: +26501: n0 1 0 0 +26501: n1 2 0 1 3 +26501: a 3 0 3 1,1,1,2 +26501: b 3 0 3 2,2,1,2 +26501: complement 12 1 2 0,1,1,2 +26501: meet 14 2 2 0,1,2 +26501: join 15 2 3 0,2 +NO CLASH, using fixed ground order +26502: Facts: +26502: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26502: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26502: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26502: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26502: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26502: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26502: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26502: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26502: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26502: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26502: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26502: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26502: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26502: Goal: +26502: Id : 1, {_}: + join (meet (complement a) (join a b)) + (join (complement b) (meet a b)) + =>= + n1 + [] by prove_weak_orthomodular_law +26502: Order: +26502: lpo +26502: Leaf order: +26502: n0 1 0 0 +26502: n1 2 0 1 3 +26502: a 3 0 3 1,1,1,2 +26502: b 3 0 3 2,2,1,2 +26502: complement 12 1 2 0,1,1,2 +26502: meet 14 2 2 0,1,2 +26502: join 15 2 3 0,2 +% SZS status Timeout for LAT049-1.p +CLASH, statistics insufficient +26530: Facts: +26530: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26530: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26530: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26530: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26530: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26530: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26530: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26530: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26530: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26530: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26530: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26530: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26530: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26530: Id : 15, {_}: + join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39 + [39, 38] by orthomodular_law ?38 ?39 +26530: Goal: +26530: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modular_law +26530: Order: +26530: nrkbo +26530: Leaf order: +26530: n1 1 0 0 +26530: n0 1 0 0 +26530: b 2 0 2 1,2,2 +26530: c 2 0 2 2,2,2,2 +26530: a 4 0 4 1,2 +26530: complement 11 1 0 +26530: meet 15 2 2 0,2,2 +26530: join 19 2 4 0,2 +CLASH, statistics insufficient +26531: Facts: +26531: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26531: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26531: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26531: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26531: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26531: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26531: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26531: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26531: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26531: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26531: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26531: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26531: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26531: Id : 15, {_}: + join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39 + [39, 38] by orthomodular_law ?38 ?39 +26531: Goal: +26531: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modular_law +26531: Order: +26531: kbo +26531: Leaf order: +26531: n1 1 0 0 +26531: n0 1 0 0 +26531: b 2 0 2 1,2,2 +26531: c 2 0 2 2,2,2,2 +26531: a 4 0 4 1,2 +26531: complement 11 1 0 +26531: meet 15 2 2 0,2,2 +26531: join 19 2 4 0,2 +CLASH, statistics insufficient +26532: Facts: +26532: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26532: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26532: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26532: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26532: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26532: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26532: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26532: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26532: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26532: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26532: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26532: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26532: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26532: Id : 15, {_}: + join ?38 (meet (complement ?38) (join ?38 ?39)) =>= join ?38 ?39 + [39, 38] by orthomodular_law ?38 ?39 +26532: Goal: +26532: Id : 1, {_}: + join a (meet b (join a c)) =>= meet (join a b) (join a c) + [] by prove_modular_law +26532: Order: +26532: lpo +26532: Leaf order: +26532: n1 1 0 0 +26532: n0 1 0 0 +26532: b 2 0 2 1,2,2 +26532: c 2 0 2 2,2,2,2 +26532: a 4 0 4 1,2 +26532: complement 11 1 0 +26532: meet 15 2 2 0,2,2 +26532: join 19 2 4 0,2 +% SZS status Timeout for LAT050-1.p +CLASH, statistics insufficient +26548: Facts: +26548: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26548: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26548: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26548: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26548: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26548: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26548: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26548: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26548: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +26548: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +26548: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +26548: Goal: +26548: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +26548: Order: +26548: nrkbo +26548: Leaf order: +26548: n1 1 0 0 +26548: n0 1 0 0 +26548: a 2 0 2 1,1,2 +26548: b 2 0 2 2,1,2 +26548: complement 7 1 3 0,2 +26548: join 11 2 1 0,1,2 +26548: meet 11 2 1 0,3 +CLASH, statistics insufficient +26549: Facts: +26549: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26549: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26549: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26549: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26549: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26549: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26549: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26549: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26549: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +26549: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +26549: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +26549: Goal: +26549: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +26549: Order: +26549: kbo +26549: Leaf order: +26549: n1 1 0 0 +26549: n0 1 0 0 +26549: a 2 0 2 1,1,2 +26549: b 2 0 2 2,1,2 +26549: complement 7 1 3 0,2 +26549: join 11 2 1 0,1,2 +26549: meet 11 2 1 0,3 +CLASH, statistics insufficient +26550: Facts: +26550: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26550: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26550: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26550: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26550: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26550: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26550: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26550: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26550: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +26550: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +26550: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +26550: Goal: +26550: Id : 1, {_}: + complement (join a b) =>= meet (complement a) (complement b) + [] by prove_compatibility_law +26550: Order: +26550: lpo +26550: Leaf order: +26550: n1 1 0 0 +26550: n0 1 0 0 +26550: a 2 0 2 1,1,2 +26550: b 2 0 2 2,1,2 +26550: complement 7 1 3 0,2 +26550: join 11 2 1 0,1,2 +26550: meet 11 2 1 0,3 +% SZS status Timeout for LAT051-1.p +CLASH, statistics insufficient +26611: Facts: +26611: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26611: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26611: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26611: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26611: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26611: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26611: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26611: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26611: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +26611: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +26611: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +26611: Id : 13, {_}: + join ?32 (meet ?33 (join ?32 ?34)) + =>= + meet (join ?32 ?33) (join ?32 ?34) + [34, 33, 32] by modular_law ?32 ?33 ?34 +26611: Goal: +26611: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +26611: Order: +26611: kbo +26611: Leaf order: +26611: n1 1 0 0 +26611: n0 1 0 0 +26611: a 2 0 2 1,1,2 +26611: b 2 0 2 2,1,2 +26611: complement 7 1 3 0,2 +26611: meet 13 2 1 0,3 +26611: join 15 2 1 0,1,2 +CLASH, statistics insufficient +26612: Facts: +26612: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26612: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26612: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26612: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26612: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26612: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26612: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26612: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26612: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +26612: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +26612: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +26612: Id : 13, {_}: + join ?32 (meet ?33 (join ?32 ?34)) + =>= + meet (join ?32 ?33) (join ?32 ?34) + [34, 33, 32] by modular_law ?32 ?33 ?34 +26612: Goal: +26612: Id : 1, {_}: + complement (join a b) =>= meet (complement a) (complement b) + [] by prove_compatibility_law +26612: Order: +26612: lpo +26612: Leaf order: +26612: n1 1 0 0 +26612: n0 1 0 0 +26612: a 2 0 2 1,1,2 +26612: b 2 0 2 2,1,2 +26612: complement 7 1 3 0,2 +26612: meet 13 2 1 0,3 +26612: join 15 2 1 0,1,2 +CLASH, statistics insufficient +26610: Facts: +26610: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26610: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26610: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26610: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26610: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26610: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26610: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26610: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26610: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by invertability1 ?26 +26610: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by invertability2 ?28 +26610: Id : 12, {_}: complement (complement ?30) =>= ?30 [30] by invertability3 ?30 +26610: Id : 13, {_}: + join ?32 (meet ?33 (join ?32 ?34)) + =>= + meet (join ?32 ?33) (join ?32 ?34) + [34, 33, 32] by modular_law ?32 ?33 ?34 +26610: Goal: +26610: Id : 1, {_}: + complement (join a b) =<= meet (complement a) (complement b) + [] by prove_compatibility_law +26610: Order: +26610: nrkbo +26610: Leaf order: +26610: n1 1 0 0 +26610: n0 1 0 0 +26610: a 2 0 2 1,1,2 +26610: b 2 0 2 2,1,2 +26610: complement 7 1 3 0,2 +26610: meet 13 2 1 0,3 +26610: join 15 2 1 0,1,2 +% SZS status Timeout for LAT052-1.p +CLASH, statistics insufficient +26628: Facts: +26628: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26628: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26628: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26628: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26628: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26628: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26628: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26628: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26628: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26628: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26628: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26628: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26628: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26628: Goal: +26628: Id : 1, {_}: + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a (meet (complement b) (complement a)))))) + =<= + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a + (meet (complement b) + (join (complement a) (meet (complement b) a))))))) + [] by prove_this +26628: Order: +26628: nrkbo +26628: Leaf order: +26628: n1 1 0 0 +26628: n0 1 0 0 +26628: b 7 0 7 1,1,2,2 +26628: a 9 0 9 1,2 +26628: complement 21 1 11 0,1,2,2 +26628: join 19 2 7 0,2 +26628: meet 19 2 7 0,2,2 +CLASH, statistics insufficient +26629: Facts: +26629: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26629: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26629: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26629: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26629: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26629: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26629: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26629: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26629: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26629: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26629: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26629: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26629: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26629: Goal: +26629: Id : 1, {_}: + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a (meet (complement b) (complement a)))))) + =<= + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a + (meet (complement b) + (join (complement a) (meet (complement b) a))))))) + [] by prove_this +26629: Order: +26629: kbo +26629: Leaf order: +26629: n1 1 0 0 +26629: n0 1 0 0 +26629: b 7 0 7 1,1,2,2 +26629: a 9 0 9 1,2 +26629: complement 21 1 11 0,1,2,2 +26629: join 19 2 7 0,2 +26629: meet 19 2 7 0,2,2 +CLASH, statistics insufficient +26630: Facts: +26630: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26630: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26630: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26630: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26630: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26630: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26630: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26630: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26630: Id : 10, {_}: + complement (join ?26 ?27) =>= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +26630: Id : 11, {_}: + complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +26630: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +26630: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +26630: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +26630: Goal: +26630: Id : 1, {_}: + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a (meet (complement b) (complement a)))))) + =<= + join a + (meet (complement b) + (join (complement a) + (meet (complement b) + (join a + (meet (complement b) + (join (complement a) (meet (complement b) a))))))) + [] by prove_this +26630: Order: +26630: lpo +26630: Leaf order: +26630: n1 1 0 0 +26630: n0 1 0 0 +26630: b 7 0 7 1,1,2,2 +26630: a 9 0 9 1,2 +26630: complement 21 1 11 0,1,2,2 +26630: join 19 2 7 0,2 +26630: meet 19 2 7 0,2,2 +% SZS status Timeout for LAT054-1.p +CLASH, statistics insufficient +26659: Facts: +26659: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26659: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26659: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26659: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26659: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26659: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26659: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26659: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26659: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +26659: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +26659: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +26659: Goal: +26659: Id : 1, {_}: + meet (join a (complement b)) + (join (join (meet a b) (meet (complement a) b)) + (meet (complement a) (complement b))) + =>= + join (meet a b) (meet (complement a) (complement b)) + [] by prove_e51 +26659: Order: +26659: nrkbo +26659: Leaf order: +26659: n1 1 0 0 +26659: n0 1 0 0 +26659: a 6 0 6 1,1,2 +26659: b 6 0 6 1,2,1,2 +26659: complement 11 1 6 0,2,1,2 +26659: join 15 2 4 0,1,2 +26659: meet 17 2 6 0,2 +CLASH, statistics insufficient +26660: Facts: +26660: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26660: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26660: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26660: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26660: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26660: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26660: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26660: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26660: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +26660: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +26660: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +26660: Goal: +26660: Id : 1, {_}: + meet (join a (complement b)) + (join (join (meet a b) (meet (complement a) b)) + (meet (complement a) (complement b))) + =>= + join (meet a b) (meet (complement a) (complement b)) + [] by prove_e51 +26660: Order: +26660: kbo +26660: Leaf order: +26660: n1 1 0 0 +26660: n0 1 0 0 +26660: a 6 0 6 1,1,2 +26660: b 6 0 6 1,2,1,2 +26660: complement 11 1 6 0,2,1,2 +26660: join 15 2 4 0,1,2 +26660: meet 17 2 6 0,2 +CLASH, statistics insufficient +26661: Facts: +26661: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26661: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26661: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26661: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26661: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26661: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26661: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26661: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26661: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +26661: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +26661: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +26661: Goal: +26661: Id : 1, {_}: + meet (join a (complement b)) + (join (join (meet a b) (meet (complement a) b)) + (meet (complement a) (complement b))) + =>= + join (meet a b) (meet (complement a) (complement b)) + [] by prove_e51 +26661: Order: +26661: lpo +26661: Leaf order: +26661: n1 1 0 0 +26661: n0 1 0 0 +26661: a 6 0 6 1,1,2 +26661: b 6 0 6 1,2,1,2 +26661: complement 11 1 6 0,2,1,2 +26661: join 15 2 4 0,1,2 +26661: meet 17 2 6 0,2 +% SZS status Timeout for LAT062-1.p +CLASH, statistics insufficient +26678: Facts: +26678: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26678: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26678: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26678: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26678: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26678: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26678: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26678: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26678: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +26678: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +26678: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +26678: Goal: +26678: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_e62 +26678: Order: +26678: nrkbo +26678: Leaf order: +26678: n1 1 0 0 +26678: n0 1 0 0 +26678: b 3 0 3 1,2,2 +26678: a 7 0 7 1,2 +26678: complement 7 1 2 0,1,2,2,2,2 +26678: join 14 2 3 0,2,2 +26678: meet 16 2 5 0,2 +CLASH, statistics insufficient +26679: Facts: +26679: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26679: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26679: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26679: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26679: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26679: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26679: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26679: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26679: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +26679: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +26679: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +26679: Goal: +26679: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_e62 +26679: Order: +26679: kbo +26679: Leaf order: +26679: n1 1 0 0 +26679: n0 1 0 0 +26679: b 3 0 3 1,2,2 +26679: a 7 0 7 1,2 +26679: complement 7 1 2 0,1,2,2,2,2 +26679: join 14 2 3 0,2,2 +26679: meet 16 2 5 0,2 +CLASH, statistics insufficient +26680: Facts: +26680: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26680: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26680: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26680: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26680: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26680: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26680: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26680: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26680: Id : 10, {_}: join (complement ?26) ?26 =>= n1 [26] by top ?26 +26680: Id : 11, {_}: meet (complement ?28) ?28 =>= n0 [28] by bottom ?28 +26680: Id : 12, {_}: + meet ?30 ?31 =<= complement (join (complement ?30) (complement ?31)) + [31, 30] by compatibility ?30 ?31 +26680: Goal: +26680: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_e62 +26680: Order: +26680: lpo +26680: Leaf order: +26680: n1 1 0 0 +26680: n0 1 0 0 +26680: b 3 0 3 1,2,2 +26680: a 7 0 7 1,2 +26680: complement 7 1 2 0,1,2,2,2,2 +26680: join 14 2 3 0,2,2 +26680: meet 16 2 5 0,2 +% SZS status Timeout for LAT063-1.p +NO CLASH, using fixed ground order +26708: Facts: +26708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26708: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26708: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26708: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26708: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26708: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28)))) + [28, 27, 26] by equation_H2 ?26 ?27 ?28 +26708: Goal: +26708: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +26708: Order: +26708: nrkbo +26708: Leaf order: +26708: c 3 0 3 2,2,2,2 +26708: b 4 0 4 1,2,2 +26708: a 5 0 5 1,2 +26708: join 17 2 4 0,2,2 +26708: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +26709: Facts: +26709: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26709: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26709: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26709: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26709: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26709: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26709: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26709: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26709: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28)))) + [28, 27, 26] by equation_H2 ?26 ?27 ?28 +26709: Goal: +26709: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +26709: Order: +26709: kbo +26709: Leaf order: +26709: c 3 0 3 2,2,2,2 +26709: b 4 0 4 1,2,2 +26709: a 5 0 5 1,2 +26709: join 17 2 4 0,2,2 +26709: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +26710: Facts: +26710: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26710: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26710: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26710: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26710: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26710: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26710: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26710: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26710: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join (meet ?26 (join ?27 ?28)) (meet ?27 ?28)))) + [28, 27, 26] by equation_H2 ?26 ?27 ?28 +26710: Goal: +26710: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +26710: Order: +26710: lpo +26710: Leaf order: +26710: c 3 0 3 2,2,2,2 +26710: b 4 0 4 1,2,2 +26710: a 5 0 5 1,2 +26710: join 17 2 4 0,2,2 +26710: meet 21 2 6 0,2 +% SZS status Timeout for LAT098-1.p +NO CLASH, using fixed ground order +26734: Facts: +26734: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26734: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26734: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26734: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26734: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26734: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26734: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26734: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26734: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +26734: Goal: +26734: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +26734: Order: +26734: nrkbo +26734: Leaf order: +26734: c 2 0 2 1,2,2,2,2 +26734: b 3 0 3 1,2,2 +26734: d 3 0 3 2,2,2,2,2 +26734: a 4 0 4 1,2 +26734: join 18 2 5 0,2,2 +26734: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26735: Facts: +26735: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26735: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26735: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26735: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26735: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26735: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26735: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26735: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26735: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +26735: Goal: +26735: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +26735: Order: +26735: kbo +26735: Leaf order: +26735: c 2 0 2 1,2,2,2,2 +26735: b 3 0 3 1,2,2 +26735: d 3 0 3 2,2,2,2,2 +26735: a 4 0 4 1,2 +26735: join 18 2 5 0,2,2 +26735: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26736: Facts: +26736: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26736: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26736: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26736: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26736: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26736: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26736: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26736: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26736: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +26736: Goal: +26736: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +26736: Order: +26736: lpo +26736: Leaf order: +26736: c 2 0 2 1,2,2,2,2 +26736: b 3 0 3 1,2,2 +26736: d 3 0 3 2,2,2,2,2 +26736: a 4 0 4 1,2 +26736: join 18 2 5 0,2,2 +26736: meet 20 2 5 0,2 +% SZS status Timeout for LAT100-1.p +NO CLASH, using fixed ground order +26775: Facts: +26775: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26775: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26775: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26775: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26775: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26775: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26775: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26775: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26775: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +26775: Goal: +26775: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +26775: Order: +26775: nrkbo +26775: Leaf order: +26775: b 3 0 3 1,2,2 +26775: c 3 0 3 2,2,2,2 +26775: a 4 0 4 1,2 +26775: join 16 2 3 0,2,2 +26775: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26776: Facts: +26776: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26776: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26776: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26776: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26776: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26776: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26776: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26776: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26776: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +26776: Goal: +26776: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +26776: Order: +26776: kbo +26776: Leaf order: +26776: b 3 0 3 1,2,2 +26776: c 3 0 3 2,2,2,2 +26776: a 4 0 4 1,2 +26776: join 16 2 3 0,2,2 +26776: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26777: Facts: +26777: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26777: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26777: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26777: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26777: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26777: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26777: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26777: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26777: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join (meet ?26 (join ?27 (meet ?26 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H6 ?26 ?27 ?28 +26777: Goal: +26777: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +26777: Order: +26777: lpo +26777: Leaf order: +26777: b 3 0 3 1,2,2 +26777: c 3 0 3 2,2,2,2 +26777: a 4 0 4 1,2 +26777: join 16 2 3 0,2,2 +26777: meet 20 2 5 0,2 +% SZS status Timeout for LAT101-1.p +NO CLASH, using fixed ground order +26819: Facts: +26819: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26819: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26819: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26819: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26819: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26819: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26819: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26819: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26819: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +26819: Goal: +26819: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +26819: Order: +26819: nrkbo +26819: Leaf order: +26819: c 2 0 2 1,2,2,2,2 +26819: b 3 0 3 1,2,2 +26819: d 3 0 3 2,2,2,2,2 +26819: a 4 0 4 1,2 +26819: join 18 2 5 0,2,2 +26819: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26820: Facts: +26820: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26820: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26820: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26820: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26820: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26820: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26820: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26820: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26820: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +26820: Goal: +26820: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +26820: Order: +26820: kbo +26820: Leaf order: +26820: c 2 0 2 1,2,2,2,2 +26820: b 3 0 3 1,2,2 +26820: d 3 0 3 2,2,2,2,2 +26820: a 4 0 4 1,2 +26820: join 18 2 5 0,2,2 +26820: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26821: Facts: +26821: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26821: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26821: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26821: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26821: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26821: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26821: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26821: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26821: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +26821: Goal: +26821: Id : 1, {_}: + meet a (join b (meet a (join c d))) + =<= + meet a (join b (meet (join a (meet b d)) (join c d))) + [] by prove_H4 +26821: Order: +26821: lpo +26821: Leaf order: +26821: c 2 0 2 1,2,2,2,2 +26821: b 3 0 3 1,2,2 +26821: d 3 0 3 2,2,2,2,2 +26821: a 4 0 4 1,2 +26821: join 18 2 5 0,2,2 +26821: meet 20 2 5 0,2 +% SZS status Timeout for LAT102-1.p +NO CLASH, using fixed ground order +26896: Facts: +26896: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26896: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26896: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26896: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26896: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26896: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26896: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26896: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26896: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28)))) + [28, 27, 26] by equation_H10 ?26 ?27 ?28 +26896: Goal: +26896: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +26896: Order: +26896: nrkbo +26896: Leaf order: +26896: b 3 0 3 1,2,2 +26896: c 3 0 3 2,2,2,2 +26896: a 6 0 6 1,2 +26896: join 16 2 4 0,2,2 +26896: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +26897: Facts: +26897: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26897: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26897: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26897: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26897: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26897: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26897: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26897: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26897: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28)))) + [28, 27, 26] by equation_H10 ?26 ?27 ?28 +26897: Goal: +26897: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +26897: Order: +26897: kbo +26897: Leaf order: +26897: b 3 0 3 1,2,2 +26897: c 3 0 3 2,2,2,2 +26897: a 6 0 6 1,2 +26897: join 16 2 4 0,2,2 +26897: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +26898: Facts: +26898: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26898: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26898: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26898: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26898: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26898: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26898: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26898: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26898: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =?= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?27 ?28)))) + [28, 27, 26] by equation_H10 ?26 ?27 ?28 +26898: Goal: +26898: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +26898: Order: +26898: lpo +26898: Leaf order: +26898: b 3 0 3 1,2,2 +26898: c 3 0 3 2,2,2,2 +26898: a 6 0 6 1,2 +26898: join 16 2 4 0,2,2 +26898: meet 20 2 6 0,2 +% SZS status Timeout for LAT103-1.p +NO CLASH, using fixed ground order +26925: Facts: +26925: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26925: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26925: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26925: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26925: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26925: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26925: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26925: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26925: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +26925: Goal: +26925: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +26925: Order: +26925: nrkbo +26925: Leaf order: +26925: c 3 0 3 2,2,2,2 +26925: b 4 0 4 1,2,2 +26925: a 5 0 5 1,2 +26925: join 17 2 4 0,2,2 +26925: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +26926: Facts: +26926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26926: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26926: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26926: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26926: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26926: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +26926: Goal: +26926: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +26926: Order: +26926: kbo +26926: Leaf order: +26926: c 3 0 3 2,2,2,2 +26926: b 4 0 4 1,2,2 +26926: a 5 0 5 1,2 +26926: join 17 2 4 0,2,2 +26926: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +26927: Facts: +26927: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26927: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26927: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26927: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26927: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26927: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26927: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26927: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26927: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +26927: Goal: +26927: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +26927: Order: +26927: lpo +26927: Leaf order: +26927: c 3 0 3 2,2,2,2 +26927: b 4 0 4 1,2,2 +26927: a 5 0 5 1,2 +26927: join 17 2 4 0,2,2 +26927: meet 21 2 6 0,2 +% SZS status Timeout for LAT104-1.p +NO CLASH, using fixed ground order +26956: Facts: +26956: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26956: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26956: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26956: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26956: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26956: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26956: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26956: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26956: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +26956: Goal: +26956: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +26956: Order: +26956: nrkbo +26956: Leaf order: +26956: b 3 0 3 1,2,2 +26956: c 3 0 3 2,2,2,2 +26956: a 4 0 4 1,2 +26956: join 16 2 3 0,2,2 +26956: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26957: Facts: +26957: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26957: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26957: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26957: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26957: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26957: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26957: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26957: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26957: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +26957: Goal: +26957: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +26957: Order: +26957: kbo +26957: Leaf order: +26957: b 3 0 3 1,2,2 +26957: c 3 0 3 2,2,2,2 +26957: a 4 0 4 1,2 +26957: join 16 2 3 0,2,2 +26957: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +26958: Facts: +26958: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +26958: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +26958: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +26958: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +26958: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +26958: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +26958: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +26958: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +26958: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +26958: Goal: +26958: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +26958: Order: +26958: lpo +26958: Leaf order: +26958: b 3 0 3 1,2,2 +26958: c 3 0 3 2,2,2,2 +26958: a 4 0 4 1,2 +26958: join 16 2 3 0,2,2 +26958: meet 20 2 5 0,2 +% SZS status Timeout for LAT105-1.p +NO CLASH, using fixed ground order +27035: Facts: +27035: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27035: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27035: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27035: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27035: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27035: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27035: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27035: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27035: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +27035: Goal: +27035: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +27035: Order: +27035: nrkbo +27035: Leaf order: +27035: c 3 0 3 2,2,2,2 +27035: b 4 0 4 1,2,2 +27035: a 5 0 5 1,2 +27035: join 17 2 4 0,2,2 +27035: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +27036: Facts: +27036: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27036: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27036: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27036: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27036: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27036: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27036: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27036: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27036: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +27036: Goal: +27036: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +27036: Order: +27036: kbo +27036: Leaf order: +27036: c 3 0 3 2,2,2,2 +27036: b 4 0 4 1,2,2 +27036: a 5 0 5 1,2 +27036: join 17 2 4 0,2,2 +27036: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +27037: Facts: +27037: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27037: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27037: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27037: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27037: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27037: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27037: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27037: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27037: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +27037: Goal: +27037: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +27037: Order: +27037: lpo +27037: Leaf order: +27037: c 3 0 3 2,2,2,2 +27037: b 4 0 4 1,2,2 +27037: a 5 0 5 1,2 +27037: join 17 2 4 0,2,2 +27037: meet 21 2 6 0,2 +% SZS status Timeout for LAT106-1.p +NO CLASH, using fixed ground order +27073: Facts: +27073: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27073: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27073: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27073: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27073: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27073: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27073: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27073: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27073: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +27073: Goal: +27073: Id : 1, {_}: + meet a (join (meet a b) (meet a c)) + =<= + meet a (join (meet b (join a (meet b c))) (meet c (join a b))) + [] by prove_H17 +27073: Order: +27073: nrkbo +27073: Leaf order: +27073: c 3 0 3 2,2,2,2 +27073: b 4 0 4 2,1,2,2 +27073: a 6 0 6 1,2 +27073: join 17 2 4 0,2,2 +27073: meet 22 2 7 0,2 +NO CLASH, using fixed ground order +27074: Facts: +27074: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27074: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27074: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27074: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27074: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27074: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27074: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27074: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27074: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +27074: Goal: +27074: Id : 1, {_}: + meet a (join (meet a b) (meet a c)) + =<= + meet a (join (meet b (join a (meet b c))) (meet c (join a b))) + [] by prove_H17 +27074: Order: +27074: kbo +27074: Leaf order: +27074: c 3 0 3 2,2,2,2 +27074: b 4 0 4 2,1,2,2 +27074: a 6 0 6 1,2 +27074: join 17 2 4 0,2,2 +27074: meet 22 2 7 0,2 +NO CLASH, using fixed ground order +27075: Facts: +27075: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27075: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27075: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27075: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27075: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27075: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27075: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27075: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27075: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +27075: Goal: +27075: Id : 1, {_}: + meet a (join (meet a b) (meet a c)) + =>= + meet a (join (meet b (join a (meet b c))) (meet c (join a b))) + [] by prove_H17 +27075: Order: +27075: lpo +27075: Leaf order: +27075: c 3 0 3 2,2,2,2 +27075: b 4 0 4 2,1,2,2 +27075: a 6 0 6 1,2 +27075: join 17 2 4 0,2,2 +27075: meet 22 2 7 0,2 +% SZS status Timeout for LAT107-1.p +NO CLASH, using fixed ground order +27091: Facts: +27091: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27091: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27091: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27091: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27091: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27091: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27091: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27091: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27091: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29 +27091: Goal: +27091: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +27091: Order: +27091: nrkbo +27091: Leaf order: +27091: d 2 0 2 2,2,2,2,2 +27091: b 3 0 3 1,2,2 +27091: c 3 0 3 1,2,2,2 +27091: a 4 0 4 1,2 +27091: join 17 2 5 0,2,2 +27091: meet 21 2 5 0,2 +NO CLASH, using fixed ground order +27092: Facts: +27092: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27092: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27092: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27092: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27092: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27092: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27092: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27092: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27092: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29 +27092: Goal: +27092: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +27092: Order: +27092: kbo +27092: Leaf order: +27092: d 2 0 2 2,2,2,2,2 +27092: b 3 0 3 1,2,2 +27092: c 3 0 3 1,2,2,2 +27092: a 4 0 4 1,2 +27092: join 17 2 5 0,2,2 +27092: meet 21 2 5 0,2 +NO CLASH, using fixed ground order +27093: Facts: +27093: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27093: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27093: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27093: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27093: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27093: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27093: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27093: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27093: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H31 ?26 ?27 ?28 ?29 +27093: Goal: +27093: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +27093: Order: +27093: lpo +27093: Leaf order: +27093: d 2 0 2 2,2,2,2,2 +27093: b 3 0 3 1,2,2 +27093: c 3 0 3 1,2,2,2 +27093: a 4 0 4 1,2 +27093: join 17 2 5 0,2,2 +27093: meet 21 2 5 0,2 +% SZS status Timeout for LAT108-1.p +NO CLASH, using fixed ground order +27126: Facts: +27126: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27126: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27126: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27126: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27126: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27126: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27126: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27126: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27126: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +27126: Goal: +27126: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27126: Order: +27126: nrkbo +27126: Leaf order: +27126: d 2 0 2 2,2,2,2,2 +27126: b 3 0 3 1,2,2 +27126: c 3 0 3 1,2,2,2 +27126: a 4 0 4 1,2 +27126: meet 19 2 5 0,2 +27126: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +27127: Facts: +27127: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27127: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27127: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27127: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27127: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27127: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27127: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27127: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27127: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +27127: Goal: +27127: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27127: Order: +27127: kbo +27127: Leaf order: +27127: d 2 0 2 2,2,2,2,2 +27127: b 3 0 3 1,2,2 +27127: c 3 0 3 1,2,2,2 +27127: a 4 0 4 1,2 +27127: meet 19 2 5 0,2 +27127: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +27128: Facts: +27128: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27128: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27128: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27128: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27128: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27128: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27128: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27128: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27128: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +27128: Goal: +27128: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27128: Order: +27128: lpo +27128: Leaf order: +27128: d 2 0 2 2,2,2,2,2 +27128: b 3 0 3 1,2,2 +27128: c 3 0 3 1,2,2,2 +27128: a 4 0 4 1,2 +27128: meet 19 2 5 0,2 +27128: join 19 2 5 0,2,2 +% SZS status Timeout for LAT109-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +27146: Facts: +NO CLASH, using fixed ground order +27146: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27146: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27146: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27146: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27146: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27146: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27146: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27146: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27146: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29 +27146: Goal: +27146: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27146: Order: +27146: lpo +27146: Leaf order: +27146: d 2 0 2 2,2,2,2,2 +27146: b 3 0 3 1,2,2 +27146: c 3 0 3 1,2,2,2 +27146: a 4 0 4 1,2 +27146: join 17 2 5 0,2,2 +27146: meet 21 2 5 0,2 +27144: Facts: +27144: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27144: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27144: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27144: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27144: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27144: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27144: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27144: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27144: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29 +27144: Goal: +27144: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27144: Order: +27144: nrkbo +27144: Leaf order: +27144: d 2 0 2 2,2,2,2,2 +27144: b 3 0 3 1,2,2 +27144: c 3 0 3 1,2,2,2 +27144: a 4 0 4 1,2 +27144: join 17 2 5 0,2,2 +27144: meet 21 2 5 0,2 +27145: Facts: +27145: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27145: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27145: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27145: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27145: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27145: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27145: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27145: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27145: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H45 ?26 ?27 ?28 ?29 +27145: Goal: +27145: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27145: Order: +27145: kbo +27145: Leaf order: +27145: d 2 0 2 2,2,2,2,2 +27145: b 3 0 3 1,2,2 +27145: c 3 0 3 1,2,2,2 +27145: a 4 0 4 1,2 +27145: join 17 2 5 0,2,2 +27145: meet 21 2 5 0,2 +% SZS status Timeout for LAT111-1.p +NO CLASH, using fixed ground order +27177: Facts: +27177: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27177: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27177: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27177: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27177: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27177: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27177: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27177: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27177: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29 +27177: Goal: +27177: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +27177: Order: +27177: nrkbo +27177: Leaf order: +27177: d 2 0 2 2,2,2,2,2 +27177: b 3 0 3 1,2,2 +27177: c 3 0 3 1,2,2,2 +27177: a 4 0 4 1,2 +27177: join 17 2 5 0,2,2 +27177: meet 21 2 5 0,2 +NO CLASH, using fixed ground order +27178: Facts: +27178: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27178: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27178: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27178: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27178: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27178: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27178: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27178: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27178: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29 +27178: Goal: +27178: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +27178: Order: +27178: kbo +27178: Leaf order: +27178: d 2 0 2 2,2,2,2,2 +27178: b 3 0 3 1,2,2 +27178: c 3 0 3 1,2,2,2 +27178: a 4 0 4 1,2 +27178: join 17 2 5 0,2,2 +27178: meet 21 2 5 0,2 +NO CLASH, using fixed ground order +27179: Facts: +27179: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27179: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27179: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27179: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27179: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27179: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27179: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27179: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27179: Id : 10, {_}: + meet ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + meet ?26 (meet ?27 (join ?28 (meet ?29 (join ?27 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H47 ?26 ?27 ?28 ?29 +27179: Goal: +27179: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +27179: Order: +27179: lpo +27179: Leaf order: +27179: d 2 0 2 2,2,2,2,2 +27179: b 3 0 3 1,2,2 +27179: c 3 0 3 1,2,2,2 +27179: a 4 0 4 1,2 +27179: join 17 2 5 0,2,2 +27179: meet 21 2 5 0,2 +% SZS status Timeout for LAT112-1.p +NO CLASH, using fixed ground order +27203: Facts: +27203: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27203: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27203: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27203: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27203: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27203: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27203: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27203: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27203: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +27203: Goal: +27203: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27203: Order: +27203: nrkbo +27203: Leaf order: +27203: d 2 0 2 2,2,2,2,2 +27203: b 3 0 3 1,2,2 +27203: c 3 0 3 1,2,2,2 +27203: a 4 0 4 1,2 +27203: meet 19 2 5 0,2 +27203: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +27204: Facts: +27204: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27204: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27204: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27204: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27204: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27204: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27204: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27204: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27204: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +27204: Goal: +27204: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27204: Order: +27204: kbo +27204: Leaf order: +27204: d 2 0 2 2,2,2,2,2 +27204: b 3 0 3 1,2,2 +27204: c 3 0 3 1,2,2,2 +27204: a 4 0 4 1,2 +27204: meet 19 2 5 0,2 +27204: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +27205: Facts: +27205: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27205: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27205: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27205: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27205: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27205: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27205: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27205: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27205: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +27205: Goal: +27205: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +27205: Order: +27205: lpo +27205: Leaf order: +27205: d 2 0 2 2,2,2,2,2 +27205: b 3 0 3 1,2,2 +27205: c 3 0 3 1,2,2,2 +27205: a 4 0 4 1,2 +27205: meet 19 2 5 0,2 +27205: join 19 2 5 0,2,2 +% SZS status Timeout for LAT113-1.p +NO CLASH, using fixed ground order +27406: Facts: +27406: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27406: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27406: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27406: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27406: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27406: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27406: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27406: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27406: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27406: Goal: +27406: Id : 1, {_}: + join (meet a b) (meet a (join b c)) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H56 +27406: Order: +27406: nrkbo +27406: Leaf order: +27406: c 2 0 2 2,2,2,2 +27406: a 5 0 5 1,1,2 +27406: b 5 0 5 2,1,2 +27406: meet 17 2 5 0,1,2 +27406: join 19 2 5 0,2 +NO CLASH, using fixed ground order +27407: Facts: +27407: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27407: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27407: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27407: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27407: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27407: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27407: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27407: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27407: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27407: Goal: +27407: Id : 1, {_}: + join (meet a b) (meet a (join b c)) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H56 +27407: Order: +27407: kbo +27407: Leaf order: +27407: c 2 0 2 2,2,2,2 +27407: a 5 0 5 1,1,2 +27407: b 5 0 5 2,1,2 +27407: meet 17 2 5 0,1,2 +27407: join 19 2 5 0,2 +NO CLASH, using fixed ground order +27408: Facts: +27408: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27408: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27408: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27408: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27408: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27408: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27408: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27408: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27408: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27408: Goal: +27408: Id : 1, {_}: + join (meet a b) (meet a (join b c)) + =>= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H56 +27408: Order: +27408: lpo +27408: Leaf order: +27408: c 2 0 2 2,2,2,2 +27408: a 5 0 5 1,1,2 +27408: b 5 0 5 2,1,2 +27408: meet 17 2 5 0,1,2 +27408: join 19 2 5 0,2 +% SZS status Timeout for LAT114-1.p +NO CLASH, using fixed ground order +27552: Facts: +27552: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27552: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27552: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27552: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27552: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27552: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27552: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27552: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27552: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27552: Goal: +27552: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +27552: Order: +27552: nrkbo +27552: Leaf order: +27552: c 2 0 2 2,1,2,2 +27552: d 2 0 2 2,2,2,2 +27552: a 3 0 3 1,2 +27552: b 5 0 5 1,1,2,2 +27552: meet 17 2 5 0,2 +27552: join 19 2 5 0,1,2,2 +NO CLASH, using fixed ground order +27553: Facts: +27553: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27553: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27553: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27553: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27553: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27553: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27553: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27553: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27553: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27553: Goal: +27553: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +27553: Order: +27553: kbo +27553: Leaf order: +27553: c 2 0 2 2,1,2,2 +27553: d 2 0 2 2,2,2,2 +27553: a 3 0 3 1,2 +27553: b 5 0 5 1,1,2,2 +27553: meet 17 2 5 0,2 +27553: join 19 2 5 0,1,2,2 +NO CLASH, using fixed ground order +27554: Facts: +27554: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27554: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27554: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27554: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27554: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27554: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27554: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27554: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27554: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27554: Goal: +27554: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +27554: Order: +27554: lpo +27554: Leaf order: +27554: c 2 0 2 2,1,2,2 +27554: d 2 0 2 2,2,2,2 +27554: a 3 0 3 1,2 +27554: b 5 0 5 1,1,2,2 +27554: meet 17 2 5 0,2 +27554: join 19 2 5 0,1,2,2 +% SZS status Timeout for LAT115-1.p +NO CLASH, using fixed ground order +27591: Facts: +27591: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27591: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27591: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27591: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27591: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27591: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27591: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27591: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27591: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27591: Goal: +27591: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b c) (join d (meet a b)))) + [] by prove_H60 +27591: Order: +27591: nrkbo +27591: Leaf order: +27591: c 2 0 2 2,1,2,2 +27591: d 2 0 2 2,2,2,2 +27591: a 3 0 3 1,2 +27591: b 5 0 5 1,1,2,2 +27591: meet 17 2 5 0,2 +27591: join 19 2 5 0,1,2,2 +NO CLASH, using fixed ground order +27592: Facts: +27592: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27592: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27592: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27592: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27592: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27592: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27592: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27592: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27592: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27592: Goal: +27592: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b c) (join d (meet a b)))) + [] by prove_H60 +27592: Order: +27592: kbo +27592: Leaf order: +27592: c 2 0 2 2,1,2,2 +27592: d 2 0 2 2,2,2,2 +27592: a 3 0 3 1,2 +27592: b 5 0 5 1,1,2,2 +27592: meet 17 2 5 0,2 +27592: join 19 2 5 0,1,2,2 +NO CLASH, using fixed ground order +27593: Facts: +27593: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27593: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27593: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27593: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27593: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27593: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27593: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27593: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27593: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +27593: Goal: +27593: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b c) (join d (meet a b)))) + [] by prove_H60 +27593: Order: +27593: lpo +27593: Leaf order: +27593: c 2 0 2 2,1,2,2 +27593: d 2 0 2 2,2,2,2 +27593: a 3 0 3 1,2 +27593: b 5 0 5 1,1,2,2 +27593: meet 17 2 5 0,2 +27593: join 19 2 5 0,1,2,2 +% SZS status Timeout for LAT116-1.p +NO CLASH, using fixed ground order +27609: Facts: +27609: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27609: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27609: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27609: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27609: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27609: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27609: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27609: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27609: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))) + [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29 +27609: Goal: +27609: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +27609: Order: +27609: nrkbo +27609: Leaf order: +27609: b 3 0 3 1,2,2 +27609: c 3 0 3 2,2,2 +27609: a 5 0 5 1,2 +27609: join 16 2 4 0,2,2 +27609: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +27610: Facts: +27610: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27610: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27610: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27610: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27610: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27610: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27610: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27610: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27610: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))) + [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29 +27610: Goal: +27610: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +27610: Order: +27610: kbo +27610: Leaf order: +27610: b 3 0 3 1,2,2 +27610: c 3 0 3 2,2,2 +27610: a 5 0 5 1,2 +27610: join 16 2 4 0,2,2 +27610: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +27611: Facts: +27611: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +27611: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +27611: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +27611: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +27611: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +27611: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +27611: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +27611: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +27611: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?26 (join (meet ?26 ?27) (meet ?28 ?29)))) + [29, 28, 27, 26] by equation_H65 ?26 ?27 ?28 ?29 +27611: Goal: +27611: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +27611: Order: +27611: lpo +27611: Leaf order: +27611: b 3 0 3 1,2,2 +27611: c 3 0 3 2,2,2 +27611: a 5 0 5 1,2 +27611: join 16 2 4 0,2,2 +27611: meet 20 2 5 0,2 +% SZS status Timeout for LAT117-1.p +NO CLASH, using fixed ground order +28243: Facts: +28243: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28243: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28243: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28243: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28243: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28243: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28243: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28243: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28243: Id : 10, {_}: + meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27))) + =>= + join (meet ?26 ?27) (meet ?26 ?28) + [28, 27, 26] by equation_H82 ?26 ?27 ?28 +28243: Goal: +28243: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +28243: Order: +28243: nrkbo +28243: Leaf order: +28243: c 3 0 3 2,2,2,2 +28243: b 4 0 4 1,2,2 +28243: a 5 0 5 1,2 +28243: join 17 2 4 0,2,2 +28243: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +28244: Facts: +28244: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28244: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28244: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28244: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28244: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28244: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28244: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28244: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28244: Id : 10, {_}: + meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27))) + =>= + join (meet ?26 ?27) (meet ?26 ?28) + [28, 27, 26] by equation_H82 ?26 ?27 ?28 +28244: Goal: +28244: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +28244: Order: +28244: kbo +28244: Leaf order: +28244: c 3 0 3 2,2,2,2 +28244: b 4 0 4 1,2,2 +28244: a 5 0 5 1,2 +28244: join 17 2 4 0,2,2 +28244: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +28246: Facts: +28246: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28246: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28246: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28246: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28246: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28246: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28246: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28246: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28246: Id : 10, {_}: + meet ?26 (join (meet ?27 (join ?26 ?28)) (meet ?28 (join ?26 ?27))) + =>= + join (meet ?26 ?27) (meet ?26 ?28) + [28, 27, 26] by equation_H82 ?26 ?27 ?28 +28246: Goal: +28246: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +28246: Order: +28246: lpo +28246: Leaf order: +28246: c 3 0 3 2,2,2,2 +28246: b 4 0 4 1,2,2 +28246: a 5 0 5 1,2 +28246: join 17 2 4 0,2,2 +28246: meet 20 2 6 0,2 +% SZS status Timeout for LAT119-1.p +NO CLASH, using fixed ground order +28653: Facts: +28653: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28653: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28653: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28653: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28653: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28653: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28653: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28653: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28653: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28)))) + [28, 27, 26] by equation_H10_dual ?26 ?27 ?28 +28653: Goal: +28653: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +28653: Order: +28653: nrkbo +28653: Leaf order: +28653: c 2 0 2 2,2,2 +28653: a 4 0 4 1,2 +28653: b 4 0 4 1,2,2 +28653: meet 16 2 4 0,2 +28653: join 18 2 4 0,2,2 +NO CLASH, using fixed ground order +28654: Facts: +28654: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28654: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28654: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28654: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28654: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28654: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28654: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28654: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28654: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28)))) + [28, 27, 26] by equation_H10_dual ?26 ?27 ?28 +28654: Goal: +28654: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +28654: Order: +28654: kbo +28654: Leaf order: +28654: c 2 0 2 2,2,2 +28654: a 4 0 4 1,2 +28654: b 4 0 4 1,2,2 +28654: meet 16 2 4 0,2 +28654: join 18 2 4 0,2,2 +NO CLASH, using fixed ground order +28655: Facts: +28655: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28655: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28655: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28655: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28655: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28655: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28655: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28655: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28655: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?27 ?28)))) + [28, 27, 26] by equation_H10_dual ?26 ?27 ?28 +28655: Goal: +28655: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +28655: Order: +28655: lpo +28655: Leaf order: +28655: c 2 0 2 2,2,2 +28655: a 4 0 4 1,2 +28655: b 4 0 4 1,2,2 +28655: meet 16 2 4 0,2 +28655: join 18 2 4 0,2,2 +% SZS status Timeout for LAT120-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +28691: Facts: +28691: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28691: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28691: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28691: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28691: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28691: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28691: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28691: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28691: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +28691: Goal: +28691: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28691: Order: +28691: kbo +28691: Leaf order: +28691: b 3 0 3 1,2,2 +28691: c 3 0 3 2,2,2,2 +28691: a 4 0 4 1,2 +28691: meet 16 2 3 0,2,2 +28691: join 20 2 5 0,2 +28690: Facts: +28690: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28690: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28690: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28690: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28690: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28690: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28690: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28690: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28690: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +28690: Goal: +28690: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28690: Order: +28690: nrkbo +28690: Leaf order: +28690: b 3 0 3 1,2,2 +28690: c 3 0 3 2,2,2,2 +28690: a 4 0 4 1,2 +28690: meet 16 2 3 0,2,2 +28690: join 20 2 5 0,2 +NO CLASH, using fixed ground order +28692: Facts: +28692: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28692: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28692: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28692: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28692: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28692: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28692: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28692: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28692: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?26 ?27) + (meet (join ?26 ?28) (join ?27 (meet ?26 ?28)))) + [28, 27, 26] by equation_H18_dual ?26 ?27 ?28 +28692: Goal: +28692: Id : 1, {_}: + join a (meet b (join a c)) + =>= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28692: Order: +28692: lpo +28692: Leaf order: +28692: b 3 0 3 1,2,2 +28692: c 3 0 3 2,2,2,2 +28692: a 4 0 4 1,2 +28692: meet 16 2 3 0,2,2 +28692: join 20 2 5 0,2 +% SZS status Timeout for LAT121-1.p +NO CLASH, using fixed ground order +28708: Facts: +28708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28708: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28708: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28708: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28708: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28708: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +28708: Goal: +28708: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28708: Order: +28708: nrkbo +28708: Leaf order: +28708: b 3 0 3 1,2,2 +28708: c 3 0 3 2,2,2,2 +28708: a 4 0 4 1,2 +28708: meet 16 2 3 0,2,2 +28708: join 20 2 5 0,2 +NO CLASH, using fixed ground order +28709: Facts: +28709: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28709: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28709: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28709: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28709: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28709: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28709: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28709: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28709: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +28709: Goal: +28709: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28709: Order: +28709: kbo +28709: Leaf order: +28709: b 3 0 3 1,2,2 +28709: c 3 0 3 2,2,2,2 +28709: a 4 0 4 1,2 +28709: meet 16 2 3 0,2,2 +28709: join 20 2 5 0,2 +NO CLASH, using fixed ground order +28710: Facts: +28710: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28710: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28710: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28710: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28710: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28710: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28710: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28710: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28710: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +28710: Goal: +28710: Id : 1, {_}: + join a (meet b (join a c)) + =>= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28710: Order: +28710: lpo +28710: Leaf order: +28710: b 3 0 3 1,2,2 +28710: c 3 0 3 2,2,2,2 +28710: a 4 0 4 1,2 +28710: meet 16 2 3 0,2,2 +28710: join 20 2 5 0,2 +% SZS status Timeout for LAT122-1.p +NO CLASH, using fixed ground order +28742: Facts: +28742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28742: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28742: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28742: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28742: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28742: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?28 (join ?26 ?27))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H22_dual ?26 ?27 ?28 +28742: Goal: +28742: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28742: Order: +28742: nrkbo +28742: Leaf order: +28742: b 3 0 3 1,2,2 +28742: c 3 0 3 2,2,2,2 +28742: a 4 0 4 1,2 +28742: meet 16 2 3 0,2,2 +28742: join 20 2 5 0,2 +NO CLASH, using fixed ground order +28743: Facts: +28743: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28743: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28743: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28743: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28743: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28743: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28743: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28743: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28743: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?28 (join ?26 ?27))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H22_dual ?26 ?27 ?28 +28743: Goal: +28743: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28743: Order: +28743: kbo +28743: Leaf order: +28743: b 3 0 3 1,2,2 +28743: c 3 0 3 2,2,2,2 +28743: a 4 0 4 1,2 +28743: meet 16 2 3 0,2,2 +28743: join 20 2 5 0,2 +NO CLASH, using fixed ground order +28744: Facts: +28744: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28744: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28744: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28744: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28744: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28744: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28744: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28744: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28744: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?28 (join ?26 ?27))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H22_dual ?26 ?27 ?28 +28744: Goal: +28744: Id : 1, {_}: + join a (meet b (join a c)) + =>= + join a (meet b (join c (meet a (join c b)))) + [] by prove_H55 +28744: Order: +28744: lpo +28744: Leaf order: +28744: b 3 0 3 1,2,2 +28744: c 3 0 3 2,2,2,2 +28744: a 4 0 4 1,2 +28744: meet 16 2 3 0,2,2 +28744: join 20 2 5 0,2 +% SZS status Timeout for LAT123-1.p +NO CLASH, using fixed ground order +28780: Facts: +28780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28780: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28780: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28780: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28780: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28780: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 (join ?28 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29 +28780: Goal: +28780: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28780: Order: +28780: nrkbo +28780: Leaf order: +28780: b 3 0 3 1,2,2 +28780: c 3 0 3 2,2,2 +28780: a 5 0 5 1,2 +28780: meet 17 2 5 0,2 +28780: join 20 2 4 0,2,2 +NO CLASH, using fixed ground order +28781: Facts: +28781: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28781: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28781: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28781: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28781: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28781: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28781: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28781: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28781: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 (join ?28 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29 +28781: Goal: +28781: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28781: Order: +28781: kbo +28781: Leaf order: +28781: b 3 0 3 1,2,2 +28781: c 3 0 3 2,2,2 +28781: a 5 0 5 1,2 +28781: meet 17 2 5 0,2 +28781: join 20 2 4 0,2,2 +NO CLASH, using fixed ground order +28782: Facts: +28782: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28782: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28782: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28782: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28782: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28782: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28782: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28782: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28782: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 (join ?28 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet (join ?26 ?29) (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H32_dual ?26 ?27 ?28 ?29 +28782: Goal: +28782: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28782: Order: +28782: lpo +28782: Leaf order: +28782: b 3 0 3 1,2,2 +28782: c 3 0 3 2,2,2 +28782: a 5 0 5 1,2 +28782: meet 17 2 5 0,2 +28782: join 20 2 4 0,2,2 +% SZS status Timeout for LAT124-1.p +NO CLASH, using fixed ground order +28810: Facts: +28810: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28810: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28810: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28810: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28810: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28810: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28810: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28810: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28810: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 ?29)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29 +28810: Goal: +28810: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28810: Order: +28810: nrkbo +28810: Leaf order: +28810: b 3 0 3 1,2,2 +28810: c 3 0 3 2,2,2 +28810: a 5 0 5 1,2 +28810: join 18 2 4 0,2,2 +28810: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +28811: Facts: +28811: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28811: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28811: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28811: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28811: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28811: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28811: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28811: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28811: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 ?29)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29 +28811: Goal: +28811: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28811: Order: +28811: kbo +28811: Leaf order: +28811: b 3 0 3 1,2,2 +28811: c 3 0 3 2,2,2 +NO CLASH, using fixed ground order +28812: Facts: +28812: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28812: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28812: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28812: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28812: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28812: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28812: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28812: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28811: a 5 0 5 1,2 +28811: join 18 2 4 0,2,2 +28811: meet 18 2 5 0,2 +28812: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 ?29)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?27 (join ?29 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H34_dual ?26 ?27 ?28 ?29 +28812: Goal: +28812: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28812: Order: +28812: lpo +28812: Leaf order: +28812: b 3 0 3 1,2,2 +28812: c 3 0 3 2,2,2 +28812: a 5 0 5 1,2 +28812: join 18 2 4 0,2,2 +28812: meet 18 2 5 0,2 +% SZS status Timeout for LAT125-1.p +NO CLASH, using fixed ground order +28829: Facts: +28829: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28829: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28829: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28829: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28829: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28829: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28829: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28829: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28829: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28)))) + [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29 +28829: Goal: +28829: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28829: Order: +28829: kbo +28829: Leaf order: +28829: b 3 0 3 1,2,2 +28829: c 3 0 3 2,2,2 +28829: a 5 0 5 1,2 +28829: join 18 2 4 0,2,2 +28829: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +28828: Facts: +28828: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28828: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28828: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28828: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28828: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28828: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28828: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28828: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28828: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28)))) + [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29 +28828: Goal: +28828: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28828: Order: +28828: nrkbo +28828: Leaf order: +28828: b 3 0 3 1,2,2 +28828: c 3 0 3 2,2,2 +28828: a 5 0 5 1,2 +28828: join 18 2 4 0,2,2 +28828: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +28830: Facts: +28830: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28830: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28830: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28830: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28830: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28830: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28830: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28830: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28830: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?28)))) + [29, 28, 27, 26] by equation_H39_dual ?26 ?27 ?28 ?29 +28830: Goal: +28830: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +28830: Order: +28830: lpo +28830: Leaf order: +28830: b 3 0 3 1,2,2 +28830: c 3 0 3 2,2,2 +28830: a 5 0 5 1,2 +28830: join 18 2 4 0,2,2 +28830: meet 18 2 5 0,2 +% SZS status Timeout for LAT126-1.p +NO CLASH, using fixed ground order +28859: Facts: +28859: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28859: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28859: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28859: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28859: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28859: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28859: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28859: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28859: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27)))) + [28, 27, 26] by equation_H55_dual ?26 ?27 ?28 +28859: Goal: +28859: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +28859: Order: +28859: nrkbo +28859: Leaf order: +28859: b 3 0 3 1,2,2 +28859: c 3 0 3 2,2,2,2 +28859: a 6 0 6 1,2 +28859: join 16 2 4 0,2,2 +28859: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +28860: Facts: +28860: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28860: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28860: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28860: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28860: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28860: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28860: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28860: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28860: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27)))) + [28, 27, 26] by equation_H55_dual ?26 ?27 ?28 +28860: Goal: +28860: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +28860: Order: +28860: kbo +28860: Leaf order: +28860: b 3 0 3 1,2,2 +28860: c 3 0 3 2,2,2,2 +28860: a 6 0 6 1,2 +28860: join 16 2 4 0,2,2 +28860: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +28861: Facts: +28861: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28861: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28861: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28861: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28861: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28861: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28861: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28861: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28861: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =?= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 ?27)))) + [28, 27, 26] by equation_H55_dual ?26 ?27 ?28 +28861: Goal: +28861: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +28861: Order: +28861: lpo +28861: Leaf order: +28861: b 3 0 3 1,2,2 +28861: c 3 0 3 2,2,2,2 +28861: a 6 0 6 1,2 +28861: join 16 2 4 0,2,2 +28861: meet 20 2 6 0,2 +% SZS status Timeout for LAT127-1.p +NO CLASH, using fixed ground order +28878: Facts: +28878: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28878: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28878: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28878: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28878: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28878: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28878: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28878: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28878: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +28878: Goal: +28878: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +28878: Order: +28878: nrkbo +28878: Leaf order: +28878: c 3 0 3 2,2,2,2 +28878: b 4 0 4 1,2,2 +28878: a 5 0 5 1,2 +28878: join 17 2 4 0,2,2 +28878: meet 19 2 6 0,2 +NO CLASH, using fixed ground order +28879: Facts: +28879: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28879: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28879: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28879: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28879: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28879: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28879: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28879: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28879: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +28879: Goal: +28879: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +28879: Order: +28879: kbo +28879: Leaf order: +28879: c 3 0 3 2,2,2,2 +28879: b 4 0 4 1,2,2 +NO CLASH, using fixed ground order +28880: Facts: +28880: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28880: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28880: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28880: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28880: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28880: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28880: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28880: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28880: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +28880: Goal: +28880: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join b (meet a (join c (meet a b)))))) + [] by prove_H3 +28880: Order: +28880: lpo +28880: Leaf order: +28880: c 3 0 3 2,2,2,2 +28880: b 4 0 4 1,2,2 +28880: a 5 0 5 1,2 +28880: join 17 2 4 0,2,2 +28880: meet 19 2 6 0,2 +28879: a 5 0 5 1,2 +28879: join 17 2 4 0,2,2 +28879: meet 19 2 6 0,2 +% SZS status Timeout for LAT128-1.p +NO CLASH, using fixed ground order +28929: Facts: +28929: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28929: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28929: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28929: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28929: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28929: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28929: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28929: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28929: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +28929: Goal: +28929: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +28929: Order: +28929: nrkbo +28929: Leaf order: +28929: b 3 0 3 1,2,2 +28929: c 3 0 3 2,2,2,2 +28929: a 4 0 4 1,2 +28929: join 16 2 3 0,2,2 +28929: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +28930: Facts: +28930: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28930: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28930: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28930: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28930: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28930: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28930: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28930: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28930: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +28930: Goal: +28930: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +28930: Order: +28930: kbo +28930: Leaf order: +28930: b 3 0 3 1,2,2 +28930: c 3 0 3 2,2,2,2 +28930: a 4 0 4 1,2 +28930: join 16 2 3 0,2,2 +28930: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +28931: Facts: +28931: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28931: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28931: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28931: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28931: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28931: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28931: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28931: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28931: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H58_dual ?26 ?27 ?28 +28931: Goal: +28931: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +28931: Order: +28931: lpo +28931: Leaf order: +28931: b 3 0 3 1,2,2 +28931: c 3 0 3 2,2,2,2 +28931: a 4 0 4 1,2 +28931: join 16 2 3 0,2,2 +28931: meet 18 2 5 0,2 +% SZS status Timeout for LAT129-1.p +NO CLASH, using fixed ground order +28978: Facts: +28978: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28978: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28978: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28978: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28978: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28978: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28978: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28978: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28978: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +28978: Goal: +28978: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet a c)))) + [] by prove_H39 +28978: Order: +28978: nrkbo +28978: Leaf order: +28978: b 2 0 2 1,2,2 +28978: d 2 0 2 2,2,2,2,2 +28978: c 3 0 3 1,2,2,2 +28978: a 4 0 4 1,2 +28978: join 17 2 4 0,2,2 +28978: meet 17 2 5 0,2 +NO CLASH, using fixed ground order +28979: Facts: +28979: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28979: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28979: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28979: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28979: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28979: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28979: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28979: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28979: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +28979: Goal: +28979: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet a c)))) + [] by prove_H39 +28979: Order: +28979: kbo +28979: Leaf order: +28979: b 2 0 2 1,2,2 +28979: d 2 0 2 2,2,2,2,2 +28979: c 3 0 3 1,2,2,2 +28979: a 4 0 4 1,2 +28979: join 17 2 4 0,2,2 +28979: meet 17 2 5 0,2 +NO CLASH, using fixed ground order +28980: Facts: +28980: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +28980: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +28980: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +28980: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +28980: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +28980: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +28980: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +28980: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +28980: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +28980: Goal: +28980: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet a c)))) + [] by prove_H39 +28980: Order: +28980: lpo +28980: Leaf order: +28980: b 2 0 2 1,2,2 +28980: d 2 0 2 2,2,2,2,2 +28980: c 3 0 3 1,2,2,2 +28980: a 4 0 4 1,2 +28980: join 17 2 4 0,2,2 +28980: meet 17 2 5 0,2 +% SZS status Timeout for LAT130-1.p +NO CLASH, using fixed ground order +29013: Facts: +29013: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29013: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29013: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29013: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29013: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29013: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29013: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29013: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29013: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +29013: Goal: +29013: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +29013: Order: +29013: nrkbo +29013: Leaf order: +29013: d 2 0 2 2,2,2,2,2 +29013: b 3 0 3 1,2,2 +29013: c 3 0 3 1,2,2,2 +29013: a 4 0 4 1,2 +29013: meet 17 2 5 0,2 +29013: join 18 2 5 0,2,2 +NO CLASH, using fixed ground order +29014: Facts: +29014: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29014: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29014: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29014: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29014: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29014: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29014: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29014: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29014: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +29014: Goal: +29014: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +29014: Order: +29014: kbo +29014: Leaf order: +29014: d 2 0 2 2,2,2,2,2 +29014: b 3 0 3 1,2,2 +29014: c 3 0 3 1,2,2,2 +29014: a 4 0 4 1,2 +29014: meet 17 2 5 0,2 +29014: join 18 2 5 0,2,2 +NO CLASH, using fixed ground order +29015: Facts: +29015: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29015: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29015: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29015: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29015: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29015: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29015: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29015: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29015: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + join ?26 (meet ?27 (join ?26 (meet ?28 (join ?26 ?27)))) + [28, 27, 26] by equation_H68_dual ?26 ?27 ?28 +29015: Goal: +29015: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +29015: Order: +29015: lpo +29015: Leaf order: +29015: d 2 0 2 2,2,2,2,2 +29015: b 3 0 3 1,2,2 +29015: c 3 0 3 1,2,2,2 +29015: a 4 0 4 1,2 +29015: meet 17 2 5 0,2 +29015: join 18 2 5 0,2,2 +% SZS status Timeout for LAT131-1.p +NO CLASH, using fixed ground order +29032: Facts: +29032: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29032: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29032: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29032: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29032: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29032: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29032: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29032: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29032: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + meet (join ?26 (meet ?28 (join ?26 ?27))) + (join ?26 (meet ?27 (join ?26 ?28))) + [28, 27, 26] by equation_H69_dual ?26 ?27 ?28 +29032: Goal: +29032: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +29032: Order: +29032: nrkbo +29032: Leaf order: +29032: d 2 0 2 2,2,2,2,2 +29032: b 3 0 3 1,2,2 +29032: c 3 0 3 1,2,2,2 +29032: a 4 0 4 1,2 +29032: meet 18 2 5 0,2 +29032: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +29033: Facts: +29033: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29033: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29033: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29033: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29033: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29033: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29033: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29033: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29033: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + meet (join ?26 (meet ?28 (join ?26 ?27))) + (join ?26 (meet ?27 (join ?26 ?28))) + [28, 27, 26] by equation_H69_dual ?26 ?27 ?28 +29033: Goal: +29033: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +29033: Order: +29033: kbo +29033: Leaf order: +29033: d 2 0 2 2,2,2,2,2 +29033: b 3 0 3 1,2,2 +29033: c 3 0 3 1,2,2,2 +29033: a 4 0 4 1,2 +29033: meet 18 2 5 0,2 +29033: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +29034: Facts: +29034: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29034: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29034: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29034: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29034: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29034: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29034: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29034: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29034: Id : 10, {_}: + join ?26 (meet ?27 ?28) + =<= + meet (join ?26 (meet ?28 (join ?26 ?27))) + (join ?26 (meet ?27 (join ?26 ?28))) + [28, 27, 26] by equation_H69_dual ?26 ?27 ?28 +29034: Goal: +29034: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +29034: Order: +29034: lpo +29034: Leaf order: +29034: d 2 0 2 2,2,2,2,2 +29034: b 3 0 3 1,2,2 +29034: c 3 0 3 1,2,2,2 +29034: a 4 0 4 1,2 +29034: meet 18 2 5 0,2 +29034: join 19 2 5 0,2,2 +% SZS status Timeout for LAT132-1.p +NO CLASH, using fixed ground order +29065: Facts: +29065: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29065: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29065: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29065: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29065: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29065: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29065: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29065: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29065: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +29065: Goal: +29065: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet (join a (meet b (join a c))) (join c (meet a b))) + [] by prove_H6_dual +29065: Order: +29065: nrkbo +29065: Leaf order: +29065: b 3 0 3 1,2,2 +29065: c 3 0 3 2,2,2,2 +29065: a 6 0 6 1,2 +29065: meet 16 2 4 0,2,2 +29065: join 20 2 6 0,2 +NO CLASH, using fixed ground order +29066: Facts: +29066: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29066: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29066: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29066: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29066: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29066: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29066: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29066: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29066: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =<= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +29066: Goal: +29066: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet (join a (meet b (join a c))) (join c (meet a b))) + [] by prove_H6_dual +29066: Order: +29066: kbo +29066: Leaf order: +29066: b 3 0 3 1,2,2 +29066: c 3 0 3 2,2,2,2 +29066: a 6 0 6 1,2 +29066: meet 16 2 4 0,2,2 +29066: join 20 2 6 0,2 +NO CLASH, using fixed ground order +29067: Facts: +29067: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29067: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29067: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29067: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29067: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29067: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29067: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29067: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29067: Id : 10, {_}: + join ?26 (meet ?27 (join ?26 ?28)) + =?= + join ?26 (meet ?27 (join ?28 (meet ?26 (join ?28 ?27)))) + [28, 27, 26] by equation_H55 ?26 ?27 ?28 +29067: Goal: +29067: Id : 1, {_}: + join a (meet b (join a c)) + =<= + join a (meet (join a (meet b (join a c))) (join c (meet a b))) + [] by prove_H6_dual +29067: Order: +29067: lpo +29067: Leaf order: +29067: b 3 0 3 1,2,2 +29067: c 3 0 3 2,2,2,2 +29067: a 6 0 6 1,2 +29067: meet 16 2 4 0,2,2 +29067: join 20 2 6 0,2 +% SZS status Timeout for LAT133-1.p +NO CLASH, using fixed ground order +29084: Facts: +29084: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29084: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29084: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29084: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29084: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29084: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29084: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29084: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29084: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28)) + [28, 27, 26] by equation_H61 ?26 ?27 ?28 +29084: Goal: +29084: Id : 1, {_}: + meet (join a b) (join a c) + =<= + join a (meet (join b (meet c (join a b))) (join c (meet a b))) + [] by prove_H22_dual +29084: Order: +29084: nrkbo +29084: Leaf order: +29084: c 3 0 3 2,2,2 +29084: b 4 0 4 2,1,2 +29084: a 5 0 5 1,1,2 +29084: meet 16 2 4 0,2 +29084: join 20 2 6 0,1,2 +NO CLASH, using fixed ground order +29085: Facts: +29085: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29085: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29085: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29085: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29085: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29085: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29085: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29085: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29085: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28)) + [28, 27, 26] by equation_H61 ?26 ?27 ?28 +29085: Goal: +29085: Id : 1, {_}: + meet (join a b) (join a c) + =<= + join a (meet (join b (meet c (join a b))) (join c (meet a b))) + [] by prove_H22_dual +29085: Order: +29085: kbo +29085: Leaf order: +29085: c 3 0 3 2,2,2 +29085: b 4 0 4 2,1,2 +29085: a 5 0 5 1,1,2 +29085: meet 16 2 4 0,2 +29085: join 20 2 6 0,1,2 +NO CLASH, using fixed ground order +29086: Facts: +29086: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29086: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29086: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29086: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29086: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29086: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29086: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29086: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29086: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 (meet (join ?26 ?27) (join (meet ?26 ?27) ?28)) + [28, 27, 26] by equation_H61 ?26 ?27 ?28 +29086: Goal: +29086: Id : 1, {_}: + meet (join a b) (join a c) + =<= + join a (meet (join b (meet c (join a b))) (join c (meet a b))) + [] by prove_H22_dual +29086: Order: +29086: lpo +29086: Leaf order: +29086: c 3 0 3 2,2,2 +29086: b 4 0 4 2,1,2 +29086: a 5 0 5 1,1,2 +29086: meet 16 2 4 0,2 +29086: join 20 2 6 0,1,2 +% SZS status Timeout for LAT134-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +29118: Facts: +29118: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29118: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29118: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29118: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29118: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29118: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29118: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29118: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29118: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +29118: Goal: +29118: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +29118: Order: +29118: kbo +29118: Leaf order: +29118: b 2 0 2 1,2,2 +29118: d 2 0 2 2,2,2,2,2 +29118: c 3 0 3 1,2,2,2 +29118: a 4 0 4 1,2 +29118: meet 17 2 4 0,2,2 +29118: join 17 2 5 0,2 +29117: Facts: +29117: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29117: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29117: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29117: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29117: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29117: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29117: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29117: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29117: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +29117: Goal: +29117: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +29117: Order: +29117: nrkbo +29117: Leaf order: +29117: b 2 0 2 1,2,2 +29117: d 2 0 2 2,2,2,2,2 +29117: c 3 0 3 1,2,2,2 +29117: a 4 0 4 1,2 +29117: meet 17 2 4 0,2,2 +29117: join 17 2 5 0,2 +NO CLASH, using fixed ground order +29119: Facts: +29119: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29119: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29119: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29119: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29119: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29119: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29119: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29119: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29119: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +29119: Goal: +29119: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +29119: Order: +29119: lpo +29119: Leaf order: +29119: b 2 0 2 1,2,2 +29119: d 2 0 2 2,2,2,2,2 +29119: c 3 0 3 1,2,2,2 +29119: a 4 0 4 1,2 +29119: meet 17 2 4 0,2,2 +29119: join 17 2 5 0,2 +% SZS status Timeout for LAT135-1.p +NO CLASH, using fixed ground order +29145: Facts: +29145: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29145: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29145: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29145: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29145: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29145: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29145: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29145: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29145: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +29145: Goal: +29145: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +29145: Order: +29145: nrkbo +29145: Leaf order: +29145: b 2 0 2 1,2,2 +29145: d 2 0 2 2,2,2,2,2 +29145: c 3 0 3 1,2,2,2 +29145: a 4 0 4 1,2 +29145: meet 18 2 4 0,2,2 +29145: join 18 2 5 0,2 +NO CLASH, using fixed ground order +29146: Facts: +29146: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29146: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29146: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29146: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29146: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29146: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29146: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29146: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29146: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +29146: Goal: +29146: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +29146: Order: +29146: kbo +29146: Leaf order: +29146: b 2 0 2 1,2,2 +29146: d 2 0 2 2,2,2,2,2 +29146: c 3 0 3 1,2,2,2 +29146: a 4 0 4 1,2 +29146: meet 18 2 4 0,2,2 +29146: join 18 2 5 0,2 +NO CLASH, using fixed ground order +29147: Facts: +29147: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29147: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29147: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29147: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29147: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29147: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29147: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29147: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29147: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +29147: Goal: +29147: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join a c)))) + [] by prove_H39_dual +29147: Order: +29147: lpo +29147: Leaf order: +29147: b 2 0 2 1,2,2 +29147: d 2 0 2 2,2,2,2,2 +29147: c 3 0 3 1,2,2,2 +29147: a 4 0 4 1,2 +29147: meet 18 2 4 0,2,2 +29147: join 18 2 5 0,2 +% SZS status Timeout for LAT136-1.p +NO CLASH, using fixed ground order +29176: Facts: +29176: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29176: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29176: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29176: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29176: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29176: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29176: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29176: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29176: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +29176: Goal: +29176: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join c (meet a b))))) + [] by prove_H40_dual +29176: Order: +29176: nrkbo +29176: Leaf order: +29176: d 2 0 2 2,2,2,2,2 +29176: b 3 0 3 1,2,2 +29176: c 3 0 3 1,2,2,2 +29176: a 4 0 4 1,2 +29176: join 18 2 5 0,2 +29176: meet 19 2 5 0,2,2 +NO CLASH, using fixed ground order +29177: Facts: +29177: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29177: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29177: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29177: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29177: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29177: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29177: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29177: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29177: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +29177: Goal: +29177: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join c (meet a b))))) + [] by prove_H40_dual +29177: Order: +29177: kbo +29177: Leaf order: +29177: d 2 0 2 2,2,2,2,2 +29177: b 3 0 3 1,2,2 +29177: c 3 0 3 1,2,2,2 +29177: a 4 0 4 1,2 +29177: join 18 2 5 0,2 +29177: meet 19 2 5 0,2,2 +NO CLASH, using fixed ground order +29178: Facts: +29178: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29178: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29178: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29178: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29178: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29178: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29178: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29178: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29178: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + join (meet ?26 (join ?28 (meet ?26 ?27))) + (meet ?26 (join ?27 (meet ?26 ?28))) + [28, 27, 26] by equation_H69 ?26 ?27 ?28 +29178: Goal: +29178: Id : 1, {_}: + join a (meet b (join c (meet a d))) + =<= + join a (meet b (join c (meet d (join c (meet a b))))) + [] by prove_H40_dual +29178: Order: +29178: lpo +29178: Leaf order: +29178: d 2 0 2 2,2,2,2,2 +29178: b 3 0 3 1,2,2 +29178: c 3 0 3 1,2,2,2 +29178: a 4 0 4 1,2 +29178: join 18 2 5 0,2 +29178: meet 19 2 5 0,2,2 +% SZS status Timeout for LAT137-1.p +NO CLASH, using fixed ground order +29197: Facts: +29197: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29197: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29197: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29197: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29197: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29197: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29197: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29197: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29197: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28)) + [28, 27, 26] by equation_H61_dual ?26 ?27 ?28 +29197: Goal: +29197: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29197: Order: +29197: nrkbo +29197: Leaf order: +29197: b 3 0 3 1,2,2 +29197: c 3 0 3 2,2,2,2 +29197: a 6 0 6 1,2 +29197: join 16 2 4 0,2,2 +29197: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +29198: Facts: +29198: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29198: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29198: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29198: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29198: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29198: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29198: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29198: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29198: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28)) + [28, 27, 26] by equation_H61_dual ?26 ?27 ?28 +29198: Goal: +29198: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29198: Order: +29198: kbo +29198: Leaf order: +29198: b 3 0 3 1,2,2 +29198: c 3 0 3 2,2,2,2 +29198: a 6 0 6 1,2 +29198: join 16 2 4 0,2,2 +29198: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +29199: Facts: +29199: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +29199: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +29199: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +29199: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +29199: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +29199: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +29199: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +29199: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +29199: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 (join (meet ?26 ?27) (meet (join ?26 ?27) ?28)) + [28, 27, 26] by equation_H61_dual ?26 ?27 ?28 +29199: Goal: +29199: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +29199: Order: +29199: lpo +29199: Leaf order: +29199: b 3 0 3 1,2,2 +29199: c 3 0 3 2,2,2,2 +29199: a 6 0 6 1,2 +29199: join 16 2 4 0,2,2 +29199: meet 20 2 6 0,2 +% SZS status Timeout for LAT171-1.p +NO CLASH, using fixed ground order +29274: Facts: +29274: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29274: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29274: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29274: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29274: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent +29274: Goal: +29274: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma +29274: Order: +29274: nrkbo +29274: Leaf order: +29274: y 2 0 0 +29274: x 2 0 1 1,2 +29274: z 2 0 1 2,2 +29274: truth 4 0 1 3 +29274: not 2 1 0 +29274: implies 16 2 1 0,2 +NO CLASH, using fixed ground order +29275: Facts: +29275: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29275: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29275: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29275: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29275: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent +29275: Goal: +29275: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma +29275: Order: +29275: kbo +29275: Leaf order: +29275: y 2 0 0 +29275: x 2 0 1 1,2 +29275: z 2 0 1 2,2 +29275: truth 4 0 1 3 +29275: not 2 1 0 +29275: implies 16 2 1 0,2 +NO CLASH, using fixed ground order +29276: Facts: +29276: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29276: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29276: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29276: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29276: Id : 6, {_}: implies x y =>= implies y z [] by lemma_antecedent +29276: Goal: +29276: Id : 1, {_}: implies x z =>= truth [] by prove_wajsberg_lemma +29276: Order: +29276: lpo +29276: Leaf order: +29276: y 2 0 0 +29276: x 2 0 1 1,2 +29276: z 2 0 1 2,2 +29276: truth 4 0 1 3 +29276: not 2 1 0 +29276: implies 16 2 1 0,2 +% SZS status Timeout for LCL136-1.p +NO CLASH, using fixed ground order +29293: Facts: +29293: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29293: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29293: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29293: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29293: Goal: +29293: Id : 1, {_}: + implies (implies (implies x y) y) + (implies (implies y z) (implies x z)) + =>= + truth + [] by prove_wajsberg_lemma +29293: Order: +29293: nrkbo +29293: Leaf order: +29293: x 2 0 2 1,1,1,2 +29293: z 2 0 2 2,1,2,2 +29293: y 3 0 3 2,1,1,2 +29293: truth 4 0 1 3 +29293: not 2 1 0 +29293: implies 19 2 6 0,2 +NO CLASH, using fixed ground order +29294: Facts: +29294: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29294: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29294: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29294: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29294: Goal: +29294: Id : 1, {_}: + implies (implies (implies x y) y) + (implies (implies y z) (implies x z)) + =>= + truth + [] by prove_wajsberg_lemma +29294: Order: +29294: kbo +29294: Leaf order: +29294: x 2 0 2 1,1,1,2 +29294: z 2 0 2 2,1,2,2 +29294: y 3 0 3 2,1,1,2 +29294: truth 4 0 1 3 +29294: not 2 1 0 +29294: implies 19 2 6 0,2 +NO CLASH, using fixed ground order +29295: Facts: +29295: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29295: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29295: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29295: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29295: Goal: +29295: Id : 1, {_}: + implies (implies (implies x y) y) + (implies (implies y z) (implies x z)) + =>= + truth + [] by prove_wajsberg_lemma +29295: Order: +29295: lpo +29295: Leaf order: +29295: x 2 0 2 1,1,1,2 +29295: z 2 0 2 2,1,2,2 +29295: y 3 0 3 2,1,1,2 +29295: truth 4 0 1 3 +29295: not 2 1 0 +29295: implies 19 2 6 0,2 +% SZS status Timeout for LCL137-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +29381: Facts: +29381: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29381: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29381: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29381: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29381: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +29381: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +29381: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +29381: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +29381: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +29381: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +29381: Goal: +29381: Id : 1, {_}: + not (or (and x (or x x)) (and x x)) + =<= + and (not x) (or (or (not x) (not x)) (and (not x) (not x))) + [] by prove_wajsberg_theorem +29381: Order: +29381: kbo +29381: Leaf order: +29381: truth 3 0 0 +29381: x 10 0 10 1,1,1,2 +29381: not 12 1 6 0,2 +29381: and 11 2 4 0,1,1,2 +29381: or 12 2 4 0,1,2 +29381: implies 14 2 0 +29380: Facts: +29380: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29380: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29380: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29380: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29380: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +29380: Id : 7, {_}: + or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +29380: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +29380: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +29380: Id : 10, {_}: + and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +29380: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +29380: Goal: +29380: Id : 1, {_}: + not (or (and x (or x x)) (and x x)) + =<= + and (not x) (or (or (not x) (not x)) (and (not x) (not x))) + [] by prove_wajsberg_theorem +29380: Order: +29380: nrkbo +29380: Leaf order: +29380: truth 3 0 0 +29380: x 10 0 10 1,1,1,2 +29380: not 12 1 6 0,2 +29380: and 11 2 4 0,1,1,2 +29380: or 12 2 4 0,1,2 +29380: implies 14 2 0 +NO CLASH, using fixed ground order +29382: Facts: +29382: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +29382: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +29382: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +29382: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +29382: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +29382: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +29382: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +29382: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +29382: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +29382: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +29382: Goal: +29382: Id : 1, {_}: + not (or (and x (or x x)) (and x x)) + =<= + and (not x) (or (or (not x) (not x)) (and (not x) (not x))) + [] by prove_wajsberg_theorem +29382: Order: +29382: lpo +29382: Leaf order: +29382: truth 3 0 0 +29382: x 10 0 10 1,1,1,2 +29382: not 12 1 6 0,2 +29382: and 11 2 4 0,1,1,2 +29382: or 12 2 4 0,1,2 +29382: implies 14 2 0 +% SZS status Timeout for LCL165-1.p +NO CLASH, using fixed ground order +29399: Facts: +29399: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29399: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29399: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29399: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29399: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29399: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29399: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29399: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29399: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29399: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29399: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29399: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29399: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29399: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29399: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29399: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29399: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29399: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29399: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29399: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29399: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29399: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29399: Goal: +29399: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +29399: Order: +29399: nrkbo +29399: Leaf order: +29399: u 2 0 2 1,3,2 +29399: v 2 0 2 2,3,2 +29399: x 3 0 3 1,2 +29399: y 3 0 3 2,2 +29399: additive_identity 8 0 0 +29399: additive_inverse 22 1 0 +29399: commutator 1 2 0 +29399: add 26 2 2 0,3,2 +29399: multiply 40 2 0 +29399: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29400: Facts: +29400: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29400: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29400: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29400: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29400: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29400: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29400: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29400: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29400: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29400: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29400: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29400: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29400: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29400: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29400: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29400: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29400: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29400: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29400: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29400: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29400: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29400: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29400: Goal: +29400: Id : 1, {_}: + associator x y (add u v) + =<= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +29400: Order: +29400: kbo +29400: Leaf order: +29400: u 2 0 2 1,3,2 +29400: v 2 0 2 2,3,2 +29400: x 3 0 3 1,2 +29400: y 3 0 3 2,2 +29400: additive_identity 8 0 0 +29400: additive_inverse 22 1 0 +29400: commutator 1 2 0 +29400: add 26 2 2 0,3,2 +29400: multiply 40 2 0 +29400: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29401: Facts: +29401: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29401: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29401: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29401: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29401: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29401: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29401: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29401: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29401: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29401: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29401: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29401: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29401: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29401: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29401: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29401: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29401: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29401: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29401: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29401: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29401: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29401: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29401: Goal: +29401: Id : 1, {_}: + associator x y (add u v) + =>= + add (associator x y u) (associator x y v) + [] by prove_linearised_form1 +29401: Order: +29401: lpo +29401: Leaf order: +29401: u 2 0 2 1,3,2 +29401: v 2 0 2 2,3,2 +29401: x 3 0 3 1,2 +29401: y 3 0 3 2,2 +29401: additive_identity 8 0 0 +29401: additive_inverse 22 1 0 +29401: commutator 1 2 0 +29401: add 26 2 2 0,3,2 +29401: multiply 40 2 0 +29401: associator 4 3 3 0,2 +% SZS status Timeout for RNG019-7.p +NO CLASH, using fixed ground order +29433: Facts: +29433: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29433: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29433: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29433: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29433: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29433: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29433: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29433: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29433: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29433: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29433: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29433: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29433: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29433: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29433: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29433: Goal: +29433: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +29433: Order: +29433: kbo +29433: Leaf order: +29433: u 2 0 2 1,2,2 +29433: v 2 0 2 2,2,2 +29433: x 3 0 3 1,2 +29433: y 3 0 3 3,2 +29433: additive_identity 8 0 0 +29433: additive_inverse 6 1 0 +29433: commutator 1 2 0 +29433: add 18 2 2 0,2,2 +29433: multiply 22 2 0 +29433: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29434: Facts: +29434: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29434: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29434: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29434: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29434: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29434: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29434: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29434: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29434: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29434: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29434: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29434: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29434: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29434: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29434: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29434: Goal: +29434: Id : 1, {_}: + associator x (add u v) y + =>= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +29434: Order: +29434: lpo +29434: Leaf order: +29434: u 2 0 2 1,2,2 +29434: v 2 0 2 2,2,2 +29434: x 3 0 3 1,2 +29434: y 3 0 3 3,2 +29434: additive_identity 8 0 0 +29434: additive_inverse 6 1 0 +29434: commutator 1 2 0 +29434: add 18 2 2 0,2,2 +29434: multiply 22 2 0 +29434: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29432: Facts: +29432: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29432: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29432: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29432: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29432: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29432: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29432: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29432: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29432: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29432: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29432: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29432: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29432: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29432: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29432: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29432: Goal: +29432: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +29432: Order: +29432: nrkbo +29432: Leaf order: +29432: u 2 0 2 1,2,2 +29432: v 2 0 2 2,2,2 +29432: x 3 0 3 1,2 +29432: y 3 0 3 3,2 +29432: additive_identity 8 0 0 +29432: additive_inverse 6 1 0 +29432: commutator 1 2 0 +29432: add 18 2 2 0,2,2 +29432: multiply 22 2 0 +29432: associator 4 3 3 0,2 +% SZS status Timeout for RNG020-6.p +NO CLASH, using fixed ground order +29471: Facts: +29471: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29471: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29471: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29471: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29471: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29471: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29471: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29471: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29471: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29471: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29471: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29471: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29471: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29471: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29471: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29471: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29471: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29471: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29471: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29471: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29471: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29471: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29471: Goal: +29471: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +29471: Order: +29471: nrkbo +29471: Leaf order: +29471: u 2 0 2 1,2,2 +29471: v 2 0 2 2,2,2 +29471: x 3 0 3 1,2 +29471: y 3 0 3 3,2 +29471: additive_identity 8 0 0 +29471: additive_inverse 22 1 0 +29471: commutator 1 2 0 +29471: add 26 2 2 0,2,2 +29471: multiply 40 2 0 +29471: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29472: Facts: +29472: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29472: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29472: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29472: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29472: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29472: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29472: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29472: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29472: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29472: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29472: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29472: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29472: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29472: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29472: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29472: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29472: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29472: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29472: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29472: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29472: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29472: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29472: Goal: +29472: Id : 1, {_}: + associator x (add u v) y + =<= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +29472: Order: +29472: kbo +29472: Leaf order: +29472: u 2 0 2 1,2,2 +29472: v 2 0 2 2,2,2 +29472: x 3 0 3 1,2 +29472: y 3 0 3 3,2 +29472: additive_identity 8 0 0 +29472: additive_inverse 22 1 0 +29472: commutator 1 2 0 +29472: add 26 2 2 0,2,2 +29472: multiply 40 2 0 +29472: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29473: Facts: +29473: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29473: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29473: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29473: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29473: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29473: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29473: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29473: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29473: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29473: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29473: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29473: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29473: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29473: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29473: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29473: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29473: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29473: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29473: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29473: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29473: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29473: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29473: Goal: +29473: Id : 1, {_}: + associator x (add u v) y + =>= + add (associator x u y) (associator x v y) + [] by prove_linearised_form2 +29473: Order: +29473: lpo +29473: Leaf order: +29473: u 2 0 2 1,2,2 +29473: v 2 0 2 2,2,2 +29473: x 3 0 3 1,2 +29473: y 3 0 3 3,2 +29473: additive_identity 8 0 0 +29473: additive_inverse 22 1 0 +29473: commutator 1 2 0 +29473: add 26 2 2 0,2,2 +29473: multiply 40 2 0 +29473: associator 4 3 3 0,2 +% SZS status Timeout for RNG020-7.p +NO CLASH, using fixed ground order +29501: Facts: +29501: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29501: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29501: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29501: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29501: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29501: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29501: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29501: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29501: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29501: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29501: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29501: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29501: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29501: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29501: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29501: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29501: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29501: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29501: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29501: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29501: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29501: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29501: Goal: +29501: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +29501: Order: +29501: nrkbo +29501: Leaf order: +29501: u 2 0 2 1,1,2 +29501: v 2 0 2 2,1,2 +29501: x 3 0 3 2,2 +29501: y 3 0 3 3,2 +29501: additive_identity 8 0 0 +29501: additive_inverse 22 1 0 +29501: commutator 1 2 0 +29501: add 26 2 2 0,1,2 +29501: multiply 40 2 0 +29501: associator 4 3 3 0,2 +NO CLASH, using fixed ground order +29502: Facts: +29502: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29502: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +NO CLASH, using fixed ground order +29503: Facts: +29502: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29502: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29502: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29502: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29502: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29502: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29502: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29502: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29502: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29502: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29502: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29502: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29502: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29502: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29502: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29502: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29502: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29502: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29502: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29502: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29502: Goal: +29502: Id : 1, {_}: + associator (add u v) x y + =<= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +29502: Order: +29502: kbo +29502: Leaf order: +29502: u 2 0 2 1,1,2 +29502: v 2 0 2 2,1,2 +29502: x 3 0 3 2,2 +29502: y 3 0 3 3,2 +29502: additive_identity 8 0 0 +29502: additive_inverse 22 1 0 +29502: commutator 1 2 0 +29502: add 26 2 2 0,1,2 +29502: multiply 40 2 0 +29502: associator 4 3 3 0,2 +29503: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29503: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29503: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29503: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29503: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29503: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29503: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29503: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29503: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29503: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29503: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29503: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29503: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29503: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29503: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29503: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +29503: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +29503: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +29503: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +29503: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +29503: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +29503: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +29503: Goal: +29503: Id : 1, {_}: + associator (add u v) x y + =>= + add (associator u x y) (associator v x y) + [] by prove_linearised_form3 +29503: Order: +29503: lpo +29503: Leaf order: +29503: u 2 0 2 1,1,2 +29503: v 2 0 2 2,1,2 +29503: x 3 0 3 2,2 +29503: y 3 0 3 3,2 +29503: additive_identity 8 0 0 +29503: additive_inverse 22 1 0 +29503: commutator 1 2 0 +29503: add 26 2 2 0,1,2 +29503: multiply 40 2 0 +29503: associator 4 3 3 0,2 +% SZS status Timeout for RNG021-7.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +29520: Facts: +29520: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29520: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29520: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29520: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29520: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29520: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29520: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29520: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29520: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29520: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29520: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29520: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29520: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29520: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29520: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29520: Goal: +29520: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +29520: Order: +29520: kbo +29520: Leaf order: +29520: x 2 0 2 1,1,2 +29520: y 2 0 2 2,1,2 +29520: z 2 0 2 3,1,2 +29520: additive_identity 9 0 1 3 +29520: additive_inverse 6 1 0 +29520: commutator 1 2 0 +29520: add 17 2 1 0,2 +29520: multiply 22 2 0 +29520: associator 3 3 2 0,1,2 +29519: Facts: +29519: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29519: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29519: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29519: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29519: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29519: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29519: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29519: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29519: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29519: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29519: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29519: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29519: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29519: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29519: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29519: Goal: +29519: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +29519: Order: +29519: nrkbo +29519: Leaf order: +29519: x 2 0 2 1,1,2 +29519: y 2 0 2 2,1,2 +29519: z 2 0 2 3,1,2 +29519: additive_identity 9 0 1 3 +29519: additive_inverse 6 1 0 +29519: commutator 1 2 0 +29519: add 17 2 1 0,2 +29519: multiply 22 2 0 +29519: associator 3 3 2 0,1,2 +NO CLASH, using fixed ground order +29521: Facts: +29521: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +29521: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +29521: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +29521: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +29521: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +29521: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +29521: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +29521: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +29521: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +29521: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +29521: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +29521: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29521: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29521: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +29521: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +29521: Goal: +29521: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +29521: Order: +29521: lpo +29521: Leaf order: +29521: x 2 0 2 1,1,2 +29521: y 2 0 2 2,1,2 +29521: z 2 0 2 3,1,2 +29521: additive_identity 9 0 1 3 +29521: additive_inverse 6 1 0 +29521: commutator 1 2 0 +29521: add 17 2 1 0,2 +29521: multiply 22 2 0 +29521: associator 3 3 2 0,1,2 +% SZS status Timeout for RNG025-4.p +NO CLASH, using fixed ground order +29553: Facts: +29553: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29553: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29553: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29553: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29553: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29553: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29553: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29553: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29553: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29553: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29553: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29553: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29553: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29553: Id : 15, {_}: + associator ?37 ?38 (add ?39 ?40) + =<= + add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40) + [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40 +29553: Id : 16, {_}: + associator ?42 (add ?43 ?44) ?45 + =<= + add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45) + [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45 +29553: Id : 17, {_}: + associator (add ?47 ?48) ?49 ?50 + =<= + add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50) + [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50 +29553: Id : 18, {_}: + commutator ?52 ?53 + =<= + add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53)) + [53, 52] by commutator ?52 ?53 +29553: Goal: +29553: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +29553: Order: +29553: nrkbo +29553: Leaf order: +29553: a 2 0 2 1,1,2 +29553: b 2 0 2 2,1,2 +29553: c 2 0 2 3,1,2 +29553: additive_identity 9 0 1 3 +29553: additive_inverse 5 1 0 +29553: commutator 1 2 0 +29553: multiply 18 2 0 +29553: add 22 2 1 0,2 +29553: associator 11 3 2 0,1,2 +NO CLASH, using fixed ground order +29554: Facts: +29554: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29554: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29554: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29554: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29554: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29554: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29554: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29554: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29554: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29554: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29554: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29554: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29554: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29554: Id : 15, {_}: + associator ?37 ?38 (add ?39 ?40) + =<= + add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40) + [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40 +29554: Id : 16, {_}: + associator ?42 (add ?43 ?44) ?45 + =<= + add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45) + [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45 +29554: Id : 17, {_}: + associator (add ?47 ?48) ?49 ?50 + =<= + add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50) + [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50 +29554: Id : 18, {_}: + commutator ?52 ?53 + =<= + add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53)) + [53, 52] by commutator ?52 ?53 +29554: Goal: +29554: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +29554: Order: +29554: kbo +29554: Leaf order: +29554: a 2 0 2 1,1,2 +29554: b 2 0 2 2,1,2 +29554: c 2 0 2 3,1,2 +29554: additive_identity 9 0 1 3 +29554: additive_inverse 5 1 0 +29554: commutator 1 2 0 +29554: multiply 18 2 0 +29554: add 22 2 1 0,2 +29554: associator 11 3 2 0,1,2 +NO CLASH, using fixed ground order +29555: Facts: +29555: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +29555: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +29555: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +29555: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +29555: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +29555: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +29555: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +29555: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +29555: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +29555: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +29555: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +29555: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +29555: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +29555: Id : 15, {_}: + associator ?37 ?38 (add ?39 ?40) + =>= + add (associator ?37 ?38 ?39) (associator ?37 ?38 ?40) + [40, 39, 38, 37] by linearised_associator1 ?37 ?38 ?39 ?40 +29555: Id : 16, {_}: + associator ?42 (add ?43 ?44) ?45 + =>= + add (associator ?42 ?43 ?45) (associator ?42 ?44 ?45) + [45, 44, 43, 42] by linearised_associator2 ?42 ?43 ?44 ?45 +29555: Id : 17, {_}: + associator (add ?47 ?48) ?49 ?50 + =>= + add (associator ?47 ?49 ?50) (associator ?48 ?49 ?50) + [50, 49, 48, 47] by linearised_associator3 ?47 ?48 ?49 ?50 +29555: Id : 18, {_}: + commutator ?52 ?53 + =<= + add (multiply ?53 ?52) (additive_inverse (multiply ?52 ?53)) + [53, 52] by commutator ?52 ?53 +29555: Goal: +29555: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +29555: Order: +29555: lpo +29555: Leaf order: +29555: a 2 0 2 1,1,2 +29555: b 2 0 2 2,1,2 +29555: c 2 0 2 3,1,2 +29555: additive_identity 9 0 1 3 +29555: additive_inverse 5 1 0 +29555: commutator 1 2 0 +29555: multiply 18 2 0 +29555: add 22 2 1 0,2 +29555: associator 11 3 2 0,1,2 +% SZS status Timeout for RNG025-8.p +NO CLASH, using fixed ground order +29571: Facts: +29571: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29571: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29571: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29571: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29571: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29571: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29571: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29571: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29571: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29571: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29571: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29571: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29571: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29571: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29571: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29571: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29571: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29571: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29571: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29571: Id : 21, {_}: + multiply (multiply ?59 ?59) ?60 =?= multiply ?59 (multiply ?59 ?60) + [60, 59] by left_alternative ?59 ?60 +29571: Id : 22, {_}: + associator ?62 ?63 (add ?64 ?65) + =<= + add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65) + [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65 +29571: Id : 23, {_}: + associator ?67 (add ?68 ?69) ?70 + =<= + add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70) + [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70 +29571: Id : 24, {_}: + associator (add ?72 ?73) ?74 ?75 + =<= + add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75) + [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75 +29571: Id : 25, {_}: + commutator ?77 ?78 + =<= + add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78)) + [78, 77] by commutator ?77 ?78 +29571: Goal: +29571: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +29571: Order: +29571: nrkbo +29571: Leaf order: +29571: a 2 0 2 1,1,2 +29571: b 2 0 2 2,1,2 +29571: c 2 0 2 3,1,2 +29571: additive_identity 9 0 1 3 +29571: additive_inverse 21 1 0 +29571: commutator 1 2 0 +29571: add 30 2 1 0,2 +29571: multiply 36 2 0 add +29571: associator 11 3 2 0,1,2 +NO CLASH, using fixed ground order +29572: Facts: +NO CLASH, using fixed ground order +29572: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29572: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29572: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29572: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29572: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29572: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29572: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29572: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29572: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29572: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29572: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29572: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29572: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29572: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29572: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29572: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29572: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29572: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29572: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29572: Id : 21, {_}: + multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60) + [60, 59] by left_alternative ?59 ?60 +29572: Id : 22, {_}: + associator ?62 ?63 (add ?64 ?65) + =<= + add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65) + [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65 +29572: Id : 23, {_}: + associator ?67 (add ?68 ?69) ?70 + =<= + add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70) + [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70 +29572: Id : 24, {_}: + associator (add ?72 ?73) ?74 ?75 + =<= + add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75) + [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75 +29572: Id : 25, {_}: + commutator ?77 ?78 + =<= + add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78)) + [78, 77] by commutator ?77 ?78 +29572: Goal: +29572: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +29572: Order: +29572: kbo +29572: Leaf order: +29572: a 2 0 2 1,1,2 +29572: b 2 0 2 2,1,2 +29572: c 2 0 2 3,1,2 +29572: additive_identity 9 0 1 3 +29572: additive_inverse 21 1 0 +29572: commutator 1 2 0 +29572: add 30 2 1 0,2 +29572: multiply 36 2 0 add +29572: associator 11 3 2 0,1,2 +29573: Facts: +29573: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +29573: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +29573: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +29573: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +29573: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +29573: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +29573: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +29573: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +29573: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +29573: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +29573: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +29573: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +29573: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +29573: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +29573: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +29573: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +29573: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +29573: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +29573: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +29573: Id : 21, {_}: + multiply (multiply ?59 ?59) ?60 =>= multiply ?59 (multiply ?59 ?60) + [60, 59] by left_alternative ?59 ?60 +29573: Id : 22, {_}: + associator ?62 ?63 (add ?64 ?65) + =>= + add (associator ?62 ?63 ?64) (associator ?62 ?63 ?65) + [65, 64, 63, 62] by linearised_associator1 ?62 ?63 ?64 ?65 +29573: Id : 23, {_}: + associator ?67 (add ?68 ?69) ?70 + =>= + add (associator ?67 ?68 ?70) (associator ?67 ?69 ?70) + [70, 69, 68, 67] by linearised_associator2 ?67 ?68 ?69 ?70 +29573: Id : 24, {_}: + associator (add ?72 ?73) ?74 ?75 + =>= + add (associator ?72 ?74 ?75) (associator ?73 ?74 ?75) + [75, 74, 73, 72] by linearised_associator3 ?72 ?73 ?74 ?75 +29573: Id : 25, {_}: + commutator ?77 ?78 + =<= + add (multiply ?78 ?77) (additive_inverse (multiply ?77 ?78)) + [78, 77] by commutator ?77 ?78 +29573: Goal: +29573: Id : 1, {_}: + add (associator a b c) (associator a c b) =>= additive_identity + [] by prove_flexible_law +29573: Order: +29573: lpo +29573: Leaf order: +29573: a 2 0 2 1,1,2 +29573: b 2 0 2 2,1,2 +29573: c 2 0 2 3,1,2 +29573: additive_identity 9 0 1 3 +29573: additive_inverse 21 1 0 +29573: commutator 1 2 0 +29573: add 30 2 1 0,2 +29573: multiply 36 2 0 add +29573: associator 11 3 2 0,1,2 +% SZS status Timeout for RNG025-9.p +NO CLASH, using fixed ground order +29618: Facts: +29618: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +29618: Id : 3, {_}: + multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) + [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +29618: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +29618: Id : 5, {_}: + pixley ?11 ?12 ?13 + =<= + add (multiply ?11 (inverse ?12)) + (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) + [13, 12, 11] by pixley_defn ?11 ?12 ?13 +29618: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +29618: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +29618: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +29618: Goal: +29618: Id : 1, {_}: + add a (multiply b c) =<= multiply (add a b) (add a c) + [] by prove_add_multiply_property +29618: Order: +29618: nrkbo +29618: Leaf order: +29618: n1 1 0 0 +29618: b 2 0 2 1,2,2 +29618: c 2 0 2 2,2,2 +29618: a 3 0 3 1,2 +29618: inverse 3 1 0 +29618: multiply 9 2 2 0,2,2 +29618: add 9 2 3 0,2 +29618: pixley 4 3 0 +NO CLASH, using fixed ground order +29619: Facts: +29619: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +29619: Id : 3, {_}: + multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) + [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +29619: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +29619: Id : 5, {_}: + pixley ?11 ?12 ?13 + =<= + add (multiply ?11 (inverse ?12)) + (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) + [13, 12, 11] by pixley_defn ?11 ?12 ?13 +29619: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +29619: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +29619: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +29619: Goal: +29619: Id : 1, {_}: + add a (multiply b c) =<= multiply (add a b) (add a c) + [] by prove_add_multiply_property +29619: Order: +29619: kbo +29619: Leaf order: +29619: n1 1 0 0 +29619: b 2 0 2 1,2,2 +29619: c 2 0 2 2,2,2 +29619: a 3 0 3 1,2 +29619: inverse 3 1 0 +29619: multiply 9 2 2 0,2,2 +29619: add 9 2 3 0,2 +29619: pixley 4 3 0 +NO CLASH, using fixed ground order +29621: Facts: +29621: Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +29621: Id : 3, {_}: + multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) + [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +29621: Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +29621: Id : 5, {_}: + pixley ?11 ?12 ?13 + =>= + add (multiply ?11 (inverse ?12)) + (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) + [13, 12, 11] by pixley_defn ?11 ?12 ?13 +29621: Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +29621: Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +29621: Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +29621: Goal: +29621: Id : 1, {_}: + add a (multiply b c) =>= multiply (add a b) (add a c) + [] by prove_add_multiply_property +29621: Order: +29621: lpo +29621: Leaf order: +29621: n1 1 0 0 +29621: b 2 0 2 1,2,2 +29621: c 2 0 2 2,2,2 +29621: a 3 0 3 1,2 +29621: inverse 3 1 0 +29621: multiply 9 2 2 0,2,2 +29621: add 9 2 3 0,2 +29621: pixley 4 3 0 +Statistics : +Max weight : 25 +Found proof, 25.954748s +% SZS status Unsatisfiable for BOO023-1.p +% SZS output start CNFRefutation for BOO023-1.p +Id : 6, {_}: pixley ?15 ?15 ?16 =>= ?16 [16, 15] by pixley1 ?15 ?16 +Id : 8, {_}: pixley ?21 ?22 ?21 =>= ?21 [22, 21] by pixley3 ?21 ?22 +Id : 7, {_}: pixley ?18 ?19 ?19 =>= ?18 [19, 18] by pixley2 ?18 ?19 +Id : 5, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (add (multiply ?11 ?13) (multiply (inverse ?12) ?13)) [13, 12, 11] by pixley_defn ?11 ?12 ?13 +Id : 4, {_}: add ?9 (inverse ?9) =>= n1 [9] by additive_inverse ?9 +Id : 12, {_}: multiply ?33 (add ?34 ?35) =<= add (multiply ?34 ?33) (multiply ?35 ?33) [35, 34, 33] by multiply_add_property ?33 ?34 ?35 +Id : 2, {_}: multiply (add ?2 ?3) ?3 =>= ?3 [3, 2] by multiply_add ?2 ?3 +Id : 3, {_}: multiply ?5 (add ?6 ?7) =<= add (multiply ?6 ?5) (multiply ?7 ?5) [7, 6, 5] by multiply_add_property ?5 ?6 ?7 +Id : 45, {_}: multiply (multiply ?127 (add ?128 ?129)) (multiply ?129 ?127) =>= multiply ?129 ?127 [129, 128, 127] by Super 2 with 3 at 1,2 +Id : 52, {_}: multiply (add ?156 ?157) (multiply ?157 (add ?158 (add ?156 ?157))) =>= multiply ?157 (add ?158 (add ?156 ?157)) [158, 157, 156] by Super 45 with 2 at 1,2 +Id : 13, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= add (multiply ?38 ?37) ?37 [39, 38, 37] by Super 12 with 2 at 2,3 +Id : 49, {_}: multiply (multiply ?143 n1) (multiply (inverse ?144) ?143) =>= multiply (inverse ?144) ?143 [144, 143] by Super 45 with 4 at 2,1,2 +Id : 21, {_}: pixley ?58 ?59 ?60 =<= add (multiply ?58 (inverse ?59)) (multiply ?60 (add ?58 (inverse ?59))) [60, 59, 58] by Demod 5 with 3 at 2,3 +Id : 24, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add (add ?69 (inverse ?70)) (inverse ?70))) [71, 70, 69] by Super 21 with 2 at 1,3 +Id : 19, {_}: pixley ?11 ?12 ?13 =<= add (multiply ?11 (inverse ?12)) (multiply ?13 (add ?11 (inverse ?12))) [13, 12, 11] by Demod 5 with 3 at 2,3 +Id : 162, {_}: multiply (pixley ?407 ?408 ?409) (multiply ?409 (add ?407 (inverse ?408))) =>= multiply ?409 (add ?407 (inverse ?408)) [409, 408, 407] by Super 2 with 19 at 1,2 +Id : 500, {_}: multiply ?959 (multiply ?960 (add ?959 (inverse ?960))) =>= multiply ?960 (add ?959 (inverse ?960)) [960, 959] by Super 162 with 7 at 1,2 +Id : 207, {_}: multiply (multiply ?494 n1) (multiply (inverse ?495) ?494) =>= multiply (inverse ?495) ?494 [495, 494] by Super 45 with 4 at 2,1,2 +Id : 211, {_}: multiply n1 (multiply (inverse ?507) (add ?508 n1)) =>= multiply (inverse ?507) (add ?508 n1) [508, 507] by Super 207 with 2 at 1,2 +Id : 16, {_}: multiply n1 (inverse ?49) =>= inverse ?49 [49] by Super 2 with 4 at 1,2 +Id : 60, {_}: multiply (inverse ?174) (add ?175 n1) =<= add (multiply ?175 (inverse ?174)) (inverse ?174) [175, 174] by Super 3 with 16 at 2,3 +Id : 61, {_}: multiply (inverse ?177) (add (add ?178 (inverse ?177)) n1) =>= add (inverse ?177) (inverse ?177) [178, 177] by Super 60 with 2 at 1,3 +Id : 14, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= add ?41 (multiply ?43 ?41) [43, 42, 41] by Super 12 with 2 at 1,3 +Id : 283, {_}: add (inverse ?177) (multiply n1 (inverse ?177)) =>= add (inverse ?177) (inverse ?177) [177] by Demod 61 with 14 at 2 +Id : 40, {_}: multiply (inverse ?110) (add n1 ?111) =<= add (inverse ?110) (multiply ?111 (inverse ?110)) [111, 110] by Super 3 with 16 at 1,3 +Id : 284, {_}: multiply (inverse ?177) (add n1 n1) =?= add (inverse ?177) (inverse ?177) [177] by Demod 283 with 40 at 2 +Id : 297, {_}: multiply n1 (add (inverse ?660) (inverse ?660)) =>= multiply (inverse ?660) (add n1 n1) [660] by Super 211 with 284 at 2,2 +Id : 505, {_}: multiply (inverse n1) (multiply (inverse n1) (add n1 n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Super 500 with 297 at 2,2 +Id : 513, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply n1 (add (inverse n1) (inverse n1)) [] by Demod 505 with 284 at 2,2 +Id : 514, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= multiply (inverse n1) (add n1 n1) [] by Demod 513 with 297 at 3 +Id : 515, {_}: multiply (inverse n1) (add (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 514 with 284 at 3 +Id : 522, {_}: pixley (inverse n1) n1 (inverse n1) =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Super 19 with 515 at 2,3 +Id : 525, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (add (inverse n1) (inverse n1)) [] by Demod 522 with 8 at 2 +Id : 543, {_}: multiply (inverse n1) (inverse n1) =<= add (multiply (multiply (inverse n1) (inverse n1)) (inverse n1)) (inverse n1) [] by Super 13 with 525 at 2,2 +Id : 39, {_}: multiply (inverse ?107) (add ?108 n1) =<= add (multiply ?108 (inverse ?107)) (inverse ?107) [108, 107] by Super 3 with 16 at 2,3 +Id : 557, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add (multiply (inverse n1) (inverse n1)) n1) [] by Demod 543 with 39 at 3 +Id : 22, {_}: pixley ?62 ?62 ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [63, 62] by Super 21 with 4 at 2,2,3 +Id : 116, {_}: ?322 =<= add (multiply ?323 (inverse ?323)) (multiply ?322 n1) [323, 322] by Demod 22 with 6 at 2 +Id : 131, {_}: ?358 =<= add (inverse n1) (multiply ?358 n1) [358] by Super 116 with 16 at 1,3 +Id : 144, {_}: add ?384 n1 =?= add (inverse n1) n1 [384] by Super 131 with 2 at 2,3 +Id : 132, {_}: add ?360 n1 =?= add (inverse n1) n1 [360] by Super 131 with 2 at 2,3 +Id : 145, {_}: add ?386 n1 =?= add ?387 n1 [387, 386] by Super 144 with 132 at 3 +Id : 730, {_}: multiply (inverse n1) (inverse n1) =<= multiply (inverse n1) (add ?1307 n1) [1307] by Super 557 with 145 at 2,3 +Id : 734, {_}: multiply (inverse n1) (inverse n1) =<= add (inverse n1) (inverse n1) [] by Super 730 with 284 at 3 +Id : 756, {_}: multiply (inverse n1) (multiply (inverse n1) (inverse n1)) =>= add (inverse n1) (inverse n1) [] by Demod 515 with 734 at 2,2 +Id : 757, {_}: multiply (inverse n1) (multiply (inverse n1) (inverse n1)) =>= multiply (inverse n1) (inverse n1) [] by Demod 756 with 734 at 3 +Id : 758, {_}: inverse n1 =<= add (multiply (inverse n1) (inverse n1)) (multiply (inverse n1) (inverse n1)) [] by Demod 525 with 734 at 2,3 +Id : 759, {_}: inverse n1 =<= multiply (inverse n1) (add (inverse n1) (inverse n1)) [] by Demod 758 with 3 at 3 +Id : 760, {_}: inverse n1 =<= multiply (inverse n1) (multiply (inverse n1) (inverse n1)) [] by Demod 759 with 734 at 2,3 +Id : 761, {_}: inverse n1 =<= multiply (inverse n1) (inverse n1) [] by Demod 757 with 760 at 2 +Id : 765, {_}: inverse n1 =<= add (inverse n1) (inverse n1) [] by Demod 734 with 761 at 2 +Id : 771, {_}: pixley (add (inverse n1) (inverse n1)) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (add (inverse n1) (inverse n1))) [1319] by Super 24 with 765 at 1,2,2,3 +Id : 809, {_}: pixley (inverse n1) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (add (inverse n1) (inverse n1))) [1319] by Demod 771 with 765 at 1,2 +Id : 810, {_}: pixley (inverse n1) n1 ?1319 =<= add (inverse n1) (multiply ?1319 (inverse n1)) [1319] by Demod 809 with 765 at 2,2,3 +Id : 859, {_}: pixley (inverse n1) n1 ?1388 =<= multiply (inverse n1) (add n1 ?1388) [1388] by Demod 810 with 40 at 3 +Id : 860, {_}: pixley (inverse n1) n1 (inverse n1) =>= multiply (inverse n1) n1 [] by Super 859 with 4 at 2,3 +Id : 885, {_}: inverse n1 =<= multiply (inverse n1) n1 [] by Demod 860 with 8 at 2 +Id : 902, {_}: multiply n1 (add ?1409 (inverse n1)) =<= add (multiply ?1409 n1) (inverse n1) [1409] by Super 3 with 885 at 2,3 +Id : 168, {_}: multiply ?429 (multiply ?430 (add ?429 (inverse ?430))) =>= multiply ?430 (add ?429 (inverse ?430)) [430, 429] by Super 162 with 7 at 1,2 +Id : 903, {_}: multiply n1 (add (inverse n1) ?1411) =<= add (inverse n1) (multiply ?1411 n1) [1411] by Super 3 with 885 at 1,3 +Id : 118, {_}: ?328 =<= add (inverse n1) (multiply ?328 n1) [328] by Super 116 with 16 at 1,3 +Id : 1013, {_}: multiply n1 (add (inverse n1) ?1510) =>= ?1510 [1510] by Demod 903 with 118 at 3 +Id : 1014, {_}: multiply n1 n1 =>= inverse (inverse n1) [] by Super 1013 with 4 at 2,2 +Id : 1051, {_}: multiply n1 (add n1 (inverse n1)) =<= add (inverse (inverse n1)) (inverse n1) [] by Super 902 with 1014 at 1,3 +Id : 1091, {_}: multiply n1 n1 =<= add (inverse (inverse n1)) (inverse n1) [] by Demod 1051 with 4 at 2,2 +Id : 1092, {_}: inverse (inverse n1) =<= add (inverse (inverse n1)) (inverse n1) [] by Demod 1091 with 1014 at 2 +Id : 1370, {_}: multiply (inverse (inverse n1)) (multiply n1 (inverse (inverse n1))) =>= multiply n1 (add (inverse (inverse n1)) (inverse n1)) [] by Super 168 with 1092 at 2,2,2 +Id : 1373, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =<= multiply n1 (add (inverse (inverse n1)) (inverse n1)) [] by Demod 1370 with 16 at 2,2 +Id : 1374, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =>= multiply n1 (inverse (inverse n1)) [] by Demod 1373 with 1092 at 2,3 +Id : 1375, {_}: multiply (inverse (inverse n1)) (inverse (inverse n1)) =>= inverse (inverse n1) [] by Demod 1374 with 16 at 3 +Id : 1407, {_}: multiply (inverse (inverse n1)) (add n1 (inverse (inverse n1))) =>= add (inverse (inverse n1)) (inverse (inverse n1)) [] by Super 40 with 1375 at 2,3 +Id : 1015, {_}: multiply n1 (add ?1513 n1) =>= n1 [1513] by Super 1013 with 145 at 2,2 +Id : 1292, {_}: n1 =<= add n1 (multiply n1 n1) [] by Super 14 with 1015 at 2 +Id : 1307, {_}: n1 =<= add n1 (inverse (inverse n1)) [] by Demod 1292 with 1014 at 2,3 +Id : 1421, {_}: multiply (inverse (inverse n1)) n1 =<= add (inverse (inverse n1)) (inverse (inverse n1)) [] by Demod 1407 with 1307 at 2,2 +Id : 1422, {_}: multiply (inverse (inverse n1)) n1 =<= multiply (inverse (inverse n1)) (add n1 n1) [] by Demod 1421 with 284 at 3 +Id : 111, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) (multiply ?63 n1) [62, 63] by Demod 22 with 6 at 2 +Id : 359, {_}: multiply (multiply ?774 n1) (add ?774 ?775) =<= add (multiply ?774 n1) (multiply ?775 (multiply ?774 n1)) [775, 774] by Super 14 with 111 at 1,2,2 +Id : 114, {_}: multiply ?317 (multiply ?317 n1) =>= multiply ?317 n1 [317] by Super 2 with 111 at 1,2 +Id : 364, {_}: multiply (multiply ?788 n1) (add ?788 ?788) =?= add (multiply ?788 n1) (multiply ?788 n1) [788] by Super 359 with 114 at 2,3 +Id : 390, {_}: multiply (multiply ?814 n1) (add ?814 ?814) =>= multiply n1 (add ?814 ?814) [814] by Demod 364 with 3 at 3 +Id : 391, {_}: multiply (multiply n1 n1) (add ?816 n1) =>= multiply n1 (add n1 n1) [816] by Super 390 with 145 at 2,2 +Id : 1050, {_}: multiply (inverse (inverse n1)) (add ?816 n1) =>= multiply n1 (add n1 n1) [816] by Demod 391 with 1014 at 1,2 +Id : 1286, {_}: multiply (inverse (inverse n1)) (add ?816 n1) =>= n1 [816] by Demod 1050 with 1015 at 3 +Id : 1423, {_}: multiply (inverse (inverse n1)) n1 =>= n1 [] by Demod 1422 with 1286 at 3 +Id : 1449, {_}: multiply n1 (add (inverse (inverse n1)) (inverse n1)) =>= add n1 (inverse n1) [] by Super 902 with 1423 at 1,3 +Id : 1452, {_}: multiply n1 (inverse (inverse n1)) =>= add n1 (inverse n1) [] by Demod 1449 with 1092 at 2,2 +Id : 1453, {_}: multiply n1 (inverse (inverse n1)) =>= n1 [] by Demod 1452 with 4 at 3 +Id : 1454, {_}: inverse (inverse n1) =>= n1 [] by Demod 1453 with 16 at 2 +Id : 1500, {_}: multiply (multiply ?2051 n1) (multiply n1 ?2051) =>= multiply (inverse (inverse n1)) ?2051 [2051] by Super 49 with 1454 at 1,2,2 +Id : 3169, {_}: multiply (multiply ?3985 n1) (multiply n1 ?3985) =>= multiply n1 ?3985 [3985] by Demod 1500 with 1454 at 1,3 +Id : 933, {_}: multiply n1 (add (inverse n1) ?1411) =>= ?1411 [1411] by Demod 903 with 118 at 3 +Id : 3175, {_}: multiply (multiply (add (inverse n1) ?3998) n1) ?3998 =>= multiply n1 (add (inverse n1) ?3998) [3998] by Super 3169 with 933 at 2,2 +Id : 1440, {_}: inverse (inverse n1) =<= add (inverse n1) n1 [] by Super 118 with 1423 at 2,3 +Id : 1591, {_}: n1 =<= add (inverse n1) n1 [] by Demod 1440 with 1454 at 2 +Id : 1602, {_}: add ?2105 n1 =>= n1 [2105] by Super 145 with 1591 at 3 +Id : 1719, {_}: multiply ?2217 n1 =<= add ?2217 (multiply n1 ?2217) [2217] by Super 14 with 1602 at 2,2 +Id : 1478, {_}: n1 =<= add n1 n1 [] by Demod 1307 with 1454 at 2,3 +Id : 1483, {_}: multiply n1 (add (inverse ?660) (inverse ?660)) =>= multiply (inverse ?660) n1 [660] by Demod 297 with 1478 at 2,3 +Id : 1482, {_}: multiply (inverse ?177) n1 =<= add (inverse ?177) (inverse ?177) [177] by Demod 284 with 1478 at 2,2 +Id : 1484, {_}: multiply n1 (multiply (inverse ?660) n1) =>= multiply (inverse ?660) n1 [660] by Demod 1483 with 1482 at 2,2 +Id : 1727, {_}: multiply (multiply (inverse ?2233) n1) n1 =<= add (multiply (inverse ?2233) n1) (multiply (inverse ?2233) n1) [2233] by Super 1719 with 1484 at 2,3 +Id : 1763, {_}: multiply (multiply (inverse ?2233) n1) n1 =<= multiply n1 (add (inverse ?2233) (inverse ?2233)) [2233] by Demod 1727 with 3 at 3 +Id : 1764, {_}: multiply (multiply (inverse ?2233) n1) n1 =>= multiply n1 (multiply (inverse ?2233) n1) [2233] by Demod 1763 with 1482 at 2,3 +Id : 1765, {_}: multiply (multiply (inverse ?2233) n1) n1 =>= multiply (inverse ?2233) n1 [2233] by Demod 1764 with 1484 at 3 +Id : 1914, {_}: multiply (inverse ?2603) n1 =<= add (inverse n1) (multiply (inverse ?2603) n1) [2603] by Super 118 with 1765 at 2,3 +Id : 1949, {_}: multiply (inverse ?2603) n1 =>= inverse ?2603 [2603] by Demod 1914 with 118 at 3 +Id : 1994, {_}: multiply n1 (add (inverse ?2679) ?2680) =<= add (inverse ?2679) (multiply ?2680 n1) [2680, 2679] by Super 3 with 1949 at 1,3 +Id : 2422, {_}: multiply n1 (multiply n1 (add (inverse n1) ?3107)) =>= multiply ?3107 n1 [3107] by Super 933 with 1994 at 2,2 +Id : 2437, {_}: multiply n1 ?3107 =?= multiply ?3107 n1 [3107] by Demod 2422 with 933 at 2,2 +Id : 3237, {_}: multiply (multiply n1 (add (inverse n1) ?3998)) ?3998 =>= multiply n1 (add (inverse n1) ?3998) [3998] by Demod 3175 with 2437 at 1,2 +Id : 3238, {_}: multiply (multiply n1 (add (inverse n1) ?3998)) ?3998 =>= ?3998 [3998] by Demod 3237 with 933 at 3 +Id : 3239, {_}: multiply ?3998 ?3998 =>= ?3998 [3998] by Demod 3238 with 933 at 1,2 +Id : 3295, {_}: multiply ?4085 (add ?4086 ?4085) =<= add (multiply ?4086 ?4085) ?4085 [4086, 4085] by Super 3 with 3239 at 2,3 +Id : 3506, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= multiply ?37 (add ?38 ?37) [39, 38, 37] by Demod 13 with 3295 at 3 +Id : 4221, {_}: multiply (add ?156 ?157) (multiply ?157 (add ?158 ?157)) =>= multiply ?157 (add ?158 (add ?156 ?157)) [158, 157, 156] by Demod 52 with 3506 at 2,2 +Id : 4233, {_}: multiply (add ?4966 ?4967) (multiply ?4967 (add ?4968 ?4967)) =>= multiply ?4967 (add ?4968 ?4967) [4968, 4967, 4966] by Demod 4221 with 3506 at 3 +Id : 1725, {_}: multiply (add (inverse n1) ?2230) n1 =<= add (add (inverse n1) ?2230) ?2230 [2230] by Super 1719 with 933 at 2,3 +Id : 2746, {_}: multiply n1 (add (inverse n1) ?2230) =<= add (add (inverse n1) ?2230) ?2230 [2230] by Demod 1725 with 2437 at 2 +Id : 2751, {_}: ?2230 =<= add (add (inverse n1) ?2230) ?2230 [2230] by Demod 2746 with 933 at 2 +Id : 4246, {_}: multiply (add ?5016 ?5017) (multiply ?5017 ?5017) =?= multiply ?5017 (add (add (inverse n1) ?5017) ?5017) [5017, 5016] by Super 4233 with 2751 at 2,2,2 +Id : 4327, {_}: multiply (add ?5016 ?5017) ?5017 =?= multiply ?5017 (add (add (inverse n1) ?5017) ?5017) [5017, 5016] by Demod 4246 with 3239 at 2,2 +Id : 3296, {_}: multiply ?4088 (add ?4088 ?4089) =<= add ?4088 (multiply ?4089 ?4088) [4089, 4088] by Super 3 with 3239 at 1,3 +Id : 3736, {_}: multiply ?41 (add (add ?42 ?41) ?43) =>= multiply ?41 (add ?41 ?43) [43, 42, 41] by Demod 14 with 3296 at 3 +Id : 4328, {_}: multiply (add ?5016 ?5017) ?5017 =?= multiply ?5017 (add ?5017 ?5017) [5017, 5016] by Demod 4327 with 3736 at 3 +Id : 4329, {_}: ?5017 =<= multiply ?5017 (add ?5017 ?5017) [5017] by Demod 4328 with 2 at 2 +Id : 3529, {_}: multiply ?4289 (add ?4290 ?4289) =<= add (multiply ?4290 ?4289) ?4289 [4290, 4289] by Super 3 with 3239 at 2,3 +Id : 3546, {_}: multiply ?4342 (add ?4342 ?4342) =>= add ?4342 ?4342 [4342] by Super 3529 with 3239 at 1,3 +Id : 4330, {_}: ?5017 =<= add ?5017 ?5017 [5017] by Demod 4329 with 3546 at 3 +Id : 4419, {_}: multiply ?5179 (add ?5180 ?5180) =>= multiply ?5180 ?5179 [5180, 5179] by Super 3 with 4330 at 3 +Id : 4472, {_}: multiply ?5179 ?5180 =?= multiply ?5180 ?5179 [5180, 5179] by Demod 4419 with 4330 at 2,2 +Id : 6559, {_}: multiply ?7216 (add ?7217 ?7218) =<= add (multiply ?7217 ?7216) (multiply ?7216 ?7218) [7218, 7217, 7216] by Super 3 with 4472 at 2,3 +Id : 4435, {_}: multiply ?5223 (add ?5224 ?5223) =<= multiply ?5223 (add ?5223 (add ?5224 ?5223)) [5224, 5223] by Super 3736 with 4330 at 2,2 +Id : 4446, {_}: multiply ?5223 (add ?5224 ?5223) =?= multiply ?5223 (add ?5223 ?5223) [5224, 5223] by Demod 4435 with 3506 at 3 +Id : 4447, {_}: multiply ?5223 (add ?5224 ?5223) =>= multiply ?5223 ?5223 [5224, 5223] by Demod 4446 with 4330 at 2,3 +Id : 4448, {_}: multiply ?5223 (add ?5224 ?5223) =>= ?5223 [5224, 5223] by Demod 4447 with 3239 at 3 +Id : 4587, {_}: multiply (add ?5347 ?5348) (add ?5349 ?5348) =<= add (multiply ?5349 (add ?5347 ?5348)) ?5348 [5349, 5348, 5347] by Super 3 with 4448 at 2,3 +Id : 13274, {_}: multiply ?16470 (add ?16471 ?16472) =<= add (multiply ?16471 ?16470) (multiply ?16470 ?16472) [16472, 16471, 16470] by Super 3 with 4472 at 2,3 +Id : 1990, {_}: inverse ?2668 =<= add (inverse n1) (inverse ?2668) [2668] by Super 118 with 1949 at 2,3 +Id : 2035, {_}: multiply (inverse n1) (multiply ?2698 (inverse ?2698)) =?= multiply ?2698 (add (inverse n1) (inverse ?2698)) [2698] by Super 168 with 1990 at 2,2,2 +Id : 2073, {_}: multiply (inverse n1) (multiply ?2698 (inverse ?2698)) =>= multiply ?2698 (inverse ?2698) [2698] by Demod 2035 with 1990 at 2,3 +Id : 3753, {_}: multiply n1 (multiply (inverse n1) (add (inverse n1) ?4498)) =>= multiply ?4498 (inverse n1) [4498] by Super 933 with 3296 at 2,2 +Id : 3737, {_}: multiply (inverse ?110) (add n1 ?111) =<= multiply (inverse ?110) (add (inverse ?110) ?111) [111, 110] by Demod 40 with 3296 at 3 +Id : 3799, {_}: multiply n1 (multiply (inverse n1) (add n1 ?4498)) =>= multiply ?4498 (inverse n1) [4498] by Demod 3753 with 3737 at 2,2 +Id : 811, {_}: pixley (inverse n1) n1 ?1319 =<= multiply (inverse n1) (add n1 ?1319) [1319] by Demod 810 with 40 at 3 +Id : 3800, {_}: multiply n1 (pixley (inverse n1) n1 ?4498) =>= multiply ?4498 (inverse n1) [4498] by Demod 3799 with 811 at 2,2 +Id : 1503, {_}: multiply (inverse (inverse n1)) (add n1 ?2058) =<= add (inverse (inverse n1)) (multiply ?2058 n1) [2058] by Super 40 with 1454 at 2,2,3 +Id : 1564, {_}: multiply n1 (add n1 ?2058) =<= add (inverse (inverse n1)) (multiply ?2058 n1) [2058] by Demod 1503 with 1454 at 1,2 +Id : 1565, {_}: multiply n1 (add n1 ?2058) =<= add n1 (multiply ?2058 n1) [2058] by Demod 1564 with 1454 at 1,3 +Id : 1981, {_}: multiply n1 (add n1 (inverse ?2643)) =>= add n1 (inverse ?2643) [2643] by Super 1565 with 1949 at 2,3 +Id : 2089, {_}: pixley n1 ?2784 n1 =<= add (multiply n1 (inverse ?2784)) (add n1 (inverse ?2784)) [2784] by Super 19 with 1981 at 2,3 +Id : 2096, {_}: n1 =<= add (multiply n1 (inverse ?2784)) (add n1 (inverse ?2784)) [2784] by Demod 2089 with 8 at 2 +Id : 2097, {_}: n1 =<= add (inverse ?2784) (add n1 (inverse ?2784)) [2784] by Demod 2096 with 16 at 1,3 +Id : 4563, {_}: ?4085 =<= add (multiply ?4086 ?4085) ?4085 [4086, 4085] by Demod 3295 with 4448 at 2 +Id : 4567, {_}: add ?5289 ?5290 =<= add ?5290 (add ?5289 ?5290) [5290, 5289] by Super 4563 with 4448 at 1,3 +Id : 5426, {_}: n1 =<= add n1 (inverse ?2784) [2784] by Demod 2097 with 4567 at 3 +Id : 5450, {_}: multiply n1 (multiply ?6117 n1) =<= multiply ?6117 (add n1 (inverse ?6117)) [6117] by Super 168 with 5426 at 2,2,2 +Id : 5478, {_}: multiply n1 (multiply ?6117 n1) =>= multiply ?6117 n1 [6117] by Demod 5450 with 5426 at 2,3 +Id : 2780, {_}: multiply n1 (add (inverse ?3598) ?3599) =<= add (inverse ?3598) (multiply n1 ?3599) [3599, 3598] by Super 1994 with 2437 at 2,3 +Id : 38, {_}: pixley n1 ?104 ?105 =<= add (inverse ?104) (multiply ?105 (add n1 (inverse ?104))) [105, 104] by Super 19 with 16 at 1,3 +Id : 5427, {_}: pixley n1 ?104 ?105 =<= add (inverse ?104) (multiply ?105 n1) [105, 104] by Demod 38 with 5426 at 2,2,3 +Id : 5431, {_}: pixley n1 ?104 ?105 =<= multiply n1 (add (inverse ?104) ?105) [105, 104] by Demod 5427 with 1994 at 3 +Id : 5434, {_}: pixley n1 ?3598 ?3599 =<= add (inverse ?3598) (multiply n1 ?3599) [3599, 3598] by Demod 2780 with 5431 at 2 +Id : 5505, {_}: pixley n1 ?6141 (multiply ?6142 n1) =>= add (inverse ?6141) (multiply ?6142 n1) [6142, 6141] by Super 5434 with 5478 at 2,3 +Id : 5432, {_}: pixley n1 ?2679 ?2680 =<= add (inverse ?2679) (multiply ?2680 n1) [2680, 2679] by Demod 1994 with 5431 at 2 +Id : 5574, {_}: pixley n1 ?6141 (multiply ?6142 n1) =>= pixley n1 ?6141 ?6142 [6142, 6141] by Demod 5505 with 5432 at 3 +Id : 5935, {_}: pixley n1 n1 ?6510 =>= multiply ?6510 n1 [6510] by Super 6 with 5574 at 2 +Id : 5952, {_}: ?6510 =<= multiply ?6510 n1 [6510] by Demod 5935 with 6 at 2 +Id : 5985, {_}: multiply n1 ?6117 =?= multiply ?6117 n1 [6117] by Demod 5478 with 5952 at 2,2 +Id : 5986, {_}: multiply n1 ?6117 =>= ?6117 [6117] by Demod 5985 with 5952 at 3 +Id : 5995, {_}: pixley (inverse n1) n1 ?4498 =>= multiply ?4498 (inverse n1) [4498] by Demod 3800 with 5986 at 2 +Id : 4560, {_}: multiply ?37 (add ?38 (add ?39 ?37)) =>= ?37 [39, 38, 37] by Demod 3506 with 4448 at 3 +Id : 4745, {_}: multiply n1 (add ?5532 (inverse n1)) =>= add ?5532 (inverse n1) [5532] by Super 933 with 4567 at 2,2 +Id : 4852, {_}: multiply ?5678 (add ?5678 (inverse n1)) =?= multiply n1 (add ?5678 (inverse n1)) [5678] by Super 168 with 4745 at 2,2 +Id : 4888, {_}: multiply ?5678 (add ?5678 (inverse n1)) =>= add ?5678 (inverse n1) [5678] by Demod 4852 with 4745 at 3 +Id : 5026, {_}: multiply (inverse ?5768) (add n1 (inverse n1)) =>= add (inverse ?5768) (inverse n1) [5768] by Super 3737 with 4888 at 3 +Id : 5122, {_}: multiply (inverse ?5768) n1 =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5026 with 4 at 2,2 +Id : 5123, {_}: multiply n1 (inverse ?5768) =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5122 with 2437 at 2 +Id : 5124, {_}: inverse ?5768 =<= add (inverse ?5768) (inverse n1) [5768] by Demod 5123 with 16 at 2 +Id : 5166, {_}: multiply (inverse n1) (add ?5860 (inverse ?5861)) =>= inverse n1 [5861, 5860] by Super 4560 with 5124 at 2,2,2 +Id : 6158, {_}: multiply ?6712 (inverse n1) =<= multiply (inverse n1) (add ?6712 (inverse (inverse n1))) [6712] by Super 168 with 5166 at 2,2 +Id : 6219, {_}: multiply ?6712 (inverse n1) =>= inverse n1 [6712] by Demod 6158 with 5166 at 3 +Id : 6251, {_}: pixley (inverse n1) n1 ?4498 =>= inverse n1 [4498] by Demod 5995 with 6219 at 3 +Id : 2037, {_}: pixley (inverse n1) ?2703 ?2704 =<= add (multiply (inverse n1) (inverse ?2703)) (multiply ?2704 (inverse ?2703)) [2704, 2703] by Super 19 with 1990 at 2,2,3 +Id : 2071, {_}: pixley (inverse n1) ?2703 ?2704 =<= multiply (inverse ?2703) (add (inverse n1) ?2704) [2704, 2703] by Demod 2037 with 3 at 3 +Id : 5976, {_}: ?63 =<= add (multiply ?62 (inverse ?62)) ?63 [62, 63] by Demod 111 with 5952 at 2,3 +Id : 6253, {_}: ?6806 =<= add (inverse n1) ?6806 [6806] by Super 5976 with 6219 at 1,3 +Id : 6304, {_}: pixley (inverse n1) ?2703 ?2704 =>= multiply (inverse ?2703) ?2704 [2704, 2703] by Demod 2071 with 6253 at 2,3 +Id : 6308, {_}: multiply (inverse n1) ?4498 =>= inverse n1 [4498] by Demod 6251 with 6304 at 2 +Id : 6315, {_}: inverse n1 =<= multiply ?2698 (inverse ?2698) [2698] by Demod 2073 with 6308 at 2 +Id : 6591, {_}: inverse n1 =<= multiply (inverse ?7342) ?7342 [7342] by Super 6315 with 4472 at 3 +Id : 13310, {_}: multiply (inverse ?16623) (add ?16624 ?16623) =?= add (multiply ?16624 (inverse ?16623)) (inverse n1) [16624, 16623] by Super 13274 with 6591 at 2,3 +Id : 6698, {_}: multiply ?7545 (add ?7545 (inverse ?7545)) =>= add ?7545 (inverse n1) [7545] by Super 3296 with 6591 at 2,3 +Id : 6721, {_}: multiply ?7545 n1 =<= add ?7545 (inverse n1) [7545] by Demod 6698 with 4 at 2,2 +Id : 6722, {_}: ?7545 =<= add ?7545 (inverse n1) [7545] by Demod 6721 with 5952 at 2 +Id : 13428, {_}: multiply (inverse ?16623) (add ?16624 ?16623) =>= multiply ?16624 (inverse ?16623) [16624, 16623] by Demod 13310 with 6722 at 3 +Id : 13655, {_}: multiply (add ?17100 ?17101) (add (inverse ?17101) ?17101) =>= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Super 4587 with 13428 at 1,3 +Id : 6531, {_}: ?7094 =<= add (multiply ?7094 ?7095) ?7094 [7095, 7094] by Super 4563 with 4472 at 1,3 +Id : 6689, {_}: multiply ?7513 (add (inverse ?7513) ?7514) =?= add (inverse n1) (multiply ?7514 ?7513) [7514, 7513] by Super 3 with 6591 at 1,3 +Id : 7566, {_}: multiply ?8615 (add (inverse ?8615) ?8616) =>= multiply ?8616 ?8615 [8616, 8615] by Demod 6689 with 6253 at 3 +Id : 7568, {_}: multiply ?8620 n1 =<= multiply (inverse (inverse ?8620)) ?8620 [8620] by Super 7566 with 4 at 2,2 +Id : 7615, {_}: ?8620 =<= multiply (inverse (inverse ?8620)) ?8620 [8620] by Demod 7568 with 5952 at 2 +Id : 7635, {_}: inverse (inverse ?8669) =<= add ?8669 (inverse (inverse ?8669)) [8669] by Super 6531 with 7615 at 1,3 +Id : 7710, {_}: pixley ?8783 (inverse ?8783) ?8784 =<= add (multiply ?8783 (inverse (inverse ?8783))) (multiply ?8784 (inverse (inverse ?8783))) [8784, 8783] by Super 19 with 7635 at 2,2,3 +Id : 9183, {_}: pixley ?10684 (inverse ?10684) ?10685 =<= multiply (inverse (inverse ?10684)) (add ?10684 ?10685) [10685, 10684] by Demod 7710 with 3 at 3 +Id : 9184, {_}: pixley ?10687 (inverse ?10687) (inverse ?10687) =>= multiply (inverse (inverse ?10687)) n1 [10687] by Super 9183 with 4 at 2,3 +Id : 9239, {_}: ?10687 =<= multiply (inverse (inverse ?10687)) n1 [10687] by Demod 9184 with 7 at 2 +Id : 9240, {_}: ?10687 =<= multiply n1 (inverse (inverse ?10687)) [10687] by Demod 9239 with 4472 at 3 +Id : 9241, {_}: ?10687 =<= inverse (inverse ?10687) [10687] by Demod 9240 with 5986 at 3 +Id : 9328, {_}: add (inverse ?10804) ?10804 =>= n1 [10804] by Super 4 with 9241 at 2,2 +Id : 13791, {_}: multiply (add ?17100 ?17101) n1 =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13655 with 9328 at 2,2 +Id : 13792, {_}: multiply n1 (add ?17100 ?17101) =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13791 with 4472 at 2 +Id : 14391, {_}: add ?18258 ?18259 =<= add (multiply ?18258 (inverse ?18259)) ?18259 [18259, 18258] by Demod 13792 with 5986 at 2 +Id : 6742, {_}: multiply ?7513 (add (inverse ?7513) ?7514) =>= multiply ?7514 ?7513 [7514, 7513] by Demod 6689 with 6253 at 3 +Id : 7563, {_}: multiply (add (inverse ?8606) ?8607) ?8606 =>= multiply ?8607 ?8606 [8607, 8606] by Super 4472 with 6742 at 3 +Id : 14401, {_}: add (add (inverse (inverse ?18285)) ?18286) ?18285 =>= add (multiply ?18286 (inverse ?18285)) ?18285 [18286, 18285] by Super 14391 with 7563 at 1,3 +Id : 14494, {_}: add (add ?18285 ?18286) ?18285 =<= add (multiply ?18286 (inverse ?18285)) ?18285 [18286, 18285] by Demod 14401 with 9241 at 1,1,2 +Id : 13793, {_}: add ?17100 ?17101 =<= add (multiply ?17100 (inverse ?17101)) ?17101 [17101, 17100] by Demod 13792 with 5986 at 2 +Id : 14495, {_}: add (add ?18285 ?18286) ?18285 =>= add ?18286 ?18285 [18286, 18285] by Demod 14494 with 13793 at 3 +Id : 6533, {_}: multiply ?7100 (add ?7100 ?7101) =<= add ?7100 (multiply ?7100 ?7101) [7101, 7100] by Super 3296 with 4472 at 2,3 +Id : 7753, {_}: pixley ?8783 (inverse ?8783) ?8784 =<= multiply (inverse (inverse ?8783)) (add ?8783 ?8784) [8784, 8783] by Demod 7710 with 3 at 3 +Id : 9278, {_}: pixley ?8783 (inverse ?8783) ?8784 =>= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 7753 with 9241 at 1,3 +Id : 7714, {_}: pixley (add ?8794 (inverse (inverse ?8794))) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (add (inverse (inverse ?8794)) (inverse (inverse ?8794)))) [8795, 8794] by Super 24 with 7635 at 1,2,2,3 +Id : 7746, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (add (inverse (inverse ?8794)) (inverse (inverse ?8794)))) [8795, 8794] by Demod 7714 with 7635 at 1,2 +Id : 7747, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= add (inverse (inverse ?8794)) (multiply ?8795 (inverse (inverse ?8794))) [8795, 8794] by Demod 7746 with 4330 at 2,2,3 +Id : 7748, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =<= multiply (inverse (inverse ?8794)) (add (inverse (inverse ?8794)) ?8795) [8795, 8794] by Demod 7747 with 3296 at 3 +Id : 7749, {_}: pixley (inverse (inverse ?8794)) (inverse ?8794) ?8795 =>= multiply (inverse (inverse ?8794)) (add n1 ?8795) [8795, 8794] by Demod 7748 with 3737 at 3 +Id : 9298, {_}: pixley ?8794 (inverse ?8794) ?8795 =?= multiply (inverse (inverse ?8794)) (add n1 ?8795) [8795, 8794] by Demod 7749 with 9241 at 1,2 +Id : 9299, {_}: pixley ?8794 (inverse ?8794) ?8795 =>= multiply ?8794 (add n1 ?8795) [8795, 8794] by Demod 9298 with 9241 at 1,3 +Id : 9310, {_}: multiply ?8783 (add n1 ?8784) =?= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9278 with 9299 at 2 +Id : 9334, {_}: n1 =<= add n1 ?10824 [10824] by Super 5426 with 9241 at 2,3 +Id : 9392, {_}: multiply ?8783 n1 =<= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9310 with 9334 at 2,2 +Id : 9393, {_}: ?8783 =<= multiply ?8783 (add ?8783 ?8784) [8784, 8783] by Demod 9392 with 5952 at 2 +Id : 9397, {_}: ?7100 =<= add ?7100 (multiply ?7100 ?7101) [7101, 7100] by Demod 6533 with 9393 at 2 +Id : 7652, {_}: multiply ?8717 (add (inverse (inverse ?8717)) ?8718) =>= add ?8717 (multiply ?8718 ?8717) [8718, 8717] by Super 3 with 7615 at 1,3 +Id : 8997, {_}: multiply ?10489 (add (inverse (inverse ?10489)) ?10490) =>= multiply ?10489 (add ?10489 ?10490) [10490, 10489] by Demod 7652 with 3296 at 3 +Id : 9013, {_}: multiply (add (inverse (inverse ?10527)) ?10528) ?10527 =>= multiply ?10527 (add ?10527 ?10528) [10528, 10527] by Super 8997 with 4472 at 2 +Id : 11578, {_}: multiply (add ?10527 ?10528) ?10527 =?= multiply ?10527 (add ?10527 ?10528) [10528, 10527] by Demod 9013 with 9241 at 1,1,2 +Id : 11579, {_}: multiply (add ?10527 ?10528) ?10527 =>= ?10527 [10528, 10527] by Demod 11578 with 9393 at 3 +Id : 11608, {_}: add ?13907 ?13908 =<= add (add ?13907 ?13908) ?13907 [13908, 13907] by Super 9397 with 11579 at 2,3 +Id : 14496, {_}: add ?18285 ?18286 =?= add ?18286 ?18285 [18286, 18285] by Demod 14495 with 11608 at 2 +Id : 20857, {_}: multiply ?26392 (add ?26393 ?26394) =<= add (multiply ?26392 ?26394) (multiply ?26393 ?26392) [26394, 26393, 26392] by Super 6559 with 14496 at 3 +Id : 6561, {_}: multiply ?7224 (add ?7225 ?7226) =<= add (multiply ?7224 ?7225) (multiply ?7226 ?7224) [7226, 7225, 7224] by Super 3 with 4472 at 1,3 +Id : 45701, {_}: multiply ?26392 (add ?26393 ?26394) =?= multiply ?26392 (add ?26394 ?26393) [26394, 26393, 26392] by Demod 20857 with 6561 at 3 +Id : 92, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (add ?268 ?269) (inverse ?270)) (add ?269 (multiply (inverse ?270) ?269)) [270, 269, 268] by Super 19 with 14 at 2,3 +Id : 88314, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (inverse ?270) (add ?268 ?269)) (add ?269 (multiply (inverse ?270) ?269)) [270, 269, 268] by Demod 92 with 4472 at 1,3 +Id : 9395, {_}: ?4088 =<= add ?4088 (multiply ?4089 ?4088) [4089, 4088] by Demod 3296 with 9393 at 2 +Id : 88315, {_}: pixley (add ?268 ?269) ?270 ?269 =<= add (multiply (inverse ?270) (add ?268 ?269)) ?269 [270, 269, 268] by Demod 88314 with 9395 at 2,3 +Id : 88452, {_}: pixley (add ?145802 ?145803) ?145804 ?145803 =<= multiply (add ?145802 ?145803) (add (inverse ?145804) ?145803) [145804, 145803, 145802] by Demod 88315 with 4587 at 3 +Id : 88455, {_}: pixley (add ?145816 ?145817) (inverse ?145818) ?145817 =>= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145818, 145817, 145816] by Super 88452 with 9241 at 1,2,3 +Id : 11, {_}: multiply (multiply ?29 (add ?30 ?31)) (multiply ?31 ?29) =>= multiply ?31 ?29 [31, 30, 29] by Super 2 with 3 at 1,2 +Id : 6691, {_}: multiply (inverse n1) (multiply ?7519 (inverse (add ?7520 ?7519))) =>= multiply ?7519 (inverse (add ?7520 ?7519)) [7520, 7519] by Super 11 with 6591 at 1,2 +Id : 6741, {_}: inverse n1 =<= multiply ?7519 (inverse (add ?7520 ?7519)) [7520, 7519] by Demod 6691 with 6308 at 2 +Id : 7453, {_}: pixley ?8439 (add ?8440 ?8439) ?8441 =<= add (inverse n1) (multiply ?8441 (add ?8439 (inverse (add ?8440 ?8439)))) [8441, 8440, 8439] by Super 19 with 6741 at 1,3 +Id : 7492, {_}: pixley ?8439 (add ?8440 ?8439) ?8441 =<= multiply ?8441 (add ?8439 (inverse (add ?8440 ?8439))) [8441, 8440, 8439] by Demod 7453 with 6253 at 3 +Id : 98274, {_}: pixley ?163996 (add ?163997 ?163996) n1 =>= add ?163996 (inverse (add ?163997 ?163996)) [163997, 163996] by Super 5986 with 7492 at 2 +Id : 4588, {_}: multiply (add ?5351 ?5352) (add ?5352 ?5353) =<= add ?5352 (multiply ?5353 (add ?5351 ?5352)) [5353, 5352, 5351] by Super 3 with 4448 at 1,3 +Id : 13309, {_}: multiply ?16620 (add ?16621 (inverse ?16620)) =?= add (multiply ?16621 ?16620) (inverse n1) [16621, 16620] by Super 13274 with 6315 at 2,3 +Id : 13427, {_}: multiply ?16620 (add ?16621 (inverse ?16620)) =>= multiply ?16621 ?16620 [16621, 16620] by Demod 13309 with 6722 at 3 +Id : 13531, {_}: multiply (add ?17007 (inverse ?17008)) (add (inverse ?17008) ?17008) =>= add (inverse ?17008) (multiply ?17007 ?17008) [17008, 17007] by Super 4588 with 13427 at 2,3 +Id : 11835, {_}: add ?14300 ?14301 =<= add (add ?14300 ?14301) ?14300 [14301, 14300] by Super 9397 with 11579 at 2,3 +Id : 11844, {_}: add ?14326 (add ?14327 ?14326) =?= add (add ?14327 ?14326) ?14326 [14327, 14326] by Super 11835 with 4567 at 1,3 +Id : 11909, {_}: add ?14327 ?14326 =<= add (add ?14327 ?14326) ?14326 [14326, 14327] by Demod 11844 with 4567 at 2 +Id : 11970, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= add (inverse ?70) (multiply ?71 (add ?69 (inverse ?70))) [71, 70, 69] by Demod 24 with 11909 at 2,2,3 +Id : 12697, {_}: pixley (add ?69 (inverse ?70)) ?70 ?71 =<= multiply (add ?69 (inverse ?70)) (add (inverse ?70) ?71) [71, 70, 69] by Demod 11970 with 4588 at 3 +Id : 13561, {_}: pixley (add ?17007 (inverse ?17008)) ?17008 ?17008 =>= add (inverse ?17008) (multiply ?17007 ?17008) [17008, 17007] by Demod 13531 with 12697 at 2 +Id : 14017, {_}: add ?17647 (inverse ?17648) =<= add (inverse ?17648) (multiply ?17647 ?17648) [17648, 17647] by Demod 13561 with 7 at 2 +Id : 10227, {_}: multiply (inverse ?12001) (add ?12001 ?12002) =>= multiply ?12002 (inverse ?12001) [12002, 12001] by Super 6742 with 9241 at 1,2,2 +Id : 10243, {_}: multiply (inverse ?12047) ?12047 =<= multiply (multiply ?12047 ?12048) (inverse ?12047) [12048, 12047] by Super 10227 with 9397 at 2,2 +Id : 10311, {_}: inverse n1 =<= multiply (multiply ?12047 ?12048) (inverse ?12047) [12048, 12047] by Demod 10243 with 6591 at 2 +Id : 10454, {_}: inverse n1 =<= multiply (inverse ?12293) (multiply ?12293 ?12294) [12294, 12293] by Demod 10311 with 4472 at 3 +Id : 10488, {_}: inverse n1 =<= multiply ?12387 (multiply (inverse ?12387) ?12388) [12388, 12387] by Super 10454 with 9241 at 1,3 +Id : 14062, {_}: add ?17790 (inverse (multiply (inverse ?17790) ?17791)) =?= add (inverse (multiply (inverse ?17790) ?17791)) (inverse n1) [17791, 17790] by Super 14017 with 10488 at 2,3 +Id : 14147, {_}: add ?17790 (inverse (multiply (inverse ?17790) ?17791)) =>= inverse (multiply (inverse ?17790) ?17791) [17791, 17790] by Demod 14062 with 6722 at 3 +Id : 20167, {_}: add ?25476 (inverse (multiply (inverse ?25476) ?25477)) =?= add (inverse (multiply (inverse ?25476) ?25477)) ?25476 [25477, 25476] by Super 11608 with 14147 at 1,3 +Id : 20309, {_}: inverse (multiply (inverse ?25476) ?25477) =<= add (inverse (multiply (inverse ?25476) ?25477)) ?25476 [25477, 25476] by Demod 20167 with 14147 at 2 +Id : 98343, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =<= add ?164219 (inverse (add (inverse (multiply (inverse ?164219) ?164220)) ?164219)) [164220, 164219] by Super 98274 with 20309 at 2,2 +Id : 98565, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164219 (inverse (inverse (multiply (inverse ?164219) ?164220))) [164220, 164219] by Demod 98343 with 20309 at 1,2,3 +Id : 98566, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164219 (multiply (inverse ?164219) ?164220) [164220, 164219] by Demod 98565 with 9241 at 2,3 +Id : 13654, {_}: multiply (add ?17097 ?17098) (add ?17098 (inverse ?17098)) =>= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Super 4588 with 13428 at 2,3 +Id : 13794, {_}: multiply (add ?17097 ?17098) n1 =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13654 with 4 at 2,2 +Id : 13795, {_}: multiply n1 (add ?17097 ?17098) =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13794 with 4472 at 2 +Id : 14561, {_}: add ?18466 ?18467 =<= add ?18467 (multiply ?18466 (inverse ?18467)) [18467, 18466] by Demod 13795 with 5986 at 2 +Id : 14565, {_}: add ?18477 ?18478 =<= add ?18478 (multiply (inverse ?18478) ?18477) [18478, 18477] by Super 14561 with 4472 at 2,3 +Id : 98567, {_}: pixley ?164219 (inverse (multiply (inverse ?164219) ?164220)) n1 =>= add ?164220 ?164219 [164220, 164219] by Demod 98566 with 14565 at 3 +Id : 7451, {_}: multiply (inverse (add ?8431 ?8432)) (add ?8433 ?8432) =?= add (multiply ?8433 (inverse (add ?8431 ?8432))) (inverse n1) [8433, 8432, 8431] by Super 3 with 6741 at 2,3 +Id : 7493, {_}: multiply (inverse (add ?8431 ?8432)) (add ?8433 ?8432) =>= multiply ?8433 (inverse (add ?8431 ?8432)) [8433, 8432, 8431] by Demod 7451 with 6722 at 3 +Id : 105415, {_}: pixley (add ?172221 ?172222) (inverse (multiply ?172223 (inverse (add ?172221 ?172222)))) n1 =>= add (add ?172223 ?172222) (add ?172221 ?172222) [172223, 172222, 172221] by Super 98567 with 7493 at 1,2,2 +Id : 10242, {_}: multiply (inverse ?12044) ?12044 =<= multiply (multiply ?12045 ?12044) (inverse ?12044) [12045, 12044] by Super 10227 with 9395 at 2,2 +Id : 10309, {_}: inverse n1 =<= multiply (multiply ?12045 ?12044) (inverse ?12044) [12044, 12045] by Demod 10242 with 6591 at 2 +Id : 10337, {_}: inverse n1 =<= multiply (inverse ?12122) (multiply ?12123 ?12122) [12123, 12122] by Demod 10309 with 4472 at 3 +Id : 10370, {_}: inverse n1 =<= multiply ?12222 (multiply ?12223 (inverse ?12222)) [12223, 12222] by Super 10337 with 9241 at 1,3 +Id : 14061, {_}: add ?17787 (inverse (multiply ?17788 (inverse ?17787))) =?= add (inverse (multiply ?17788 (inverse ?17787))) (inverse n1) [17788, 17787] by Super 14017 with 10370 at 2,3 +Id : 14146, {_}: add ?17787 (inverse (multiply ?17788 (inverse ?17787))) =>= inverse (multiply ?17788 (inverse ?17787)) [17788, 17787] by Demod 14061 with 6722 at 3 +Id : 19953, {_}: add ?25324 (inverse (multiply ?25325 (inverse ?25324))) =?= add (inverse (multiply ?25325 (inverse ?25324))) ?25324 [25325, 25324] by Super 11608 with 14146 at 1,3 +Id : 20011, {_}: inverse (multiply ?25325 (inverse ?25324)) =<= add (inverse (multiply ?25325 (inverse ?25324))) ?25324 [25324, 25325] by Demod 19953 with 14146 at 2 +Id : 98342, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =<= add ?164216 (inverse (add (inverse (multiply ?164217 (inverse ?164216))) ?164216)) [164217, 164216] by Super 98274 with 20011 at 2,2 +Id : 98562, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164216 (inverse (inverse (multiply ?164217 (inverse ?164216)))) [164217, 164216] by Demod 98342 with 20011 at 1,2,3 +Id : 98563, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164216 (multiply ?164217 (inverse ?164216)) [164217, 164216] by Demod 98562 with 9241 at 2,3 +Id : 13796, {_}: add ?17097 ?17098 =<= add ?17098 (multiply ?17097 (inverse ?17098)) [17098, 17097] by Demod 13795 with 5986 at 2 +Id : 98564, {_}: pixley ?164216 (inverse (multiply ?164217 (inverse ?164216))) n1 =>= add ?164217 ?164216 [164217, 164216] by Demod 98563 with 13796 at 3 +Id : 106322, {_}: add ?173840 (add ?173841 ?173842) =<= add (add ?173840 ?173842) (add ?173841 ?173842) [173842, 173841, 173840] by Demod 105415 with 98564 at 2 +Id : 106366, {_}: add ?174020 (add ?174021 (multiply ?174021 ?174022)) =?= add (add ?174020 (multiply ?174021 ?174022)) ?174021 [174022, 174021, 174020] by Super 106322 with 9397 at 2,3 +Id : 110603, {_}: add ?183991 ?183992 =<= add (add ?183991 (multiply ?183992 ?183993)) ?183992 [183993, 183992, 183991] by Demod 106366 with 9397 at 2,2 +Id : 111365, {_}: add (multiply ?185632 (inverse ?185633)) ?185634 =<= add (pixley ?185632 ?185633 ?185634) ?185634 [185634, 185633, 185632] by Super 110603 with 19 at 1,3 +Id : 5975, {_}: multiply ?143 (multiply (inverse ?144) ?143) =>= multiply (inverse ?144) ?143 [144, 143] by Demod 49 with 5952 at 1,2 +Id : 6517, {_}: multiply ?7054 (multiply ?7054 (inverse ?7055)) =>= multiply (inverse ?7055) ?7054 [7055, 7054] by Super 5975 with 4472 at 2,2 +Id : 7244, {_}: multiply (multiply ?8105 (inverse ?8106)) ?8105 =>= multiply (inverse ?8106) ?8105 [8106, 8105] by Super 4472 with 6517 at 3 +Id : 9315, {_}: multiply (multiply ?10762 ?10763) ?10762 =>= multiply (inverse (inverse ?10763)) ?10762 [10763, 10762] by Super 7244 with 9241 at 2,1,2 +Id : 9383, {_}: multiply (multiply ?10762 ?10763) ?10762 =>= multiply ?10763 ?10762 [10763, 10762] by Demod 9315 with 9241 at 1,3 +Id : 10069, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =<= add (multiply ?11746 (inverse ?11745)) (multiply ?11747 (add (multiply (inverse ?11745) ?11746) (inverse ?11745))) [11747, 11746, 11745] by Super 19 with 9383 at 1,3 +Id : 10131, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =<= add (multiply ?11746 (inverse ?11745)) (multiply ?11747 (inverse ?11745)) [11747, 11746, 11745] by Demod 10069 with 6531 at 2,2,3 +Id : 10132, {_}: pixley (multiply (inverse ?11745) ?11746) ?11745 ?11747 =>= multiply (inverse ?11745) (add ?11746 ?11747) [11747, 11746, 11745] by Demod 10131 with 3 at 3 +Id : 111375, {_}: add (multiply (multiply (inverse ?185663) ?185664) (inverse ?185663)) ?185665 =?= add (multiply (inverse ?185663) (add ?185664 ?185665)) ?185665 [185665, 185664, 185663] by Super 111365 with 10132 at 1,3 +Id : 111673, {_}: add (multiply (inverse ?185663) (multiply (inverse ?185663) ?185664)) ?185665 =?= add (multiply (inverse ?185663) (add ?185664 ?185665)) ?185665 [185665, 185664, 185663] by Demod 111375 with 4472 at 1,2 +Id : 111674, {_}: add (multiply (inverse ?185663) (multiply (inverse ?185663) ?185664)) ?185665 =?= multiply (add ?185664 ?185665) (add (inverse ?185663) ?185665) [185665, 185664, 185663] by Demod 111673 with 4587 at 3 +Id : 9338, {_}: multiply ?10835 (multiply ?10835 ?10836) =?= multiply (inverse (inverse ?10836)) ?10835 [10836, 10835] by Super 6517 with 9241 at 2,2,2 +Id : 9347, {_}: multiply ?10835 (multiply ?10835 ?10836) =>= multiply ?10836 ?10835 [10836, 10835] by Demod 9338 with 9241 at 1,3 +Id : 111675, {_}: add (multiply ?185664 (inverse ?185663)) ?185665 =<= multiply (add ?185664 ?185665) (add (inverse ?185663) ?185665) [185665, 185663, 185664] by Demod 111674 with 9347 at 1,2 +Id : 88316, {_}: pixley (add ?268 ?269) ?270 ?269 =<= multiply (add ?268 ?269) (add (inverse ?270) ?269) [270, 269, 268] by Demod 88315 with 4587 at 3 +Id : 111676, {_}: add (multiply ?185664 (inverse ?185663)) ?185665 =<= pixley (add ?185664 ?185665) ?185663 ?185665 [185665, 185663, 185664] by Demod 111675 with 88316 at 3 +Id : 111830, {_}: add (multiply ?145816 (inverse (inverse ?145818))) ?145817 =?= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145817, 145818, 145816] by Demod 88455 with 111676 at 2 +Id : 111831, {_}: add (multiply ?145816 ?145818) ?145817 =<= multiply (add ?145816 ?145817) (add ?145818 ?145817) [145817, 145818, 145816] by Demod 111830 with 9241 at 2,1,2 +Id : 112319, {_}: add a (multiply b c) === add a (multiply b c) [] by Demod 112318 with 14496 at 3 +Id : 112318, {_}: add a (multiply b c) =<= add (multiply b c) a [] by Demod 112317 with 111831 at 3 +Id : 112317, {_}: add a (multiply b c) =<= multiply (add b a) (add c a) [] by Demod 112316 with 4472 at 3 +Id : 112316, {_}: add a (multiply b c) =<= multiply (add c a) (add b a) [] by Demod 112315 with 45701 at 3 +Id : 112315, {_}: add a (multiply b c) =<= multiply (add c a) (add a b) [] by Demod 112314 with 4472 at 3 +Id : 112314, {_}: add a (multiply b c) =<= multiply (add a b) (add c a) [] by Demod 1 with 45701 at 3 +Id : 1, {_}: add a (multiply b c) =<= multiply (add a b) (add a c) [] by prove_add_multiply_property +% SZS output end CNFRefutation for BOO023-1.p +29618: solved BOO023-1.p in 25.957622 using nrkbo +29618: status Unsatisfiable for BOO023-1.p +NO CLASH, using fixed ground order +29626: Facts: +29626: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +29626: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +29626: Id : 4, {_}: + multiply ?11 ?11 ?12 =>= ?11 + [12, 11] by ternary_multiply_2 ?11 ?12 +29626: Id : 5, {_}: + multiply (inverse ?14) ?14 ?15 =>= ?15 + [15, 14] by left_inverse ?14 ?15 +29626: Id : 6, {_}: + multiply ?17 ?18 (inverse ?18) =>= ?17 + [18, 17] by right_inverse ?17 ?18 +29626: Goal: +29626: Id : 1, {_}: + multiply (multiply a (inverse a) b) + (inverse (multiply (multiply c d e) f (multiply c d g))) + (multiply d (multiply g f e) c) + =>= + b + [] by prove_single_axiom +29626: Order: +29626: nrkbo +29626: Leaf order: +29626: a 2 0 2 1,1,2 +29626: f 2 0 2 2,1,2,2 +29626: e 2 0 2 3,1,1,2,2 +29626: b 2 0 2 3,1,2 +29626: g 2 0 2 3,3,1,2,2 +29626: c 3 0 3 1,1,1,2,2 +29626: d 3 0 3 2,1,1,2,2 +29626: inverse 4 1 2 0,2,1,2 +29626: multiply 16 3 7 0,2 +NO CLASH, using fixed ground order +29627: Facts: +29627: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +29627: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +29627: Id : 4, {_}: + multiply ?11 ?11 ?12 =>= ?11 + [12, 11] by ternary_multiply_2 ?11 ?12 +29627: Id : 5, {_}: + multiply (inverse ?14) ?14 ?15 =>= ?15 + [15, 14] by left_inverse ?14 ?15 +29627: Id : 6, {_}: + multiply ?17 ?18 (inverse ?18) =>= ?17 + [18, 17] by right_inverse ?17 ?18 +29627: Goal: +29627: Id : 1, {_}: + multiply (multiply a (inverse a) b) + (inverse (multiply (multiply c d e) f (multiply c d g))) + (multiply d (multiply g f e) c) + =>= + b + [] by prove_single_axiom +29627: Order: +29627: kbo +29627: Leaf order: +29627: a 2 0 2 1,1,2 +29627: f 2 0 2 2,1,2,2 +29627: e 2 0 2 3,1,1,2,2 +29627: b 2 0 2 3,1,2 +29627: g 2 0 2 3,3,1,2,2 +29627: c 3 0 3 1,1,1,2,2 +29627: d 3 0 3 2,1,1,2,2 +29627: inverse 4 1 2 0,2,1,2 +29627: multiply 16 3 7 0,2 +NO CLASH, using fixed ground order +29628: Facts: +29628: Id : 2, {_}: + multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) + =>= + multiply ?2 ?3 (multiply ?4 ?5 ?6) + [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +29628: Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +29628: Id : 4, {_}: + multiply ?11 ?11 ?12 =>= ?11 + [12, 11] by ternary_multiply_2 ?11 ?12 +29628: Id : 5, {_}: + multiply (inverse ?14) ?14 ?15 =>= ?15 + [15, 14] by left_inverse ?14 ?15 +29628: Id : 6, {_}: + multiply ?17 ?18 (inverse ?18) =>= ?17 + [18, 17] by right_inverse ?17 ?18 +29628: Goal: +29628: Id : 1, {_}: + multiply (multiply a (inverse a) b) + (inverse (multiply (multiply c d e) f (multiply c d g))) + (multiply d (multiply g f e) c) + =>= + b + [] by prove_single_axiom +29628: Order: +29628: lpo +29628: Leaf order: +29628: a 2 0 2 1,1,2 +29628: f 2 0 2 2,1,2,2 +29628: e 2 0 2 3,1,1,2,2 +29628: b 2 0 2 3,1,2 +29628: g 2 0 2 3,3,1,2,2 +29628: c 3 0 3 1,1,1,2,2 +29628: d 3 0 3 2,1,1,2,2 +29628: inverse 4 1 2 0,2,1,2 +29628: multiply 16 3 7 0,2 +Statistics : +Max weight : 24 +Found proof, 10.457305s +% SZS status Unsatisfiable for BOO034-1.p +% SZS output start CNFRefutation for BOO034-1.p +Id : 5, {_}: multiply (inverse ?14) ?14 ?15 =>= ?15 [15, 14] by left_inverse ?14 ?15 +Id : 6, {_}: multiply ?17 ?18 (inverse ?18) =>= ?17 [18, 17] by right_inverse ?17 ?18 +Id : 4, {_}: multiply ?11 ?11 ?12 =>= ?11 [12, 11] by ternary_multiply_2 ?11 ?12 +Id : 3, {_}: multiply ?8 ?9 ?9 =>= ?9 [9, 8] by ternary_multiply_1 ?8 ?9 +Id : 2, {_}: multiply (multiply ?2 ?3 ?4) ?5 (multiply ?2 ?3 ?6) =>= multiply ?2 ?3 (multiply ?4 ?5 ?6) [6, 5, 4, 3, 2] by associativity ?2 ?3 ?4 ?5 ?6 +Id : 13, {_}: multiply ?53 ?54 (multiply ?55 ?53 ?56) =?= multiply ?55 ?53 (multiply ?53 ?54 ?56) [56, 55, 54, 53] by Super 2 with 3 at 1,2 +Id : 12, {_}: multiply (multiply ?48 ?49 ?50) ?51 ?49 =?= multiply ?48 ?49 (multiply ?50 ?51 ?49) [51, 50, 49, 48] by Super 2 with 3 at 3,2 +Id : 919, {_}: multiply (multiply ?2933 ?2934 ?2935) ?2933 ?2934 =?= multiply ?2935 ?2933 (multiply ?2933 ?2934 ?2934) [2935, 2934, 2933] by Super 12 with 13 at 3 +Id : 1358, {_}: multiply (multiply ?4047 ?4048 ?4049) ?4047 ?4048 =>= multiply ?4049 ?4047 ?4048 [4049, 4048, 4047] by Demod 919 with 3 at 3,3 +Id : 518, {_}: multiply (multiply ?1782 ?1783 ?1784) ?1785 ?1783 =?= multiply ?1782 ?1783 (multiply ?1784 ?1785 ?1783) [1785, 1784, 1783, 1782] by Super 2 with 3 at 3,2 +Id : 658, {_}: multiply (multiply ?2168 ?2169 ?2170) ?2170 ?2169 =>= multiply ?2168 ?2169 ?2170 [2170, 2169, 2168] by Super 518 with 4 at 3,3 +Id : 663, {_}: multiply ?2187 (inverse ?2188) ?2188 =?= multiply ?2187 ?2188 (inverse ?2188) [2188, 2187] by Super 658 with 6 at 1,2 +Id : 700, {_}: multiply ?2187 (inverse ?2188) ?2188 =>= ?2187 [2188, 2187] by Demod 663 with 6 at 3 +Id : 1370, {_}: multiply ?4102 ?4102 (inverse ?4103) =?= multiply ?4103 ?4102 (inverse ?4103) [4103, 4102] by Super 1358 with 700 at 1,2 +Id : 1414, {_}: ?4102 =<= multiply ?4103 ?4102 (inverse ?4103) [4103, 4102] by Demod 1370 with 4 at 2 +Id : 1523, {_}: multiply ?4433 ?4434 (multiply ?4435 ?4433 (inverse ?4433)) =>= multiply ?4435 ?4433 ?4434 [4435, 4434, 4433] by Super 13 with 1414 at 3,3 +Id : 1537, {_}: multiply ?4433 ?4434 ?4435 =?= multiply ?4435 ?4433 ?4434 [4435, 4434, 4433] by Demod 1523 with 6 at 3,2 +Id : 1363, {_}: multiply ?4066 ?4066 ?4067 =?= multiply (inverse ?4067) ?4066 ?4067 [4067, 4066] by Super 1358 with 6 at 1,2 +Id : 1412, {_}: ?4066 =<= multiply (inverse ?4067) ?4066 ?4067 [4067, 4066] by Demod 1363 with 4 at 2 +Id : 1452, {_}: multiply (multiply ?4284 ?4285 (inverse ?4285)) ?4286 ?4285 =>= multiply ?4284 ?4285 ?4286 [4286, 4285, 4284] by Super 12 with 1412 at 3,3 +Id : 1474, {_}: multiply ?4284 ?4286 ?4285 =?= multiply ?4284 ?4285 ?4286 [4285, 4286, 4284] by Demod 1452 with 6 at 1,2 +Id : 726, {_}: inverse (inverse ?2325) =>= ?2325 [2325] by Super 5 with 700 at 2 +Id : 760, {_}: multiply ?2416 (inverse ?2416) ?2417 =>= ?2417 [2417, 2416] by Super 5 with 726 at 1,2 +Id : 41048, {_}: b === b [] by Demod 41047 with 700 at 2 +Id : 41047, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply f e g)) =>= b [] by Demod 41046 with 1474 at 3,3,2 +Id : 41046, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply f g e)) =>= b [] by Demod 41045 with 1537 at 3,3,2 +Id : 41045, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply e f g)) =>= b [] by Demod 41044 with 1474 at 3,3,2 +Id : 41044, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply e g f)) =>= b [] by Demod 41043 with 1537 at 3,3,2 +Id : 41043, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c d (multiply g f e)) =>= b [] by Demod 41042 with 1474 at 3,2 +Id : 41042, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply c (multiply g f e) d) =>= b [] by Demod 41041 with 1537 at 3,2 +Id : 41041, {_}: multiply b (inverse (multiply c d (multiply f e g))) (multiply d c (multiply g f e)) =>= b [] by Demod 41040 with 1474 at 3,1,2,2 +Id : 41040, {_}: multiply b (inverse (multiply c d (multiply f g e))) (multiply d c (multiply g f e)) =>= b [] by Demod 41039 with 1474 at 2 +Id : 41039, {_}: multiply b (multiply d c (multiply g f e)) (inverse (multiply c d (multiply f g e))) =>= b [] by Demod 41038 with 1537 at 2 +Id : 41038, {_}: multiply (inverse (multiply c d (multiply f g e))) b (multiply d c (multiply g f e)) =>= b [] by Demod 41037 with 1474 at 3,2 +Id : 41037, {_}: multiply (inverse (multiply c d (multiply f g e))) b (multiply d (multiply g f e) c) =>= b [] by Demod 41036 with 760 at 2,2 +Id : 41036, {_}: multiply (inverse (multiply c d (multiply f g e))) (multiply a (inverse a) b) (multiply d (multiply g f e) c) =>= b [] by Demod 41035 with 1537 at 3,1,1,2 +Id : 41035, {_}: multiply (inverse (multiply c d (multiply e f g))) (multiply a (inverse a) b) (multiply d (multiply g f e) c) =>= b [] by Demod 41034 with 1474 at 2 +Id : 41034, {_}: multiply (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) (multiply a (inverse a) b) =>= b [] by Demod 11 with 1537 at 2 +Id : 11, {_}: multiply (multiply a (inverse a) b) (inverse (multiply c d (multiply e f g))) (multiply d (multiply g f e) c) =>= b [] by Demod 1 with 2 at 1,2,2 +Id : 1, {_}: multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c) =>= b [] by prove_single_axiom +% SZS output end CNFRefutation for BOO034-1.p +29626: solved BOO034-1.p in 10.42465 using nrkbo +29626: status Unsatisfiable for BOO034-1.p +CLASH, statistics insufficient +29634: Facts: +29634: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +29634: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +29634: Goal: +29634: Id : 1, {_}: + apply (apply ?1 (f ?1)) (g ?1) + =<= + apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1)) + [1] by prove_u_combinator ?1 +29634: Order: +29634: nrkbo +29634: Leaf order: +29634: s 1 0 0 +29634: k 1 0 0 +29634: f 3 1 3 0,2,1,2 +29634: g 3 1 3 0,2,2 +29634: apply 13 2 5 0,2 +CLASH, statistics insufficient +29635: Facts: +29635: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +29635: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +29635: Goal: +29635: Id : 1, {_}: + apply (apply ?1 (f ?1)) (g ?1) + =<= + apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1)) + [1] by prove_u_combinator ?1 +29635: Order: +29635: kbo +29635: Leaf order: +29635: s 1 0 0 +29635: k 1 0 0 +29635: f 3 1 3 0,2,1,2 +29635: g 3 1 3 0,2,2 +29635: apply 13 2 5 0,2 +CLASH, statistics insufficient +29636: Facts: +29636: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +29636: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +29636: Goal: +29636: Id : 1, {_}: + apply (apply ?1 (f ?1)) (g ?1) + =<= + apply (g ?1) (apply (apply (f ?1) (f ?1)) (g ?1)) + [1] by prove_u_combinator ?1 +29636: Order: +29636: lpo +29636: Leaf order: +29636: s 1 0 0 +29636: k 1 0 0 +29636: f 3 1 3 0,2,1,2 +29636: g 3 1 3 0,2,2 +29636: apply 13 2 5 0,2 +% SZS status Timeout for COL004-1.p +NO CLASH, using fixed ground order +29663: Facts: +29663: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +29663: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +29663: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply (apply s (apply k s)) k)) + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + [] by strong_fixed_point +29663: Goal: +29663: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +29663: Order: +29663: nrkbo +29663: Leaf order: +29663: strong_fixed_point 3 0 2 1,2 +29663: fixed_pt 3 0 3 2,2 +29663: s 11 0 0 +29663: k 13 0 0 +29663: apply 32 2 3 0,2 +NO CLASH, using fixed ground order +29664: Facts: +29664: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +29664: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +29664: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply (apply s (apply k s)) k)) + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + [] by strong_fixed_point +29664: Goal: +29664: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +29664: Order: +29664: kbo +29664: Leaf order: +29664: strong_fixed_point 3 0 2 1,2 +29664: fixed_pt 3 0 3 2,2 +29664: s 11 0 0 +29664: k 13 0 0 +29664: apply 32 2 3 0,2 +NO CLASH, using fixed ground order +29665: Facts: +29665: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +29665: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +29665: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply (apply s (apply k s)) k)) + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + [] by strong_fixed_point +29665: Goal: +29665: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +29665: Order: +29665: lpo +29665: Leaf order: +29665: strong_fixed_point 3 0 2 1,2 +29665: fixed_pt 3 0 3 2,2 +29665: s 11 0 0 +29665: k 13 0 0 +29665: apply 32 2 3 0,2 +% SZS status Timeout for COL006-6.p +CLASH, statistics insufficient +29690: Facts: +29690: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +29690: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +29690: Id : 4, {_}: + apply (apply t ?11) ?12 =>= apply ?12 ?11 + [12, 11] by t_definition ?11 ?12 +29690: Goal: +29690: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +29690: Order: +29690: nrkbo +29690: Leaf order: +29690: s 1 0 0 +29690: b 1 0 0 +29690: t 1 0 0 +29690: f 3 1 3 0,2,2 +29690: apply 17 2 3 0,2 +CLASH, statistics insufficient +29691: Facts: +29691: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +29691: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +29691: Id : 4, {_}: + apply (apply t ?11) ?12 =>= apply ?12 ?11 + [12, 11] by t_definition ?11 ?12 +29691: Goal: +29691: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +29691: Order: +29691: kbo +29691: Leaf order: +29691: s 1 0 0 +29691: b 1 0 0 +29691: t 1 0 0 +29691: f 3 1 3 0,2,2 +29691: apply 17 2 3 0,2 +CLASH, statistics insufficient +29692: Facts: +29692: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +29692: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +29692: Id : 4, {_}: + apply (apply t ?11) ?12 =?= apply ?12 ?11 + [12, 11] by t_definition ?11 ?12 +29692: Goal: +29692: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +29692: Order: +29692: lpo +29692: Leaf order: +29692: s 1 0 0 +29692: b 1 0 0 +29692: t 1 0 0 +29692: f 3 1 3 0,2,2 +29692: apply 17 2 3 0,2 +% SZS status Timeout for COL036-1.p +CLASH, statistics insufficient +29776: Facts: +29776: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +29776: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +29776: Goal: +29776: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (g ?1)) (f ?1) + [1] by prove_f_combinator ?1 +29776: Order: +29776: nrkbo +29776: Leaf order: +29776: b 1 0 0 +29776: t 1 0 0 +29776: f 2 1 2 0,2,1,1,2 +29776: g 2 1 2 0,2,1,2 +29776: h 2 1 2 0,2,2 +29776: apply 13 2 5 0,2 +CLASH, statistics insufficient +29777: Facts: +29777: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +29777: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +29777: Goal: +29777: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (g ?1)) (f ?1) + [1] by prove_f_combinator ?1 +29777: Order: +29777: kbo +29777: Leaf order: +29777: b 1 0 0 +29777: t 1 0 0 +29777: f 2 1 2 0,2,1,1,2 +29777: g 2 1 2 0,2,1,2 +29777: h 2 1 2 0,2,2 +29777: apply 13 2 5 0,2 +CLASH, statistics insufficient +29778: Facts: +29778: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +29778: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +29778: Goal: +29778: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (g ?1)) (f ?1) + [1] by prove_f_combinator ?1 +29778: Order: +29778: lpo +29778: Leaf order: +29778: b 1 0 0 +29778: t 1 0 0 +29778: f 2 1 2 0,2,1,1,2 +29778: g 2 1 2 0,2,1,2 +29778: h 2 1 2 0,2,2 +29778: apply 13 2 5 0,2 +Goal subsumed +Statistics : +Max weight : 100 +Found proof, 5.339173s +% SZS status Unsatisfiable for COL063-1.p +% SZS output start CNFRefutation for COL063-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 3189, {_}: apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t)))) [] by Super 3184 with 3 at 2 +Id : 3184, {_}: apply (apply ?10590 (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) =>= apply (apply (h (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) (g (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590))))) (f (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) ?10590)))) [10590] by Super 3164 with 3 at 2,2 +Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2 +Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (f (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (g (apply (apply b ?18) ?19))) (f (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (g ?1)) (f ?1) [1] by prove_f_combinator ?1 +% SZS output end CNFRefutation for COL063-1.p +29776: solved COL063-1.p in 5.300331 using nrkbo +29776: status Unsatisfiable for COL063-1.p +NO CLASH, using fixed ground order +29785: Facts: +29785: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29785: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29785: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29785: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29785: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29785: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29785: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29785: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29785: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29785: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29785: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29785: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29785: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29785: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29785: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29785: Goal: +29785: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +29785: Order: +29785: nrkbo +29785: Leaf order: +29785: a 3 0 3 2 +29785: identity 4 0 2 2,1,3 +29785: inverse 1 1 0 +29785: least_upper_bound 14 2 1 0,1,3 +29785: greatest_lower_bound 14 2 1 0,2,3 +29785: multiply 19 2 1 0,3 +NO CLASH, using fixed ground order +29786: Facts: +29786: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29786: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29786: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29786: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29786: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29786: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29786: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29786: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29786: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29786: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29786: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29786: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29786: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29786: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29786: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29786: Goal: +29786: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +29786: Order: +29786: kbo +29786: Leaf order: +29786: a 3 0 3 2 +29786: identity 4 0 2 2,1,3 +29786: inverse 1 1 0 +29786: least_upper_bound 14 2 1 0,1,3 +29786: greatest_lower_bound 14 2 1 0,2,3 +29786: multiply 19 2 1 0,3 +NO CLASH, using fixed ground order +29787: Facts: +29787: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29787: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29787: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29787: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29787: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29787: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29787: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29787: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29787: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29787: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29787: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29787: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29787: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29787: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29787: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29787: Goal: +29787: Id : 1, {_}: + a + =<= + multiply (least_upper_bound a identity) + (greatest_lower_bound a identity) + [] by prove_p19 +29787: Order: +29787: lpo +29787: Leaf order: +29787: a 3 0 3 2 +29787: identity 4 0 2 2,1,3 +29787: inverse 1 1 0 +29787: least_upper_bound 14 2 1 0,1,3 +29787: greatest_lower_bound 14 2 1 0,2,3 +29787: multiply 19 2 1 0,3 +% SZS status Timeout for GRP167-3.p +NO CLASH, using fixed ground order +29831: Facts: +29831: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29831: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29831: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29831: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29831: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29831: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29831: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29831: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29831: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29831: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29831: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29831: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29831: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29831: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29831: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29831: Goal: +29831: Id : 1, {_}: + inverse (least_upper_bound a b) + =<= + greatest_lower_bound (inverse a) (inverse b) + [] by prove_p10 +29831: Order: +29831: nrkbo +29831: Leaf order: +29831: identity 2 0 0 +29831: a 2 0 2 1,1,2 +29831: b 2 0 2 2,1,2 +29831: inverse 4 1 3 0,2 +29831: least_upper_bound 14 2 1 0,1,2 +29831: greatest_lower_bound 14 2 1 0,3 +29831: multiply 18 2 0 +NO CLASH, using fixed ground order +29832: Facts: +29832: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29832: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29832: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29832: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29832: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29832: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29832: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29832: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +NO CLASH, using fixed ground order +29833: Facts: +29833: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29833: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29833: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29833: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29833: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29833: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29832: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29832: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29832: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29832: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29832: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29832: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29832: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29832: Goal: +29832: Id : 1, {_}: + inverse (least_upper_bound a b) + =<= + greatest_lower_bound (inverse a) (inverse b) + [] by prove_p10 +29832: Order: +29832: kbo +29832: Leaf order: +29832: identity 2 0 0 +29832: a 2 0 2 1,1,2 +29832: b 2 0 2 2,1,2 +29832: inverse 4 1 3 0,2 +29832: least_upper_bound 14 2 1 0,1,2 +29832: greatest_lower_bound 14 2 1 0,3 +29832: multiply 18 2 0 +29833: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29833: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29833: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29833: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29833: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29833: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29833: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29833: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29833: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29833: Goal: +29833: Id : 1, {_}: + inverse (least_upper_bound a b) + =<= + greatest_lower_bound (inverse a) (inverse b) + [] by prove_p10 +29833: Order: +29833: lpo +29833: Leaf order: +29833: identity 2 0 0 +29833: a 2 0 2 1,1,2 +29833: b 2 0 2 2,1,2 +29833: inverse 4 1 3 0,2 +29833: least_upper_bound 14 2 1 0,1,2 +29833: greatest_lower_bound 14 2 1 0,3 +29833: multiply 18 2 0 +% SZS status Timeout for GRP179-1.p +NO CLASH, using fixed ground order +29866: Facts: +29866: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29866: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29866: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29866: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29866: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29866: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29866: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29866: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29866: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29866: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29866: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29866: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29866: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29866: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29866: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29866: Goal: +29866: Id : 1, {_}: + least_upper_bound (inverse a) identity + =>= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +29866: Order: +29866: nrkbo +29866: Leaf order: +29866: a 2 0 2 1,1,2 +29866: identity 4 0 2 2,2 +29866: inverse 3 1 2 0,1,2 +29866: greatest_lower_bound 14 2 1 0,1,3 +29866: least_upper_bound 14 2 1 0,2 +29866: multiply 18 2 0 +NO CLASH, using fixed ground order +29867: Facts: +29867: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29867: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29867: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29867: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29867: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29867: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29867: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29867: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29867: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29867: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29867: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29867: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29867: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29867: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29867: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29867: Goal: +29867: Id : 1, {_}: + least_upper_bound (inverse a) identity + =>= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +29867: Order: +29867: kbo +29867: Leaf order: +29867: a 2 0 2 1,1,2 +29867: identity 4 0 2 2,2 +29867: inverse 3 1 2 0,1,2 +29867: greatest_lower_bound 14 2 1 0,1,3 +29867: least_upper_bound 14 2 1 0,2 +29867: multiply 18 2 0 +NO CLASH, using fixed ground order +29868: Facts: +29868: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29868: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29868: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29868: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29868: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29868: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29868: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29868: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29868: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29868: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29868: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29868: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29868: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29868: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29868: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29868: Goal: +29868: Id : 1, {_}: + least_upper_bound (inverse a) identity + =>= + inverse (greatest_lower_bound a identity) + [] by prove_p18 +29868: Order: +29868: lpo +29868: Leaf order: +29868: a 2 0 2 1,1,2 +29868: identity 4 0 2 2,2 +29868: inverse 3 1 2 0,1,2 +29868: greatest_lower_bound 14 2 1 0,1,3 +29868: least_upper_bound 14 2 1 0,2 +29868: multiply 18 2 0 +% SZS status Timeout for GRP179-2.p +NO CLASH, using fixed ground order +29889: Facts: +29889: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29889: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29889: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29889: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29889: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29889: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29889: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29889: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29889: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29889: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29889: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29889: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29889: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29889: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29889: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29889: Goal: +29889: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +29889: Order: +29889: nrkbo +29889: Leaf order: +29889: identity 2 0 0 +29889: a 3 0 3 1,2 +29889: b 3 0 3 2,1,1,2,2 +29889: inverse 2 1 1 0,1,2,2 +29889: greatest_lower_bound 14 2 1 0,1,1,2,2 +29889: least_upper_bound 14 2 1 0,3 +29889: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +29890: Facts: +29890: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29890: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29890: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29890: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29890: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29890: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29890: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29890: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29890: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29890: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29890: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29890: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29890: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29890: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29890: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29890: Goal: +29890: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +29890: Order: +29890: kbo +29890: Leaf order: +29890: identity 2 0 0 +29890: a 3 0 3 1,2 +29890: b 3 0 3 2,1,1,2,2 +29890: inverse 2 1 1 0,1,2,2 +29890: greatest_lower_bound 14 2 1 0,1,1,2,2 +29890: least_upper_bound 14 2 1 0,3 +29890: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +29891: Facts: +29891: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29891: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29891: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29891: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29891: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29891: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29891: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29891: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29891: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29891: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29891: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29891: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29891: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29891: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29891: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29891: Goal: +29891: Id : 1, {_}: + multiply a (multiply (inverse (greatest_lower_bound a b)) b) + =>= + least_upper_bound a b + [] by prove_p11 +29891: Order: +29891: lpo +29891: Leaf order: +29891: identity 2 0 0 +29891: a 3 0 3 1,2 +29891: b 3 0 3 2,1,1,2,2 +29891: inverse 2 1 1 0,1,2,2 +29891: greatest_lower_bound 14 2 1 0,1,1,2,2 +29891: least_upper_bound 14 2 1 0,3 +29891: multiply 20 2 2 0,2 +% SZS status Timeout for GRP180-1.p +NO CLASH, using fixed ground order +29925: Facts: +29925: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29925: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29925: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29925: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29925: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29925: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29925: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29925: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29925: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29925: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29925: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29925: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29925: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29925: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29925: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29925: Id : 17, {_}: inverse identity =>= identity [] by p20_1 +29925: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51 +29925: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20_3 ?53 ?54 +29925: Goal: +29925: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +29925: Order: +29925: nrkbo +29925: Leaf order: +29925: a 2 0 2 1,1,2 +29925: identity 7 0 3 2,1,2 +29925: inverse 8 1 1 0,2,2 +29925: least_upper_bound 14 2 1 0,1,2 +29925: greatest_lower_bound 15 2 2 0,2 +29925: multiply 20 2 0 +NO CLASH, using fixed ground order +29926: Facts: +29926: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29926: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29926: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29926: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29926: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29926: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29926: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29926: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29926: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29926: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29926: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29926: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29926: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29926: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29926: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29926: Id : 17, {_}: inverse identity =>= identity [] by p20_1 +29926: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51 +29926: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20_3 ?53 ?54 +29926: Goal: +29926: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +29926: Order: +29926: kbo +29926: Leaf order: +29926: a 2 0 2 1,1,2 +29926: identity 7 0 3 2,1,2 +29926: inverse 8 1 1 0,2,2 +29926: least_upper_bound 14 2 1 0,1,2 +29926: greatest_lower_bound 15 2 2 0,2 +29926: multiply 20 2 0 +NO CLASH, using fixed ground order +29928: Facts: +29928: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29928: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29928: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29928: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29928: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29928: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29928: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29928: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29928: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29928: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29928: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29928: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29928: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29928: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29928: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29928: Id : 17, {_}: inverse identity =>= identity [] by p20_1 +29928: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p20_2 ?51 +29928: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p20_3 ?53 ?54 +29928: Goal: +29928: Id : 1, {_}: + greatest_lower_bound (least_upper_bound a identity) + (inverse (greatest_lower_bound a identity)) + =>= + identity + [] by prove_p20 +29928: Order: +29928: lpo +29928: Leaf order: +29928: a 2 0 2 1,1,2 +29928: identity 7 0 3 2,1,2 +29928: inverse 8 1 1 0,2,2 +29928: least_upper_bound 14 2 1 0,1,2 +29928: greatest_lower_bound 15 2 2 0,2 +29928: multiply 20 2 0 +% SZS status Timeout for GRP183-2.p +NO CLASH, using fixed ground order +29950: Facts: +29950: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29950: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29950: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29950: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29950: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29950: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29950: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29950: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29950: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29950: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29950: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29950: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29950: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29950: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29950: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29950: Goal: +29950: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +29950: Order: +29950: nrkbo +29950: Leaf order: +29950: b 2 0 2 2,1,2 +29950: identity 3 0 1 2,2 +29950: a 3 0 3 1,1,2 +29950: inverse 3 1 2 0,2,3 +29950: greatest_lower_bound 14 2 1 0,1,2,3 +29950: least_upper_bound 14 2 1 0,2 +29950: multiply 20 2 2 0,1,2 +NO CLASH, using fixed ground order +29951: Facts: +29951: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29951: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29951: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29951: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29951: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29951: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29951: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29951: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29951: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29951: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29951: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29951: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29951: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29951: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29951: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29951: Goal: +29951: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +29951: Order: +29951: kbo +29951: Leaf order: +29951: b 2 0 2 2,1,2 +29951: identity 3 0 1 2,2 +29951: a 3 0 3 1,1,2 +29951: inverse 3 1 2 0,2,3 +29951: greatest_lower_bound 14 2 1 0,1,2,3 +29951: least_upper_bound 14 2 1 0,2 +29951: multiply 20 2 2 0,1,2 +NO CLASH, using fixed ground order +29952: Facts: +29952: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +29952: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +29952: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +29952: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +29952: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +29952: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +29952: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +29952: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +29952: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +29952: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +29952: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +29952: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +29952: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +29952: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +29952: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +29952: Goal: +29952: Id : 1, {_}: + least_upper_bound (multiply a b) identity + =<= + multiply a (inverse (greatest_lower_bound a (inverse b))) + [] by prove_p23 +29952: Order: +29952: lpo +29952: Leaf order: +29952: b 2 0 2 2,1,2 +29952: identity 3 0 1 2,2 +29952: a 3 0 3 1,1,2 +29952: inverse 3 1 2 0,2,3 +29952: greatest_lower_bound 14 2 1 0,1,2,3 +29952: least_upper_bound 14 2 1 0,2 +29952: multiply 20 2 2 0,1,2 +% SZS status Timeout for GRP186-1.p +NO CLASH, using fixed ground order +29976: Facts: +29976: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +29976: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +29976: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +29976: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +29976: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +29976: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +29976: Id : 8, {_}: + join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +29976: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +29976: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +29976: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +29976: Goal: +29976: Id : 1, {_}: + join a + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (join (meet (complement a) b) + (meet (complement a) (complement b))))) + =>= + n1 + [] by prove_e2 +29976: Order: +29976: nrkbo +29976: Leaf order: +29976: n0 1 0 0 +29976: n1 2 0 1 3 +29976: b 4 0 4 1,2,1,2,1,2,2 +29976: a 7 0 7 1,2 +29976: complement 15 1 6 0,1,1,2,2 +29976: meet 14 2 5 0,1,2,2 +29976: join 17 2 5 0,2 +NO CLASH, using fixed ground order +29977: Facts: +29977: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +29977: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +29977: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +29977: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +29977: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +29977: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +29977: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +29977: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +29977: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +29977: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +29977: Goal: +29977: Id : 1, {_}: + join a + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (join (meet (complement a) b) + (meet (complement a) (complement b))))) + =>= + n1 + [] by prove_e2 +29977: Order: +29977: kbo +29977: Leaf order: +29977: n0 1 0 0 +29977: n1 2 0 1 3 +29977: b 4 0 4 1,2,1,2,1,2,2 +29977: a 7 0 7 1,2 +29977: complement 15 1 6 0,1,1,2,2 +29977: meet 14 2 5 0,1,2,2 +29977: join 17 2 5 0,2 +NO CLASH, using fixed ground order +29978: Facts: +29978: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +29978: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +29978: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +29978: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +29978: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +29978: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +29978: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +29978: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +29978: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +29978: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +29978: Goal: +29978: Id : 1, {_}: + join a + (join + (meet (complement a) (meet (join a (complement b)) (join a b))) + (meet (complement a) + (join (meet (complement a) b) + (meet (complement a) (complement b))))) + =>= + n1 + [] by prove_e2 +29978: Order: +29978: lpo +29978: Leaf order: +29978: n0 1 0 0 +29978: n1 2 0 1 3 +29978: b 4 0 4 1,2,1,2,1,2,2 +29978: a 7 0 7 1,2 +29978: complement 15 1 6 0,1,1,2,2 +29978: meet 14 2 5 0,1,2,2 +29978: join 17 2 5 0,2 +% SZS status Timeout for LAT017-1.p +NO CLASH, using fixed ground order +30001: Facts: +30001: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +30001: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +30001: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +30001: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +30001: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =?= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +30001: Id : 7, {_}: + join (join ?16 ?17) ?18 =?= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +30001: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +30001: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +30001: Id : 10, {_}: + join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28) + =<= + meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28) + [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30 +30001: Goal: +30001: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +30001: Order: +30001: nrkbo +30001: Leaf order: +30001: b 2 0 2 1,2,2 +30001: c 2 0 2 2,2,2 +30001: a 3 0 3 1,2 +30001: join 20 2 2 0,2,2 +30001: meet 21 2 3 0,2 +NO CLASH, using fixed ground order +30002: Facts: +30002: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +30002: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +30002: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +30002: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +30002: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +30002: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +30002: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +30002: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +30002: Id : 10, {_}: + join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28) + =<= + meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28) + [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30 +30002: Goal: +30002: Id : 1, {_}: + meet a (join b c) =<= join (meet a b) (meet a c) + [] by prove_distributivity +30002: Order: +30002: kbo +30002: Leaf order: +30002: b 2 0 2 1,2,2 +30002: c 2 0 2 2,2,2 +30002: a 3 0 3 1,2 +30002: join 20 2 2 0,2,2 +30002: meet 21 2 3 0,2 +NO CLASH, using fixed ground order +30003: Facts: +30003: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +30003: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +30003: Id : 4, {_}: meet ?6 ?7 =?= meet ?7 ?6 [7, 6] by commutativity_of_meet ?6 ?7 +30003: Id : 5, {_}: + join ?9 ?10 =?= join ?10 ?9 + [10, 9] by commutativity_of_join ?9 ?10 +30003: Id : 6, {_}: + meet (meet ?12 ?13) ?14 =>= meet ?12 (meet ?13 ?14) + [14, 13, 12] by associativity_of_meet ?12 ?13 ?14 +30003: Id : 7, {_}: + join (join ?16 ?17) ?18 =>= join ?16 (join ?17 ?18) + [18, 17, 16] by associativity_of_join ?16 ?17 ?18 +30003: Id : 8, {_}: + join (meet ?20 (join ?21 ?22)) (meet ?20 ?21) + =>= + meet ?20 (join ?21 ?22) + [22, 21, 20] by quasi_lattice1 ?20 ?21 ?22 +30003: Id : 9, {_}: + meet (join ?24 (meet ?25 ?26)) (join ?24 ?25) + =>= + join ?24 (meet ?25 ?26) + [26, 25, 24] by quasi_lattice2 ?24 ?25 ?26 +30003: Id : 10, {_}: + join (meet (join (meet ?28 ?29) ?30) ?29) (meet ?30 ?28) + =<= + meet (join (meet (join ?28 ?29) ?30) ?29) (join ?30 ?28) + [30, 29, 28] by self_dual_distributivity ?28 ?29 ?30 +30003: Goal: +30003: Id : 1, {_}: + meet a (join b c) =>= join (meet a b) (meet a c) + [] by prove_distributivity +30003: Order: +30003: lpo +30003: Leaf order: +30003: b 2 0 2 1,2,2 +30003: c 2 0 2 2,2,2 +30003: a 3 0 3 1,2 +30003: join 20 2 2 0,2,2 +30003: meet 21 2 3 0,2 +% SZS status Timeout for LAT020-1.p +NO CLASH, using fixed ground order +30025: Facts: +30025: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +30025: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +30025: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +30025: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +30025: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +30025: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +30025: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +30025: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +30025: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +30025: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +30025: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +30025: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +30025: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +30025: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +30025: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +30025: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +30025: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +30025: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +30025: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +30025: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +30025: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +30025: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +30025: Goal: +30025: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +30025: Order: +30025: nrkbo +30025: Leaf order: +30025: x 2 0 2 1,1,2 +30025: y 2 0 2 2,1,2 +30025: z 2 0 2 3,1,2 +30025: additive_identity 9 0 1 3 +30025: additive_inverse 22 1 0 +30025: commutator 1 2 0 +30025: add 25 2 1 0,2 +30025: multiply 40 2 0 +30025: associator 3 3 2 0,1,2 +NO CLASH, using fixed ground order +30026: Facts: +30026: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +30026: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +30026: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +30026: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +30026: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +30026: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +30026: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +30026: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +30026: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +30026: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +30026: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +30026: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +30026: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +30026: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +30026: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +30026: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +30026: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +30026: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +30026: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +30026: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +30026: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +30026: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +30026: Goal: +30026: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +30026: Order: +30026: kbo +30026: Leaf order: +30026: x 2 0 2 1,1,2 +30026: y 2 0 2 2,1,2 +30026: z 2 0 2 3,1,2 +30026: additive_identity 9 0 1 3 +30026: additive_inverse 22 1 0 +30026: commutator 1 2 0 +30026: add 25 2 1 0,2 +30026: multiply 40 2 0 +30026: associator 3 3 2 0,1,2 +NO CLASH, using fixed ground order +30027: Facts: +30027: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +30027: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +30027: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +30027: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +30027: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +30027: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +30027: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +30027: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +30027: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +30027: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +30027: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +30027: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +30027: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +30027: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +30027: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +30027: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +30027: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +30027: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +30027: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +30027: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +30027: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +30027: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +30027: Goal: +30027: Id : 1, {_}: + add (associator x y z) (associator x z y) =>= additive_identity + [] by prove_equation +30027: Order: +30027: lpo +30027: Leaf order: +30027: x 2 0 2 1,1,2 +30027: y 2 0 2 2,1,2 +30027: z 2 0 2 3,1,2 +30027: additive_identity 9 0 1 3 +30027: additive_inverse 22 1 0 +30027: commutator 1 2 0 +30027: add 25 2 1 0,2 +30027: multiply 40 2 0 +30027: associator 3 3 2 0,1,2 +% SZS status Timeout for RNG025-5.p +NO CLASH, using fixed ground order +30048: Facts: +30048: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +30048: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +30048: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +30048: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +30048: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +30048: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +30048: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +30048: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +30048: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +30048: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +30048: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +30048: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +30048: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +30048: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +30048: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +30048: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +30048: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +30048: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +30048: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +30048: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +30048: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +30048: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +30048: Goal: +30048: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +30048: Order: +30048: nrkbo +30048: Leaf order: +30048: y 1 0 1 2,2 +30048: x 2 0 2 1,2 +30048: additive_identity 9 0 1 3 +30048: additive_inverse 22 1 0 +30048: commutator 1 2 0 +30048: add 24 2 0 +30048: multiply 40 2 0 +30048: associator 2 3 1 0,2 +NO CLASH, using fixed ground order +30049: Facts: +30049: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +30049: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +30049: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +30049: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +30049: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +30049: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +30049: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +30049: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +30049: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +30049: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +30049: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +30049: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +30049: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +30049: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +30049: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +30049: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +30049: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +30049: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +30049: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +30049: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +30049: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +30049: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +30049: Goal: +30049: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +30049: Order: +30049: kbo +30049: Leaf order: +30049: y 1 0 1 2,2 +30049: x 2 0 2 1,2 +30049: additive_identity 9 0 1 3 +30049: additive_inverse 22 1 0 +30049: commutator 1 2 0 +30049: add 24 2 0 +30049: multiply 40 2 0 +30049: associator 2 3 1 0,2 +NO CLASH, using fixed ground order +30050: Facts: +30050: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +30050: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +30050: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +30050: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +30050: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +30050: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +30050: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +30050: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +30050: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +30050: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +30050: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +30050: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +30050: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +30050: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +30050: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +30050: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +30050: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +30050: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +30050: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +30050: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +30050: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +30050: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +30050: Goal: +30050: Id : 1, {_}: associator x y x =>= additive_identity [] by prove_flexible_law +30050: Order: +30050: lpo +30050: Leaf order: +30050: y 1 0 1 2,2 +30050: x 2 0 2 1,2 +30050: additive_identity 9 0 1 3 +30050: additive_inverse 22 1 0 +30050: commutator 1 2 0 +30050: add 24 2 0 +30050: multiply 40 2 0 +30050: associator 2 3 1 0,2 +% SZS status Timeout for RNG025-7.p +CLASH, statistics insufficient +30088: Facts: +30088: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +30088: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +30088: Goal: +30088: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +30088: Order: +30088: nrkbo +30088: Leaf order: +30088: s 1 0 0 +30088: k 1 0 0 +30088: f 3 1 3 0,2,2 +30088: apply 11 2 3 0,2 +CLASH, statistics insufficient +30089: Facts: +30089: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +30089: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +30089: Goal: +30089: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +30089: Order: +30089: kbo +30089: Leaf order: +30089: s 1 0 0 +30089: k 1 0 0 +30089: f 3 1 3 0,2,2 +30089: apply 11 2 3 0,2 +CLASH, statistics insufficient +30090: Facts: +30090: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +30090: Id : 3, {_}: apply (apply k ?7) ?8 =>= ?7 [8, 7] by k_definition ?7 ?8 +30090: Goal: +30090: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +30090: Order: +30090: lpo +30090: Leaf order: +30090: s 1 0 0 +30090: k 1 0 0 +30090: f 3 1 3 0,2,2 +30090: apply 11 2 3 0,2 +% SZS status Timeout for COL006-1.p +NO CLASH, using fixed ground order +30176: Facts: +30176: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +30176: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +30176: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply k (apply (apply s s) (apply s k)))) + (apply (apply s (apply k s)) k)) + [] by strong_fixed_point +30176: Goal: +30176: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30176: Order: +30176: nrkbo +30176: Leaf order: +30176: strong_fixed_point 3 0 2 1,2 +30176: fixed_pt 3 0 3 2,2 +30176: k 10 0 0 +30176: s 11 0 0 +30176: apply 29 2 3 0,2 +NO CLASH, using fixed ground order +30177: Facts: +30177: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +30177: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +30177: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply k (apply (apply s s) (apply s k)))) + (apply (apply s (apply k s)) k)) + [] by strong_fixed_point +30177: Goal: +30177: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30177: Order: +30177: kbo +30177: Leaf order: +30177: strong_fixed_point 3 0 2 1,2 +30177: fixed_pt 3 0 3 2,2 +30177: k 10 0 0 +30177: s 11 0 0 +30177: apply 29 2 3 0,2 +NO CLASH, using fixed ground order +30178: Facts: +30178: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +30178: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +30178: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) + (apply (apply s (apply k (apply (apply s s) (apply s k)))) + (apply (apply s (apply k s)) k)) + [] by strong_fixed_point +30178: Goal: +30178: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30178: Order: +30178: lpo +30178: Leaf order: +30178: strong_fixed_point 3 0 2 1,2 +30178: fixed_pt 3 0 3 2,2 +30178: k 10 0 0 +30178: s 11 0 0 +30178: apply 29 2 3 0,2 +% SZS status Timeout for COL006-5.p +NO CLASH, using fixed ground order +30201: Facts: +30201: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +30201: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +30201: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply (apply s s) (apply (apply s k) k)) + (apply (apply s s) (apply s k))))) + (apply (apply s (apply k s)) k) + [] by strong_fixed_point +30201: Goal: +30201: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30201: Order: +30201: nrkbo +30201: Leaf order: +30201: strong_fixed_point 3 0 2 1,2 +30201: fixed_pt 3 0 3 2,2 +30201: k 7 0 0 +30201: s 10 0 0 +30201: apply 25 2 3 0,2 +NO CLASH, using fixed ground order +30202: Facts: +30202: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +30202: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +30202: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply (apply s s) (apply (apply s k) k)) + (apply (apply s s) (apply s k))))) + (apply (apply s (apply k s)) k) + [] by strong_fixed_point +30202: Goal: +30202: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30202: Order: +30202: kbo +30202: Leaf order: +30202: strong_fixed_point 3 0 2 1,2 +30202: fixed_pt 3 0 3 2,2 +30202: k 7 0 0 +30202: s 10 0 0 +30202: apply 25 2 3 0,2 +NO CLASH, using fixed ground order +30203: Facts: +30203: Id : 2, {_}: + apply (apply (apply s ?2) ?3) ?4 + =?= + apply (apply ?2 ?4) (apply ?3 ?4) + [4, 3, 2] by s_definition ?2 ?3 ?4 +30203: Id : 3, {_}: apply (apply k ?6) ?7 =>= ?6 [7, 6] by k_definition ?6 ?7 +30203: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply s + (apply k + (apply (apply (apply s s) (apply (apply s k) k)) + (apply (apply s s) (apply s k))))) + (apply (apply s (apply k s)) k) + [] by strong_fixed_point +30203: Goal: +30203: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30203: Order: +30203: lpo +30203: Leaf order: +30203: strong_fixed_point 3 0 2 1,2 +30203: fixed_pt 3 0 3 2,2 +30203: k 7 0 0 +30203: s 10 0 0 +30203: apply 25 2 3 0,2 +% SZS status Timeout for COL006-7.p +NO CLASH, using fixed ground order +30224: Facts: +30224: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +30224: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +NO CLASH, using fixed ground order +30225: Facts: +30225: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +30225: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +30225: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply (apply b b) n)) n))) n)) b)) b + [] by strong_fixed_point +30225: Goal: +30225: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30225: Order: +30225: kbo +30225: Leaf order: +30225: strong_fixed_point 3 0 2 1,2 +30225: fixed_pt 3 0 3 2,2 +30225: n 6 0 0 +30225: b 9 0 0 +30225: apply 26 2 3 0,2 +NO CLASH, using fixed ground order +30226: Facts: +30226: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +30226: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +30226: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply (apply b b) n)) n))) n)) b)) b + [] by strong_fixed_point +30226: Goal: +30226: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30226: Order: +30226: lpo +30226: Leaf order: +30226: strong_fixed_point 3 0 2 1,2 +30226: fixed_pt 3 0 3 2,2 +30226: n 6 0 0 +30226: b 9 0 0 +30226: apply 26 2 3 0,2 +30224: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply (apply b b) n)) n))) n)) b)) b + [] by strong_fixed_point +30224: Goal: +30224: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30224: Order: +30224: nrkbo +30224: Leaf order: +30224: strong_fixed_point 3 0 2 1,2 +30224: fixed_pt 3 0 3 2,2 +30224: n 6 0 0 +30224: b 9 0 0 +30224: apply 26 2 3 0,2 +% SZS status Timeout for COL044-6.p +NO CLASH, using fixed ground order +30249: Facts: +30249: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +30249: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +30249: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply n (apply b b))) n))) n)) b)) b + [] by strong_fixed_point +30249: Goal: +30249: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30249: Order: +30249: nrkbo +30249: Leaf order: +30249: strong_fixed_point 3 0 2 1,2 +30249: fixed_pt 3 0 3 2,2 +30249: n 6 0 0 +30249: b 9 0 0 +30249: apply 26 2 3 0,2 +NO CLASH, using fixed ground order +30250: Facts: +30250: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +30250: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +30250: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply n (apply b b))) n))) n)) b)) b + [] by strong_fixed_point +30250: Goal: +30250: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30250: Order: +30250: kbo +30250: Leaf order: +30250: strong_fixed_point 3 0 2 1,2 +30250: fixed_pt 3 0 3 2,2 +30250: n 6 0 0 +30250: b 9 0 0 +30250: apply 26 2 3 0,2 +NO CLASH, using fixed ground order +30251: Facts: +30251: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +30251: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +30251: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply (apply b b) + (apply (apply n (apply n (apply b b))) n))) n)) b)) b + [] by strong_fixed_point +30251: Goal: +30251: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +30251: Order: +30251: lpo +30251: Leaf order: +30251: strong_fixed_point 3 0 2 1,2 +30251: fixed_pt 3 0 3 2,2 +30251: n 6 0 0 +30251: b 9 0 0 +30251: apply 26 2 3 0,2 +% SZS status Timeout for COL044-7.p +CLASH, statistics insufficient +30275: Facts: +30275: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +30275: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +30275: Goal: +30275: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (f ?1)) (g ?1) + [1] by prove_v_combinator ?1 +30275: Order: +30275: nrkbo +30275: Leaf order: +30275: b 1 0 0 +30275: t 1 0 0 +30275: f 2 1 2 0,2,1,1,2 +30275: g 2 1 2 0,2,1,2 +30275: h 2 1 2 0,2,2 +30275: apply 13 2 5 0,2 +CLASH, statistics insufficient +30276: Facts: +30276: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +30276: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +30276: Goal: +30276: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (f ?1)) (g ?1) + [1] by prove_v_combinator ?1 +30276: Order: +30276: kbo +30276: Leaf order: +30276: b 1 0 0 +30276: t 1 0 0 +30276: f 2 1 2 0,2,1,1,2 +30276: g 2 1 2 0,2,1,2 +30276: h 2 1 2 0,2,2 +30276: apply 13 2 5 0,2 +CLASH, statistics insufficient +30277: Facts: +30277: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +30277: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +30277: Goal: +30277: Id : 1, {_}: + apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) + =>= + apply (apply (h ?1) (f ?1)) (g ?1) + [1] by prove_v_combinator ?1 +30277: Order: +30277: lpo +30277: Leaf order: +30277: b 1 0 0 +30277: t 1 0 0 +30277: f 2 1 2 0,2,1,1,2 +30277: g 2 1 2 0,2,1,2 +30277: h 2 1 2 0,2,2 +30277: apply 13 2 5 0,2 +Goal subsumed +Statistics : +Max weight : 124 +Found proof, 34.381663s +% SZS status Unsatisfiable for COL064-1.p +% SZS output start CNFRefutation for COL064-1.p +Id : 3, {_}: apply (apply t ?7) ?8 =>= apply ?8 ?7 [8, 7] by t_definition ?7 ?8 +Id : 2, {_}: apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) [5, 4, 3] by b_definition ?3 ?4 ?5 +Id : 10997, {_}: apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) === apply (apply (h (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t)))) [] by Super 10996 with 3 at 2 +Id : 10996, {_}: apply (apply ?37685 (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b b) ?37685))) (apply (apply b b) (apply (apply b b) t)))) [37685] by Super 3193 with 2 at 2 +Id : 3193, {_}: apply (apply (apply ?10612 (apply ?10613 (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))))) (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t (apply (apply b ?10612) ?10613))) (apply (apply b b) (apply (apply b b) t)))) [10613, 10612] by Super 3188 with 2 at 1,1,2 +Id : 3188, {_}: apply (apply (apply ?10602 (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) =>= apply (apply (h (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) (f (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t))))) (g (apply (apply b (apply t ?10602)) (apply (apply b b) (apply (apply b b) t)))) [10602] by Super 3164 with 3 at 2 +Id : 3164, {_}: apply (apply ?10539 (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (apply (apply ?10540 (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) =>= apply (apply (h (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) (f (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539))))) (g (apply (apply b (apply t ?10540)) (apply (apply b b) (apply (apply b b) ?10539)))) [10540, 10539] by Super 442 with 2 at 2 +Id : 442, {_}: apply (apply (apply ?1394 (apply ?1395 (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (apply ?1396 (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))))) (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) =>= apply (apply (h (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) (f (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395))))) (g (apply (apply b (apply t ?1396)) (apply (apply b b) (apply (apply b ?1394) ?1395)))) [1396, 1395, 1394] by Super 277 with 2 at 1,1,2 +Id : 277, {_}: apply (apply (apply ?900 (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (apply ?901 (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))))) (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) =>= apply (apply (h (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) (f (apply (apply b (apply t ?901)) (apply (apply b b) ?900)))) (g (apply (apply b (apply t ?901)) (apply (apply b b) ?900))) [901, 900] by Super 29 with 2 at 1,2 +Id : 29, {_}: apply (apply (apply (apply ?85 (apply ?86 (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))))) ?87) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) =>= apply (apply (h (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) (f (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86)))) (g (apply (apply b (apply t ?87)) (apply (apply b ?85) ?86))) [87, 86, 85] by Super 13 with 3 at 1,1,2 +Id : 13, {_}: apply (apply (apply ?33 (apply ?34 (apply ?35 (f (apply (apply b ?33) (apply (apply b ?34) ?35)))))) (g (apply (apply b ?33) (apply (apply b ?34) ?35)))) (h (apply (apply b ?33) (apply (apply b ?34) ?35))) =>= apply (apply (h (apply (apply b ?33) (apply (apply b ?34) ?35))) (f (apply (apply b ?33) (apply (apply b ?34) ?35)))) (g (apply (apply b ?33) (apply (apply b ?34) ?35))) [35, 34, 33] by Super 6 with 2 at 2,1,1,2 +Id : 6, {_}: apply (apply (apply ?18 (apply ?19 (f (apply (apply b ?18) ?19)))) (g (apply (apply b ?18) ?19))) (h (apply (apply b ?18) ?19)) =>= apply (apply (h (apply (apply b ?18) ?19)) (f (apply (apply b ?18) ?19))) (g (apply (apply b ?18) ?19)) [19, 18] by Super 1 with 2 at 1,1,2 +Id : 1, {_}: apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1) =>= apply (apply (h ?1) (f ?1)) (g ?1) [1] by prove_v_combinator ?1 +% SZS output end CNFRefutation for COL064-1.p +30275: solved COL064-1.p in 34.366147 using nrkbo +30275: status Unsatisfiable for COL064-1.p +CLASH, statistics insufficient +30288: Facts: +30288: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +30288: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +30288: Goal: +30288: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) + =>= + apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) + [1] by prove_g_combinator ?1 +30288: Order: +30288: nrkbo +30288: Leaf order: +30288: b 1 0 0 +30288: t 1 0 0 +30288: f 2 1 2 0,2,1,1,1,2 +30288: g 2 1 2 0,2,1,1,2 +30288: h 2 1 2 0,2,1,2 +30288: i 2 1 2 0,2,2 +30288: apply 15 2 7 0,2 +CLASH, statistics insufficient +30289: Facts: +30289: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +30289: Id : 3, {_}: + apply (apply t ?7) ?8 =>= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +30289: Goal: +30289: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) + =>= + apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) + [1] by prove_g_combinator ?1 +30289: Order: +30289: kbo +30289: Leaf order: +30289: b 1 0 0 +30289: t 1 0 0 +30289: f 2 1 2 0,2,1,1,1,2 +30289: g 2 1 2 0,2,1,1,2 +30289: h 2 1 2 0,2,1,2 +30289: i 2 1 2 0,2,2 +30289: apply 15 2 7 0,2 +CLASH, statistics insufficient +30290: Facts: +30290: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +30290: Id : 3, {_}: + apply (apply t ?7) ?8 =?= apply ?8 ?7 + [8, 7] by t_definition ?7 ?8 +30290: Goal: +30290: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (h ?1)) (i ?1) + =>= + apply (apply (f ?1) (i ?1)) (apply (g ?1) (h ?1)) + [1] by prove_g_combinator ?1 +30290: Order: +30290: lpo +30290: Leaf order: +30290: b 1 0 0 +30290: t 1 0 0 +30290: f 2 1 2 0,2,1,1,1,2 +30290: g 2 1 2 0,2,1,1,2 +30290: h 2 1 2 0,2,1,2 +30290: i 2 1 2 0,2,2 +30290: apply 15 2 7 0,2 +% SZS status Timeout for COL065-1.p +CLASH, statistics insufficient +30319: Facts: +30319: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30319: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30319: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30319: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30319: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30319: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30319: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30319: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30319: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30319: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30319: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30319: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30319: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30319: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30319: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30319: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_1 +30319: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2 +30319: Goal: +30319: Id : 1, {_}: a =>= b [] by prove_p12 +30319: Order: +30319: nrkbo +30319: Leaf order: +30319: identity 2 0 0 +30319: a 3 0 1 2 +30319: b 3 0 1 3 +30319: c 4 0 0 +30319: inverse 1 1 0 +30319: greatest_lower_bound 15 2 0 +30319: least_upper_bound 15 2 0 +30319: multiply 18 2 0 +CLASH, statistics insufficient +30320: Facts: +30320: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30320: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30320: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30320: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30320: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30320: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30320: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30320: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30320: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30320: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30320: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30320: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30320: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30320: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30320: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30320: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_1 +30320: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2 +30320: Goal: +30320: Id : 1, {_}: a =>= b [] by prove_p12 +30320: Order: +30320: kbo +30320: Leaf order: +30320: identity 2 0 0 +30320: a 3 0 1 2 +30320: b 3 0 1 3 +30320: c 4 0 0 +30320: inverse 1 1 0 +30320: greatest_lower_bound 15 2 0 +30320: least_upper_bound 15 2 0 +30320: multiply 18 2 0 +CLASH, statistics insufficient +30321: Facts: +30321: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30321: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30321: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30321: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30321: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30321: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30321: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30321: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30321: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30321: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30321: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30321: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30321: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30321: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30321: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30321: Id : 17, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_1 +30321: Id : 18, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_2 +30321: Goal: +30321: Id : 1, {_}: a =>= b [] by prove_p12 +30321: Order: +30321: lpo +30321: Leaf order: +30321: identity 2 0 0 +30321: a 3 0 1 2 +30321: b 3 0 1 3 +30321: c 4 0 0 +30321: inverse 1 1 0 +30321: greatest_lower_bound 15 2 0 +30321: least_upper_bound 15 2 0 +30321: multiply 18 2 0 +% SZS status Timeout for GRP181-1.p +CLASH, statistics insufficient +30347: Facts: +30347: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30347: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30347: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30347: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30347: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30347: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30347: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30347: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30347: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30347: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30347: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30347: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30347: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30347: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30347: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30347: Id : 17, {_}: inverse identity =>= identity [] by p12_1 +30347: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51 +30347: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12_3 ?53 ?54 +30347: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_4 +30347: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5 +30347: Goal: +30347: Id : 1, {_}: a =>= b [] by prove_p12 +30347: Order: +30347: nrkbo +30347: Leaf order: +30347: a 3 0 1 2 +30347: b 3 0 1 3 +30347: identity 4 0 0 +30347: c 4 0 0 +30347: inverse 7 1 0 +30347: greatest_lower_bound 15 2 0 +30347: least_upper_bound 15 2 0 +30347: multiply 20 2 0 +CLASH, statistics insufficient +30348: Facts: +30348: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30348: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30348: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30348: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30348: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30348: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30348: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30348: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30348: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30348: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30348: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30348: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30348: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30348: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30348: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30348: Id : 17, {_}: inverse identity =>= identity [] by p12_1 +30348: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51 +30348: Id : 19, {_}: + inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12_3 ?53 ?54 +30348: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_4 +30348: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5 +30348: Goal: +30348: Id : 1, {_}: a =>= b [] by prove_p12 +30348: Order: +30348: kbo +30348: Leaf order: +30348: a 3 0 1 2 +30348: b 3 0 1 3 +30348: identity 4 0 0 +30348: c 4 0 0 +30348: inverse 7 1 0 +30348: greatest_lower_bound 15 2 0 +30348: least_upper_bound 15 2 0 +30348: multiply 20 2 0 +CLASH, statistics insufficient +30349: Facts: +30349: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30349: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30349: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30349: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30349: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30349: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30349: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30349: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30349: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30349: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30349: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30349: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30349: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30349: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30349: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30349: Id : 17, {_}: inverse identity =>= identity [] by p12_1 +30349: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p12_2 ?51 +30349: Id : 19, {_}: + inverse (multiply ?53 ?54) =?= multiply (inverse ?54) (inverse ?53) + [54, 53] by p12_3 ?53 ?54 +30349: Id : 20, {_}: + greatest_lower_bound a c =>= greatest_lower_bound b c + [] by p12_4 +30349: Id : 21, {_}: least_upper_bound a c =>= least_upper_bound b c [] by p12_5 +30349: Goal: +30349: Id : 1, {_}: a =>= b [] by prove_p12 +30349: Order: +30349: lpo +30349: Leaf order: +30349: a 3 0 1 2 +30349: b 3 0 1 3 +30349: identity 4 0 0 +30349: c 4 0 0 +30349: inverse 7 1 0 +30349: greatest_lower_bound 15 2 0 +30349: least_upper_bound 15 2 0 +30349: multiply 20 2 0 +% SZS status Timeout for GRP181-2.p +NO CLASH, using fixed ground order +30391: Facts: +30391: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30391: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30391: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30391: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30391: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30391: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30391: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30391: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30391: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30391: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30391: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30391: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30391: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30391: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30391: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30391: Id : 17, {_}: + greatest_lower_bound (least_upper_bound a (inverse a)) + (least_upper_bound b (inverse b)) + =>= + identity + [] by p33_1 +30391: Goal: +30391: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33 +30391: Order: +30391: nrkbo +30391: Leaf order: +30391: identity 3 0 0 +30391: a 4 0 2 1,2 +30391: b 4 0 2 2,2 +30391: inverse 3 1 0 +30391: greatest_lower_bound 14 2 0 +30391: least_upper_bound 15 2 0 +30391: multiply 20 2 2 0,2 +NO CLASH, using fixed ground order +30392: Facts: +30392: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30392: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30392: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30392: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30392: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30392: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30392: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30392: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30392: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30392: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +NO CLASH, using fixed ground order +30393: Facts: +30393: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +30393: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +30393: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +30393: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +30393: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +30393: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +30393: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +30393: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +30393: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +30393: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +30393: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30393: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30393: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30393: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30393: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30393: Id : 17, {_}: + greatest_lower_bound (least_upper_bound a (inverse a)) + (least_upper_bound b (inverse b)) + =>= + identity + [] by p33_1 +30393: Goal: +30393: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33 +30393: Order: +30393: lpo +30393: Leaf order: +30393: identity 3 0 0 +30393: a 4 0 2 1,2 +30393: b 4 0 2 2,2 +30393: inverse 3 1 0 +30393: greatest_lower_bound 14 2 0 +30393: least_upper_bound 15 2 0 +30393: multiply 20 2 2 0,2 +30392: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +30392: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +30392: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +30392: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +30392: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +30392: Id : 17, {_}: + greatest_lower_bound (least_upper_bound a (inverse a)) + (least_upper_bound b (inverse b)) + =>= + identity + [] by p33_1 +30392: Goal: +30392: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_p33 +30392: Order: +30392: kbo +30392: Leaf order: +30392: identity 3 0 0 +30392: a 4 0 2 1,2 +30392: b 4 0 2 2,2 +30392: inverse 3 1 0 +30392: greatest_lower_bound 14 2 0 +30392: least_upper_bound 15 2 0 +30392: multiply 20 2 2 0,2 +% SZS status Timeout for GRP187-1.p +NO CLASH, using fixed ground order +30417: Facts: +30417: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30417: Goal: +30417: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +30417: Order: +30417: nrkbo +30417: Leaf order: +30417: a1 2 0 2 1,1,2 +30417: b1 2 0 2 1,1,3 +30417: inverse 9 1 2 0,1,2 +30417: multiply 12 2 2 0,2 +NO CLASH, using fixed ground order +30418: Facts: +30418: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30418: Goal: +30418: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +30418: Order: +30418: kbo +30418: Leaf order: +30418: a1 2 0 2 1,1,2 +30418: b1 2 0 2 1,1,3 +30418: inverse 9 1 2 0,1,2 +30418: multiply 12 2 2 0,2 +NO CLASH, using fixed ground order +30419: Facts: +30419: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30419: Goal: +30419: Id : 1, {_}: + multiply (inverse a1) a1 =<= multiply (inverse b1) b1 + [] by prove_these_axioms_1 +30419: Order: +30419: lpo +30419: Leaf order: +30419: a1 2 0 2 1,1,2 +30419: b1 2 0 2 1,1,3 +30419: inverse 9 1 2 0,1,2 +30419: multiply 12 2 2 0,2 +% SZS status Timeout for GRP505-1.p +NO CLASH, using fixed ground order +30445: Facts: +30445: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30445: Goal: +30445: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +30445: Order: +30445: nrkbo +30445: Leaf order: +30445: a3 2 0 2 1,1,2 +30445: b3 2 0 2 2,1,2 +30445: c3 2 0 2 2,2 +30445: inverse 7 1 0 +30445: multiply 14 2 4 0,2 +NO CLASH, using fixed ground order +30446: Facts: +30446: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30446: Goal: +30446: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +30446: Order: +30446: kbo +30446: Leaf order: +30446: a3 2 0 2 1,1,2 +30446: b3 2 0 2 2,1,2 +30446: c3 2 0 2 2,2 +30446: inverse 7 1 0 +30446: multiply 14 2 4 0,2 +NO CLASH, using fixed ground order +30447: Facts: +30447: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30447: Goal: +30447: Id : 1, {_}: + multiply (multiply a3 b3) c3 =>= multiply a3 (multiply b3 c3) + [] by prove_these_axioms_3 +30447: Order: +30447: lpo +30447: Leaf order: +30447: a3 2 0 2 1,1,2 +30447: b3 2 0 2 2,1,2 +30447: c3 2 0 2 2,2 +30447: inverse 7 1 0 +30447: multiply 14 2 4 0,2 +% SZS status Timeout for GRP507-1.p +NO CLASH, using fixed ground order +30481: Facts: +30481: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30481: Goal: +30481: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4 +30481: Order: +30481: nrkbo +30481: Leaf order: +30481: a 2 0 2 1,2 +30481: b 2 0 2 2,2 +30481: inverse 7 1 0 +30481: multiply 12 2 2 0,2 +NO CLASH, using fixed ground order +30482: Facts: +30482: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30482: Goal: +30482: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4 +30482: Order: +30482: kbo +30482: Leaf order: +30482: a 2 0 2 1,2 +30482: b 2 0 2 2,2 +30482: inverse 7 1 0 +30482: multiply 12 2 2 0,2 +NO CLASH, using fixed ground order +30483: Facts: +30483: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +30483: Goal: +30483: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_these_axioms_4 +30483: Order: +30483: lpo +30483: Leaf order: +30483: a 2 0 2 1,2 +30483: b 2 0 2 2,2 +30483: inverse 7 1 0 +30483: multiply 12 2 2 0,2 +% SZS status Timeout for GRP508-1.p +NO CLASH, using fixed ground order +31468: Facts: +31468: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +31468: Goal: +31468: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1 +31468: Order: +31468: nrkbo +31468: Leaf order: +31468: a 3 0 3 1,2 +31468: meet 19 2 1 0,2 +31468: join 20 2 0 +NO CLASH, using fixed ground order +31469: Facts: +31469: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +31469: Goal: +31469: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1 +31469: Order: +31469: kbo +31469: Leaf order: +31469: a 3 0 3 1,2 +31469: meet 19 2 1 0,2 +31469: join 20 2 0 +NO CLASH, using fixed ground order +31470: Facts: +31470: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +31470: Goal: +31470: Id : 1, {_}: meet a a =>= a [] by prove_normal_axioms_1 +31470: Order: +31470: lpo +31470: Leaf order: +31470: a 3 0 3 1,2 +31470: meet 19 2 1 0,2 +31470: join 20 2 0 +% SZS status Timeout for LAT080-1.p +NO CLASH, using fixed ground order +31492: Facts: +31492: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +31492: Goal: +31492: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4 +31492: Order: +31492: nrkbo +31492: Leaf order: +31492: a 3 0 3 1,2 +31492: meet 18 2 0 +31492: join 21 2 1 0,2 +NO CLASH, using fixed ground order +31493: Facts: +31493: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +31493: Goal: +31493: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4 +31493: Order: +31493: kbo +31493: Leaf order: +31493: a 3 0 3 1,2 +31493: meet 18 2 0 +31493: join 21 2 1 0,2 +NO CLASH, using fixed ground order +31494: Facts: +31494: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +31494: Goal: +31494: Id : 1, {_}: join a a =>= a [] by prove_normal_axioms_4 +31494: Order: +31494: lpo +31494: Leaf order: +31494: a 3 0 3 1,2 +31494: meet 18 2 0 +31494: join 21 2 1 0,2 +% SZS status Timeout for LAT083-1.p +NO CLASH, using fixed ground order +31519: Facts: +31519: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31519: Goal: +31519: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1 +31519: Order: +31519: nrkbo +31519: Leaf order: +31519: a 3 0 3 1,2 +31519: join 18 2 0 +31519: meet 19 2 1 0,2 +NO CLASH, using fixed ground order +31521: Facts: +31521: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31521: Goal: +31521: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1 +31521: Order: +31521: lpo +31521: Leaf order: +31521: a 3 0 3 1,2 +31521: join 18 2 0 +31521: meet 19 2 1 0,2 +NO CLASH, using fixed ground order +31520: Facts: +31520: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31520: Goal: +31520: Id : 1, {_}: meet a a =>= a [] by prove_wal_axioms_1 +31520: Order: +31520: kbo +31520: Leaf order: +31520: a 3 0 3 1,2 +31520: join 18 2 0 +31520: meet 19 2 1 0,2 +% SZS status Timeout for LAT092-1.p +NO CLASH, using fixed ground order +31546: Facts: +31546: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31546: Goal: +31546: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2 +31546: Order: +31546: nrkbo +31546: Leaf order: +31546: b 2 0 2 1,2 +31546: a 2 0 2 2,2 +31546: join 18 2 0 +31546: meet 20 2 2 0,2 +NO CLASH, using fixed ground order +31547: Facts: +31547: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31547: Goal: +31547: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2 +31547: Order: +31547: kbo +31547: Leaf order: +31547: b 2 0 2 1,2 +31547: a 2 0 2 2,2 +31547: join 18 2 0 +31547: meet 20 2 2 0,2 +NO CLASH, using fixed ground order +31548: Facts: +31548: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31548: Goal: +31548: Id : 1, {_}: meet b a =<= meet a b [] by prove_wal_axioms_2 +31548: Order: +31548: lpo +31548: Leaf order: +31548: b 2 0 2 1,2 +31548: a 2 0 2 2,2 +31548: join 18 2 0 +31548: meet 20 2 2 0,2 +% SZS status Timeout for LAT093-1.p +NO CLASH, using fixed ground order +31571: Facts: +31571: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31571: Goal: +31571: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3 +31571: Order: +31571: nrkbo +31571: Leaf order: +31571: a 3 0 3 1,2 +31571: meet 18 2 0 +31571: join 19 2 1 0,2 +NO CLASH, using fixed ground order +31572: Facts: +31572: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31572: Goal: +31572: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3 +31572: Order: +31572: kbo +31572: Leaf order: +31572: a 3 0 3 1,2 +31572: meet 18 2 0 +31572: join 19 2 1 0,2 +NO CLASH, using fixed ground order +31573: Facts: +31573: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31573: Goal: +31573: Id : 1, {_}: join a a =>= a [] by prove_wal_axioms_3 +31573: Order: +31573: lpo +31573: Leaf order: +31573: a 3 0 3 1,2 +31573: meet 18 2 0 +31573: join 19 2 1 0,2 +% SZS status Timeout for LAT094-1.p +NO CLASH, using fixed ground order +31595: Facts: +31595: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31595: Goal: +31595: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4 +31595: Order: +31595: nrkbo +31595: Leaf order: +31595: b 2 0 2 1,2 +31595: a 2 0 2 2,2 +31595: meet 18 2 0 +31595: join 20 2 2 0,2 +NO CLASH, using fixed ground order +31596: Facts: +31596: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31596: Goal: +31596: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4 +31596: Order: +31596: kbo +31596: Leaf order: +31596: b 2 0 2 1,2 +31596: a 2 0 2 2,2 +31596: meet 18 2 0 +31596: join 20 2 2 0,2 +NO CLASH, using fixed ground order +31597: Facts: +31597: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31597: Goal: +31597: Id : 1, {_}: join b a =<= join a b [] by prove_wal_axioms_4 +31597: Order: +31597: lpo +31597: Leaf order: +31597: b 2 0 2 1,2 +31597: a 2 0 2 2,2 +31597: meet 18 2 0 +31597: join 20 2 2 0,2 +% SZS status Timeout for LAT095-1.p +NO CLASH, using fixed ground order +31621: Facts: +31621: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31621: Goal: +31621: Id : 1, {_}: + meet (meet (join a b) (join c b)) b =>= b + [] by prove_wal_axioms_5 +31621: Order: +31621: nrkbo +31621: Leaf order: +31621: a 1 0 1 1,1,1,2 +31621: c 1 0 1 1,2,1,2 +31621: b 4 0 4 2,1,1,2 +31621: join 20 2 2 0,1,1,2 +31621: meet 20 2 2 0,2 +NO CLASH, using fixed ground order +31622: Facts: +31622: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31622: Goal: +31622: Id : 1, {_}: + meet (meet (join a b) (join c b)) b =>= b + [] by prove_wal_axioms_5 +31622: Order: +31622: kbo +31622: Leaf order: +31622: a 1 0 1 1,1,1,2 +31622: c 1 0 1 1,2,1,2 +31622: b 4 0 4 2,1,1,2 +31622: join 20 2 2 0,1,1,2 +31622: meet 20 2 2 0,2 +NO CLASH, using fixed ground order +31623: Facts: +31623: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31623: Goal: +31623: Id : 1, {_}: + meet (meet (join a b) (join c b)) b =>= b + [] by prove_wal_axioms_5 +31623: Order: +31623: lpo +31623: Leaf order: +31623: a 1 0 1 1,1,1,2 +31623: c 1 0 1 1,2,1,2 +31623: b 4 0 4 2,1,1,2 +31623: join 20 2 2 0,1,1,2 +31623: meet 20 2 2 0,2 +% SZS status Timeout for LAT096-1.p +NO CLASH, using fixed ground order +31646: Facts: +31646: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31646: Goal: +31646: Id : 1, {_}: + join (join (meet a b) (meet c b)) b =>= b + [] by prove_wal_axioms_6 +31646: Order: +31646: nrkbo +31646: Leaf order: +31646: a 1 0 1 1,1,1,2 +31646: c 1 0 1 1,2,1,2 +31646: b 4 0 4 2,1,1,2 +31646: meet 20 2 2 0,1,1,2 +31646: join 20 2 2 0,2 +NO CLASH, using fixed ground order +31647: Facts: +31647: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31647: Goal: +31647: Id : 1, {_}: + join (join (meet a b) (meet c b)) b =>= b + [] by prove_wal_axioms_6 +31647: Order: +31647: kbo +31647: Leaf order: +31647: a 1 0 1 1,1,1,2 +31647: c 1 0 1 1,2,1,2 +31647: b 4 0 4 2,1,1,2 +31647: meet 20 2 2 0,1,1,2 +31647: join 20 2 2 0,2 +NO CLASH, using fixed ground order +31648: Facts: +31648: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)) + (meet + (join (meet ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)) + (meet ?7 + (join ?3 (meet (meet (join ?3 ?5) (join ?6 ?3)) ?3)))) + (join ?2 (join (join (meet ?3 ?5) (meet ?6 ?3)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +31648: Goal: +31648: Id : 1, {_}: + join (join (meet a b) (meet c b)) b =>= b + [] by prove_wal_axioms_6 +31648: Order: +31648: lpo +31648: Leaf order: +31648: a 1 0 1 1,1,1,2 +31648: c 1 0 1 1,2,1,2 +31648: b 4 0 4 2,1,1,2 +31648: meet 20 2 2 0,1,1,2 +31648: join 20 2 2 0,2 +% SZS status Timeout for LAT097-1.p +NO CLASH, using fixed ground order +31673: Facts: +31673: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31673: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31673: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31673: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31673: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31673: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31673: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31673: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31673: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +31673: Goal: +31673: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (meet d (join a (meet b d))))) + [] by prove_H28 +31673: Order: +31673: nrkbo +31673: Leaf order: +31673: c 2 0 2 1,2,2,2,2 +31673: b 3 0 3 1,2,2 +31673: d 3 0 3 2,2,2,2,2 +31673: a 4 0 4 1,2 +31673: join 16 2 3 0,2,2 +31673: meet 21 2 7 0,2 +NO CLASH, using fixed ground order +31675: Facts: +31675: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31675: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31675: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31675: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31675: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31675: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31675: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31675: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31675: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +31675: Goal: +31675: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (meet d (join a (meet b d))))) + [] by prove_H28 +31675: Order: +31675: lpo +31675: Leaf order: +31675: c 2 0 2 1,2,2,2,2 +31675: b 3 0 3 1,2,2 +31675: d 3 0 3 2,2,2,2,2 +31675: a 4 0 4 1,2 +31675: join 16 2 3 0,2,2 +31675: meet 21 2 7 0,2 +NO CLASH, using fixed ground order +31674: Facts: +31674: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31674: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31674: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31674: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31674: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31674: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31674: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31674: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31674: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +31674: Goal: +31674: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (meet d (join a (meet b d))))) + [] by prove_H28 +31674: Order: +31674: kbo +31674: Leaf order: +31674: c 2 0 2 1,2,2,2,2 +31674: b 3 0 3 1,2,2 +31674: d 3 0 3 2,2,2,2,2 +31674: a 4 0 4 1,2 +31674: join 16 2 3 0,2,2 +31674: meet 21 2 7 0,2 +% SZS status Timeout for LAT146-1.p +NO CLASH, using fixed ground order +31717: Facts: +31717: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31717: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31717: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31717: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31717: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31717: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31717: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31717: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31717: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +31717: Goal: +31717: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +31717: Order: +31717: nrkbo +31717: Leaf order: +31717: c 2 0 2 2,2,2,2 +31717: b 4 0 4 1,2,2 +31717: a 6 0 6 1,2 +31717: join 17 2 4 0,2,2 +31717: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +31718: Facts: +31718: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31718: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31718: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31718: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31718: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31718: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31718: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31718: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31718: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +31718: Goal: +31718: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +31718: Order: +31718: kbo +31718: Leaf order: +31718: c 2 0 2 2,2,2,2 +31718: b 4 0 4 1,2,2 +31718: a 6 0 6 1,2 +31718: join 17 2 4 0,2,2 +31718: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +31719: Facts: +31719: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31719: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31719: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31719: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31719: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31719: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31719: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31719: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31719: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +31719: Goal: +31719: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +31719: Order: +31719: lpo +31719: Leaf order: +31719: c 2 0 2 2,2,2,2 +31719: b 4 0 4 1,2,2 +31719: a 6 0 6 1,2 +31719: join 17 2 4 0,2,2 +31719: meet 20 2 6 0,2 +% SZS status Timeout for LAT148-1.p +NO CLASH, using fixed ground order +31740: Facts: +31740: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31740: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31740: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31740: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31740: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31740: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31740: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31740: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31740: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +31740: Goal: +31740: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +31740: Order: +31740: nrkbo +31740: Leaf order: +31740: b 3 0 3 1,2,2 +31740: c 3 0 3 2,2,2,2 +31740: a 6 0 6 1,2 +31740: join 18 2 4 0,2,2 +31740: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +31741: Facts: +31741: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31741: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31741: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31741: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31741: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31741: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31741: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31741: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31741: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +31741: Goal: +31741: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +31741: Order: +31741: kbo +31741: Leaf order: +31741: b 3 0 3 1,2,2 +31741: c 3 0 3 2,2,2,2 +31741: a 6 0 6 1,2 +31741: join 18 2 4 0,2,2 +31741: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +31742: Facts: +31742: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31742: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31742: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31742: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31742: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31742: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31742: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31742: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31742: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +31742: Goal: +31742: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +31742: Order: +31742: lpo +31742: Leaf order: +31742: b 3 0 3 1,2,2 +31742: c 3 0 3 2,2,2,2 +31742: a 6 0 6 1,2 +31742: join 18 2 4 0,2,2 +31742: meet 20 2 6 0,2 +% SZS status Timeout for LAT156-1.p +NO CLASH, using fixed ground order +31822: Facts: +31822: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31822: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31822: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31822: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31822: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31822: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31822: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31822: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31822: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29 +31822: Goal: +31822: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c d))) + [] by prove_H51 +31822: Order: +31822: nrkbo +31822: Leaf order: +31822: b 2 0 2 1,2,2 +31822: d 2 0 2 2,2,2,2,2 +31822: c 3 0 3 1,2,2,2 +31822: a 4 0 4 1,2 +31822: join 18 2 4 0,2,2 +31822: meet 19 2 5 0,2 +NO CLASH, using fixed ground order +31823: Facts: +31823: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31823: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31823: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31823: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31823: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31823: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31823: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31823: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31823: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29 +31823: Goal: +31823: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c d))) + [] by prove_H51 +31823: Order: +31823: kbo +31823: Leaf order: +31823: b 2 0 2 1,2,2 +31823: d 2 0 2 2,2,2,2,2 +31823: c 3 0 3 1,2,2,2 +31823: a 4 0 4 1,2 +31823: join 18 2 4 0,2,2 +31823: meet 19 2 5 0,2 +NO CLASH, using fixed ground order +31824: Facts: +31824: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +31824: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +31824: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +31824: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +31824: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +31824: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +31824: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +31824: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +31824: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (join (meet ?28 ?29) (meet ?28 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H52 ?26 ?27 ?28 ?29 +31824: Goal: +31824: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c d))) + [] by prove_H51 +31824: Order: +31824: lpo +31824: Leaf order: +31824: b 2 0 2 1,2,2 +31824: d 2 0 2 2,2,2,2,2 +31824: c 3 0 3 1,2,2,2 +31824: a 4 0 4 1,2 +31824: join 18 2 4 0,2,2 +31824: meet 19 2 5 0,2 +% SZS status Timeout for LAT160-1.p +NO CLASH, using fixed ground order +31846: Facts: +31846: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +31846: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +31846: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +31846: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +31846: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +31846: Id : 7, {_}: + or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +31846: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +31846: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +31846: Id : 10, {_}: + and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +31846: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +31846: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +31846: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +31846: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +31846: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +31846: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +31846: Id : 17, {_}: not truth =>= falsehood [] by false_definition +31846: Goal: +31846: Id : 1, {_}: + and_star (xor (and_star (xor truth x) y) truth) y + =<= + and_star (xor (and_star (xor truth y) x) truth) x + [] by prove_alternative_wajsberg_axiom +31846: Order: +31846: nrkbo +31846: Leaf order: +31846: falsehood 1 0 0 +31846: x 3 0 3 2,1,1,1,2 +31846: y 3 0 3 2,1,1,2 +31846: truth 8 0 4 1,1,1,1,2 +31846: not 12 1 0 +31846: xor 7 2 4 0,1,2 +31846: and 9 2 0 +31846: or 10 2 0 +31846: and_star 11 2 4 0,2 +31846: implies 14 2 0 +NO CLASH, using fixed ground order +31847: Facts: +31847: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +31847: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +31847: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +31847: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +31847: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +31847: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +31847: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +31847: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +31847: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +31847: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +31847: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +31847: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +31847: Id : 14, {_}: + and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +31847: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +31847: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +31847: Id : 17, {_}: not truth =>= falsehood [] by false_definition +31847: Goal: +31847: Id : 1, {_}: + and_star (xor (and_star (xor truth x) y) truth) y + =?= + and_star (xor (and_star (xor truth y) x) truth) x + [] by prove_alternative_wajsberg_axiom +31847: Order: +31847: kbo +31847: Leaf order: +31847: falsehood 1 0 0 +31847: x 3 0 3 2,1,1,1,2 +31847: y 3 0 3 2,1,1,2 +31847: truth 8 0 4 1,1,1,1,2 +31847: not 12 1 0 +31847: xor 7 2 4 0,1,2 +31847: and 9 2 0 +31847: or 10 2 0 +31847: and_star 11 2 4 0,2 +31847: implies 14 2 0 +NO CLASH, using fixed ground order +31848: Facts: +31848: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2 +31848: Id : 3, {_}: + implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) + =>= + truth + [6, 5, 4] by wajsberg_2 ?4 ?5 ?6 +31848: Id : 4, {_}: + implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 + [9, 8] by wajsberg_3 ?8 ?9 +31848: Id : 5, {_}: + implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth + [12, 11] by wajsberg_4 ?11 ?12 +31848: Id : 6, {_}: + or ?14 ?15 =<= implies (not ?14) ?15 + [15, 14] by or_definition ?14 ?15 +31848: Id : 7, {_}: + or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) + [19, 18, 17] by or_associativity ?17 ?18 ?19 +31848: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22 +31848: Id : 9, {_}: + and ?24 ?25 =<= not (or (not ?24) (not ?25)) + [25, 24] by and_definition ?24 ?25 +31848: Id : 10, {_}: + and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) + [29, 28, 27] by and_associativity ?27 ?28 ?29 +31848: Id : 11, {_}: + and ?31 ?32 =?= and ?32 ?31 + [32, 31] by and_commutativity ?31 ?32 +31848: Id : 12, {_}: + xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) + [35, 34] by xor_definition ?34 ?35 +31848: Id : 13, {_}: + xor ?37 ?38 =?= xor ?38 ?37 + [38, 37] by xor_commutativity ?37 ?38 +31848: Id : 14, {_}: + and_star ?40 ?41 =>= not (or (not ?40) (not ?41)) + [41, 40] by and_star_definition ?40 ?41 +31848: Id : 15, {_}: + and_star (and_star ?43 ?44) ?45 =>= and_star ?43 (and_star ?44 ?45) + [45, 44, 43] by and_star_associativity ?43 ?44 ?45 +31848: Id : 16, {_}: + and_star ?47 ?48 =?= and_star ?48 ?47 + [48, 47] by and_star_commutativity ?47 ?48 +31848: Id : 17, {_}: not truth =>= falsehood [] by false_definition +31848: Goal: +31848: Id : 1, {_}: + and_star (xor (and_star (xor truth x) y) truth) y + =<= + and_star (xor (and_star (xor truth y) x) truth) x + [] by prove_alternative_wajsberg_axiom +31848: Order: +31848: lpo +31848: Leaf order: +31848: falsehood 1 0 0 +31848: x 3 0 3 2,1,1,1,2 +31848: y 3 0 3 2,1,1,2 +31848: truth 8 0 4 1,1,1,1,2 +31848: not 12 1 0 +31848: xor 7 2 4 0,1,2 +31848: and 9 2 0 +31848: or 10 2 0 +31848: and_star 11 2 4 0,2 +31848: implies 14 2 0 +% SZS status Timeout for LCL160-1.p +NO CLASH, using fixed ground order +31871: Facts: +31871: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2 +31871: Id : 3, {_}: + add ?4 (additive_inverse ?4) =>= additive_identity + [4] by right_additive_inverse ?4 +31871: Id : 4, {_}: + multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8) + [8, 7, 6] by distribute1 ?6 ?7 ?8 +31871: Id : 5, {_}: + multiply (add ?10 ?11) ?12 + =<= + add (multiply ?10 ?12) (multiply ?11 ?12) + [12, 11, 10] by distribute2 ?10 ?11 ?12 +31871: Id : 6, {_}: + add (add ?14 ?15) ?16 =?= add ?14 (add ?15 ?16) + [16, 15, 14] by associative_addition ?14 ?15 ?16 +31871: Id : 7, {_}: + add ?18 ?19 =?= add ?19 ?18 + [19, 18] by commutative_addition ?18 ?19 +31871: Id : 8, {_}: + multiply (multiply ?21 ?22) ?23 =?= multiply ?21 (multiply ?22 ?23) + [23, 22, 21] by associative_multiplication ?21 ?22 ?23 +31871: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25 +31871: Goal: +31871: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity +31871: Order: +31871: nrkbo +31871: Leaf order: +31871: additive_identity 2 0 0 +31871: a 2 0 2 1,2 +31871: b 2 0 2 2,2 +31871: additive_inverse 1 1 0 +31871: add 12 2 0 +31871: multiply 14 2 2 0,2 +NO CLASH, using fixed ground order +31872: Facts: +31872: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2 +31872: Id : 3, {_}: + add ?4 (additive_inverse ?4) =>= additive_identity + [4] by right_additive_inverse ?4 +31872: Id : 4, {_}: + multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8) + [8, 7, 6] by distribute1 ?6 ?7 ?8 +31872: Id : 5, {_}: + multiply (add ?10 ?11) ?12 + =<= + add (multiply ?10 ?12) (multiply ?11 ?12) + [12, 11, 10] by distribute2 ?10 ?11 ?12 +31872: Id : 6, {_}: + add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16) + [16, 15, 14] by associative_addition ?14 ?15 ?16 +31872: Id : 7, {_}: + add ?18 ?19 =?= add ?19 ?18 + [19, 18] by commutative_addition ?18 ?19 +31872: Id : 8, {_}: + multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23) + [23, 22, 21] by associative_multiplication ?21 ?22 ?23 +31872: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25 +31872: Goal: +31872: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity +31872: Order: +31872: kbo +31872: Leaf order: +31872: additive_identity 2 0 0 +31872: a 2 0 2 1,2 +31872: b 2 0 2 2,2 +31872: additive_inverse 1 1 0 +31872: add 12 2 0 +31872: multiply 14 2 2 0,2 +NO CLASH, using fixed ground order +31873: Facts: +31873: Id : 2, {_}: add ?2 additive_identity =>= ?2 [2] by right_identity ?2 +31873: Id : 3, {_}: + add ?4 (additive_inverse ?4) =>= additive_identity + [4] by right_additive_inverse ?4 +31873: Id : 4, {_}: + multiply ?6 (add ?7 ?8) =>= add (multiply ?6 ?7) (multiply ?6 ?8) + [8, 7, 6] by distribute1 ?6 ?7 ?8 +31873: Id : 5, {_}: + multiply (add ?10 ?11) ?12 + =>= + add (multiply ?10 ?12) (multiply ?11 ?12) + [12, 11, 10] by distribute2 ?10 ?11 ?12 +31873: Id : 6, {_}: + add (add ?14 ?15) ?16 =>= add ?14 (add ?15 ?16) + [16, 15, 14] by associative_addition ?14 ?15 ?16 +31873: Id : 7, {_}: + add ?18 ?19 =?= add ?19 ?18 + [19, 18] by commutative_addition ?18 ?19 +31873: Id : 8, {_}: + multiply (multiply ?21 ?22) ?23 =>= multiply ?21 (multiply ?22 ?23) + [23, 22, 21] by associative_multiplication ?21 ?22 ?23 +31873: Id : 9, {_}: multiply ?25 (multiply ?25 ?25) =>= ?25 [25] by x_cubed_is_x ?25 +31873: Goal: +31873: Id : 1, {_}: multiply a b =<= multiply b a [] by prove_commutativity +31873: Order: +31873: lpo +31873: Leaf order: +31873: additive_identity 2 0 0 +31873: a 2 0 2 1,2 +31873: b 2 0 2 2,2 +31873: additive_inverse 1 1 0 +31873: add 12 2 0 +31873: multiply 14 2 2 0,2 +% SZS status Timeout for RNG009-5.p +NO CLASH, using fixed ground order +31898: Facts: +31898: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31898: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31898: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +31898: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +31898: Id : 6, {_}: + add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +31898: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +31898: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +31898: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +31898: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +31898: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29 +31898: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +31898: Goal: +31898: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +31898: Order: +31898: nrkbo +31898: Leaf order: +31898: b 2 0 1 1,2 +31898: a 2 0 1 2,2 +31898: c 2 0 1 3 +31898: additive_identity 4 0 0 +31898: additive_inverse 2 1 0 +31898: add 14 2 0 +31898: multiply 14 2 1 0,2 +NO CLASH, using fixed ground order +31899: Facts: +31899: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31899: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31899: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +31899: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +31899: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +31899: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +31899: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +31899: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +31899: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +31899: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29 +31899: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +31899: Goal: +31899: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +31899: Order: +31899: kbo +31899: Leaf order: +31899: b 2 0 1 1,2 +31899: a 2 0 1 2,2 +31899: c 2 0 1 3 +31899: additive_identity 4 0 0 +31899: additive_inverse 2 1 0 +31899: add 14 2 0 +31899: multiply 14 2 1 0,2 +NO CLASH, using fixed ground order +31900: Facts: +31900: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31900: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31900: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +31900: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +31900: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +31900: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +31900: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +31900: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +31900: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +31900: Id : 11, {_}: multiply ?29 (multiply ?29 ?29) =>= ?29 [29] by x_cubed_is_x ?29 +31900: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +31900: Goal: +31900: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +31900: Order: +31900: lpo +31900: Leaf order: +31900: b 2 0 1 1,2 +31900: a 2 0 1 2,2 +31900: c 2 0 1 3 +31900: additive_identity 4 0 0 +31900: additive_inverse 2 1 0 +31900: add 14 2 0 +31900: multiply 14 2 1 0,2 +% SZS status Timeout for RNG009-7.p +NO CLASH, using fixed ground order +31923: Facts: +31923: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31923: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31923: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +31923: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +31923: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +31923: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +31923: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +31923: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +31923: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +31923: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +31923: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +31923: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +31923: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +31923: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +31923: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +31923: Goal: +31923: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +31923: Order: +31923: nrkbo +31923: Leaf order: +31923: a 5 0 5 1,1,1,1,2 +31923: b 5 0 5 2,1,1,1,2 +31923: c 5 0 5 2,1,1,2 +31923: d 5 0 5 3,1,1,2 +31923: additive_identity 9 0 1 3 +31923: additive_inverse 7 1 1 0,2,2 +31923: commutator 1 2 0 +31923: add 20 2 4 0,2 +31923: multiply 27 2 5 0,1,1,1,2 +31923: associator 6 3 5 0,1,1,2 +NO CLASH, using fixed ground order +31924: Facts: +31924: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31924: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31924: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +31924: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +31924: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +31924: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +31924: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +31924: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +31924: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +31924: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +31924: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +31924: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +31924: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +31924: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +31924: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +31924: Goal: +31924: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +31924: Order: +31924: kbo +31924: Leaf order: +31924: a 5 0 5 1,1,1,1,2 +31924: b 5 0 5 2,1,1,1,2 +31924: c 5 0 5 2,1,1,2 +31924: d 5 0 5 3,1,1,2 +31924: additive_identity 9 0 1 3 +31924: additive_inverse 7 1 1 0,2,2 +31924: commutator 1 2 0 +31924: add 20 2 4 0,2 +31924: multiply 27 2 5 0,1,1,1,2 +31924: associator 6 3 5 0,1,1,2 +NO CLASH, using fixed ground order +31925: Facts: +31925: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31925: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31925: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +31925: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +31925: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +31925: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +31925: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +31925: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +31925: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +31925: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +31925: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +31925: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +31925: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +31925: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +31925: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +31925: Goal: +31925: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +31925: Order: +31925: lpo +31925: Leaf order: +31925: a 5 0 5 1,1,1,1,2 +31925: b 5 0 5 2,1,1,1,2 +31925: c 5 0 5 2,1,1,2 +31925: d 5 0 5 3,1,1,2 +31925: additive_identity 9 0 1 3 +31925: additive_inverse 7 1 1 0,2,2 +31925: commutator 1 2 0 +31925: add 20 2 4 0,2 +31925: multiply 27 2 5 0,1,1,1,2 +31925: associator 6 3 5 0,1,1,2 +% SZS status Timeout for RNG026-6.p +NO CLASH, using fixed ground order +31946: Facts: +31946: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31946: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31946: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +31946: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +31946: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +31946: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +31946: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +31946: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +31946: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +31946: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +31946: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +31946: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +31946: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +31946: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +31946: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +31946: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +31946: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +31946: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +31946: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +31946: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +31946: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +31946: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +31946: Goal: +31946: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +31946: Order: +31946: nrkbo +31946: Leaf order: +31946: a 5 0 5 1,1,1,1,2 +31946: b 5 0 5 2,1,1,1,2 +31946: c 5 0 5 2,1,1,2 +31946: d 5 0 5 3,1,1,2 +31946: additive_identity 9 0 1 3 +31946: additive_inverse 23 1 1 0,2,2 +31946: commutator 1 2 0 +31946: add 28 2 4 0,2 +31946: multiply 45 2 5 0,1,1,1,2 +31946: associator 6 3 5 0,1,1,2 +NO CLASH, using fixed ground order +31947: Facts: +31947: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31947: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31947: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +31947: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +31947: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +31947: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +31947: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +31947: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +31947: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +31947: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +31947: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +31947: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +31947: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +31947: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +31947: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +31947: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +31947: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +31947: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +31947: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +31947: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +31947: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +31947: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +31947: Goal: +31947: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +31947: Order: +31947: kbo +31947: Leaf order: +31947: a 5 0 5 1,1,1,1,2 +31947: b 5 0 5 2,1,1,1,2 +31947: c 5 0 5 2,1,1,2 +31947: d 5 0 5 3,1,1,2 +31947: additive_identity 9 0 1 3 +31947: additive_inverse 23 1 1 0,2,2 +31947: commutator 1 2 0 +31947: add 28 2 4 0,2 +31947: multiply 45 2 5 0,1,1,1,2 +31947: associator 6 3 5 0,1,1,2 +NO CLASH, using fixed ground order +31948: Facts: +31948: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +31948: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +31948: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +31948: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +31948: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +31948: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +31948: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +31948: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +31948: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +31948: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +31948: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +31948: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +31948: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +31948: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +31948: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +31948: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +31948: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +31948: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +31948: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +31948: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +31948: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +31948: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +31948: Goal: +31948: Id : 1, {_}: + add + (add (associator (multiply a b) c d) + (associator a b (multiply c d))) + (additive_inverse + (add + (add (associator a (multiply b c) d) + (multiply a (associator b c d))) + (multiply (associator a b c) d))) + =>= + additive_identity + [] by prove_teichmuller_identity +31948: Order: +31948: lpo +31948: Leaf order: +31948: a 5 0 5 1,1,1,1,2 +31948: b 5 0 5 2,1,1,1,2 +31948: c 5 0 5 2,1,1,2 +31948: d 5 0 5 3,1,1,2 +31948: additive_identity 9 0 1 3 +31948: additive_inverse 23 1 1 0,2,2 +31948: commutator 1 2 0 +31948: add 28 2 4 0,2 +31948: multiply 45 2 5 0,1,1,1,2 +31948: associator 6 3 5 0,1,1,2 +% SZS status Timeout for RNG026-7.p +NO CLASH, using fixed ground order +31979: Facts: +31979: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by sh_1 ?2 ?3 ?4 +31979: Goal: +31979: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +31979: Order: +31979: nrkbo +31979: Leaf order: +31979: c 2 0 2 2,2,2,2 +31979: a 3 0 3 1,2 +31979: b 3 0 3 1,2,2 +31979: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +31980: Facts: +31980: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by sh_1 ?2 ?3 ?4 +31980: Goal: +31980: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +31980: Order: +31980: kbo +31980: Leaf order: +31980: c 2 0 2 2,2,2,2 +31980: a 3 0 3 1,2 +31980: b 3 0 3 1,2,2 +31980: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +31981: Facts: +31981: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by sh_1 ?2 ?3 ?4 +31981: Goal: +31981: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +31981: Order: +31981: lpo +31981: Leaf order: +31981: c 2 0 2 2,2,2,2 +31981: a 3 0 3 1,2 +31981: b 3 0 3 1,2,2 +31981: nand 12 2 6 0,2 +% SZS status Timeout for BOO076-1.p +CLASH, statistics insufficient +32007: Facts: +32007: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32007: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +32007: Goal: +32007: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +32007: Order: +32007: nrkbo +32007: Leaf order: +32007: b 1 0 0 +32007: w 1 0 0 +32007: f 3 1 3 0,2,2 +32007: apply 12 2 3 0,2 +CLASH, statistics insufficient +32008: Facts: +32008: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32008: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +32008: Goal: +32008: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +32008: Order: +32008: kbo +32008: Leaf order: +32008: b 1 0 0 +32008: w 1 0 0 +32008: f 3 1 3 0,2,2 +32008: apply 12 2 3 0,2 +CLASH, statistics insufficient +32009: Facts: +32009: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32009: Id : 3, {_}: + apply (apply w ?7) ?8 =?= apply (apply ?7 ?8) ?8 + [8, 7] by w_definition ?7 ?8 +32009: Goal: +32009: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_strong_fixed_point ?1 +32009: Order: +32009: lpo +32009: Leaf order: +32009: b 1 0 0 +32009: w 1 0 0 +32009: f 3 1 3 0,2,2 +32009: apply 12 2 3 0,2 +% SZS status Timeout for COL003-1.p +CLASH, statistics insufficient +32036: Facts: +32036: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +CLASH, statistics insufficient +32037: Facts: +32037: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32037: Id : 3, {_}: + apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7 + [8, 7] by w1_definition ?7 ?8 +32037: Goal: +32037: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +32037: Order: +32037: kbo +32037: Leaf order: +32037: b 1 0 0 +32037: w1 1 0 0 +32037: f 3 1 3 0,2,2 +32037: apply 12 2 3 0,2 +32036: Id : 3, {_}: + apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7 + [8, 7] by w1_definition ?7 ?8 +32036: Goal: +32036: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +32036: Order: +32036: nrkbo +32036: Leaf order: +32036: b 1 0 0 +32036: w1 1 0 0 +32036: f 3 1 3 0,2,2 +32036: apply 12 2 3 0,2 +CLASH, statistics insufficient +32038: Facts: +32038: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32038: Id : 3, {_}: + apply (apply w1 ?7) ?8 =?= apply (apply ?8 ?7) ?7 + [8, 7] by w1_definition ?7 ?8 +32038: Goal: +32038: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +32038: Order: +32038: lpo +32038: Leaf order: +32038: b 1 0 0 +32038: w1 1 0 0 +32038: f 3 1 3 0,2,2 +32038: apply 12 2 3 0,2 +% SZS status Timeout for COL042-1.p +NO CLASH, using fixed ground order +32071: Facts: +32071: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32071: Id : 3, {_}: + apply (apply (apply h ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?7) ?8) ?7 + [8, 7, 6] by h_definition ?6 ?7 ?8 +32071: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply h + (apply (apply b (apply (apply b h) (apply b b))) + (apply h (apply (apply b h) (apply b b))))) h)) b)) b + [] by strong_fixed_point +32071: Goal: +32071: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32071: Order: +32071: nrkbo +32071: Leaf order: +32071: strong_fixed_point 3 0 2 1,2 +32071: fixed_pt 3 0 3 2,2 +32071: h 6 0 0 +32071: b 12 0 0 +32071: apply 29 2 3 0,2 +NO CLASH, using fixed ground order +32072: Facts: +32072: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32072: Id : 3, {_}: + apply (apply (apply h ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?7) ?8) ?7 + [8, 7, 6] by h_definition ?6 ?7 ?8 +32072: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply h + (apply (apply b (apply (apply b h) (apply b b))) + (apply h (apply (apply b h) (apply b b))))) h)) b)) b + [] by strong_fixed_point +32072: Goal: +32072: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32072: Order: +32072: kbo +32072: Leaf order: +32072: strong_fixed_point 3 0 2 1,2 +32072: fixed_pt 3 0 3 2,2 +32072: h 6 0 0 +32072: b 12 0 0 +32072: apply 29 2 3 0,2 +NO CLASH, using fixed ground order +32073: Facts: +32073: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32073: Id : 3, {_}: + apply (apply (apply h ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?7) ?8) ?7 + [8, 7, 6] by h_definition ?6 ?7 ?8 +32073: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply h + (apply (apply b (apply (apply b h) (apply b b))) + (apply h (apply (apply b h) (apply b b))))) h)) b)) b + [] by strong_fixed_point +32073: Goal: +32073: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32073: Order: +32073: lpo +32073: Leaf order: +32073: strong_fixed_point 3 0 2 1,2 +32073: fixed_pt 3 0 3 2,2 +32073: h 6 0 0 +32073: b 12 0 0 +32073: apply 29 2 3 0,2 +% SZS status Timeout for COL043-3.p +NO CLASH, using fixed ground order +32095: Facts: +NO CLASH, using fixed ground order +32096: Facts: +32096: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32096: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +32096: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply (apply b b) n))))) n)) b)) b + [] by strong_fixed_point +32096: Goal: +32096: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32096: Order: +32096: kbo +32096: Leaf order: +32096: strong_fixed_point 3 0 2 1,2 +32096: fixed_pt 3 0 3 2,2 +32096: n 6 0 0 +32096: b 10 0 0 +32096: apply 27 2 3 0,2 +NO CLASH, using fixed ground order +32097: Facts: +32097: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32097: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +32097: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply (apply b b) n))))) n)) b)) b + [] by strong_fixed_point +32097: Goal: +32097: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32097: Order: +32097: lpo +32097: Leaf order: +32097: strong_fixed_point 3 0 2 1,2 +32097: fixed_pt 3 0 3 2,2 +32097: n 6 0 0 +32097: b 10 0 0 +32097: apply 27 2 3 0,2 +32095: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32095: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +32095: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply (apply b b) n))))) n)) b)) b + [] by strong_fixed_point +32095: Goal: +32095: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32095: Order: +32095: nrkbo +32095: Leaf order: +32095: strong_fixed_point 3 0 2 1,2 +32095: fixed_pt 3 0 3 2,2 +32095: n 6 0 0 +32095: b 10 0 0 +32095: apply 27 2 3 0,2 +% SZS status Timeout for COL044-8.p +NO CLASH, using fixed ground order +32149: Facts: +32149: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32149: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +32149: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply n (apply b b)))))) n)) b)) b + [] by strong_fixed_point +32149: Goal: +32149: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32149: Order: +32149: nrkbo +32149: Leaf order: +32149: strong_fixed_point 3 0 2 1,2 +32149: fixed_pt 3 0 3 2,2 +32149: n 6 0 0 +32149: b 10 0 0 +32149: apply 27 2 3 0,2 +NO CLASH, using fixed ground order +32150: Facts: +32150: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32150: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +32150: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply n (apply b b)))))) n)) b)) b + [] by strong_fixed_point +32150: Goal: +32150: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32150: Order: +32150: kbo +32150: Leaf order: +32150: strong_fixed_point 3 0 2 1,2 +32150: fixed_pt 3 0 3 2,2 +32150: n 6 0 0 +32150: b 10 0 0 +32150: apply 27 2 3 0,2 +NO CLASH, using fixed ground order +32151: Facts: +32151: Id : 2, {_}: + apply (apply (apply b ?2) ?3) ?4 =>= apply ?2 (apply ?3 ?4) + [4, 3, 2] by b_definition ?2 ?3 ?4 +32151: Id : 3, {_}: + apply (apply (apply n ?6) ?7) ?8 + =?= + apply (apply (apply ?6 ?8) ?7) ?8 + [8, 7, 6] by n_definition ?6 ?7 ?8 +32151: Id : 4, {_}: + strong_fixed_point + =<= + apply + (apply b + (apply + (apply b + (apply + (apply n + (apply n + (apply (apply b (apply b b)) + (apply n (apply n (apply b b)))))) n)) b)) b + [] by strong_fixed_point +32151: Goal: +32151: Id : 1, {_}: + apply strong_fixed_point fixed_pt + =<= + apply fixed_pt (apply strong_fixed_point fixed_pt) + [] by prove_strong_fixed_point +32151: Order: +32151: lpo +32151: Leaf order: +32151: strong_fixed_point 3 0 2 1,2 +32151: fixed_pt 3 0 3 2,2 +32151: n 6 0 0 +32151: b 10 0 0 +32151: apply 27 2 3 0,2 +% SZS status Timeout for COL044-9.p +NO CLASH, using fixed ground order +32174: Facts: +32174: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +32174: Goal: +32174: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +32174: Order: +32174: nrkbo +32174: Leaf order: +32174: b2 2 0 2 1,1,1,2 +32174: a2 2 0 2 2,2 +32174: inverse 8 1 1 0,1,1,2 +32174: multiply 12 2 2 0,2 +NO CLASH, using fixed ground order +32175: Facts: +32175: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +32175: Goal: +32175: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +32175: Order: +32175: kbo +32175: Leaf order: +32175: b2 2 0 2 1,1,1,2 +32175: a2 2 0 2 2,2 +32175: inverse 8 1 1 0,1,1,2 +32175: multiply 12 2 2 0,2 +NO CLASH, using fixed ground order +32176: Facts: +32176: Id : 2, {_}: + multiply + (inverse + (multiply + (inverse + (multiply (inverse (multiply ?2 ?3)) (multiply ?3 ?2))) + (multiply (inverse (multiply ?4 ?5)) + (multiply ?4 + (inverse + (multiply (multiply ?6 (inverse ?7)) (inverse ?5))))))) + ?7 + =>= + ?6 + [7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 +32176: Goal: +32176: Id : 1, {_}: + multiply (multiply (inverse b2) b2) a2 =>= a2 + [] by prove_these_axioms_2 +32176: Order: +32176: lpo +32176: Leaf order: +32176: b2 2 0 2 1,1,1,2 +32176: a2 2 0 2 2,2 +32176: inverse 8 1 1 0,1,1,2 +32176: multiply 12 2 2 0,2 +% SZS status Timeout for GRP506-1.p +NO CLASH, using fixed ground order +32197: Facts: +32197: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32197: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +NO CLASH, using fixed ground order +32198: Facts: +32198: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32198: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32198: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32198: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32198: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32198: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32198: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32198: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32198: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +32198: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +32198: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +32198: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +32198: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +32197: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32197: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32197: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32197: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32197: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32197: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32197: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +NO CLASH, using fixed ground order +32197: Id : 11, {_}: + complement (meet ?29 ?30) =<= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +32197: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +32197: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +32197: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +32197: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by megill ?38 ?39 +32197: Goal: +32197: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_this +32197: Order: +32197: nrkbo +32197: Leaf order: +32197: n0 1 0 0 +32197: n1 2 0 0 +32197: b 3 0 3 1,2,2 +32197: a 7 0 7 1,2 +32197: complement 14 1 2 0,1,2,2,2,2 +32197: join 18 2 3 0,2,2 +32197: meet 19 2 5 0,2 +32199: Facts: +32199: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32199: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32199: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32199: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32199: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32199: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32199: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32199: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32199: Id : 10, {_}: + complement (join ?26 ?27) =<= meet (complement ?26) (complement ?27) + [27, 26] by compatibility1 ?26 ?27 +32199: Id : 11, {_}: + complement (meet ?29 ?30) =>= join (complement ?29) (complement ?30) + [30, 29] by compatibility2 ?29 ?30 +32199: Id : 12, {_}: join (complement ?32) ?32 =>= n1 [32] by invertability1 ?32 +32199: Id : 13, {_}: meet (complement ?34) ?34 =>= n0 [34] by invertability2 ?34 +32199: Id : 14, {_}: complement (complement ?36) =>= ?36 [36] by invertability3 ?36 +32199: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by megill ?38 ?39 +32199: Goal: +32199: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_this +32199: Order: +32199: lpo +32199: Leaf order: +32199: n0 1 0 0 +32199: n1 2 0 0 +32199: b 3 0 3 1,2,2 +32199: a 7 0 7 1,2 +32199: complement 14 1 2 0,1,2,2,2,2 +32199: join 18 2 3 0,2,2 +32199: meet 19 2 5 0,2 +32198: Id : 15, {_}: + join (meet (complement ?38) (join ?38 ?39)) + (join (complement ?39) (meet ?38 ?39)) + =>= + n1 + [39, 38] by megill ?38 ?39 +32198: Goal: +32198: Id : 1, {_}: + meet a (join b (meet a (join (complement a) (meet a b)))) + =>= + meet a (join (complement a) (meet a b)) + [] by prove_this +32198: Order: +32198: kbo +32198: Leaf order: +32198: n0 1 0 0 +32198: n1 2 0 0 +32198: b 3 0 3 1,2,2 +32198: a 7 0 7 1,2 +32198: complement 14 1 2 0,1,2,2,2,2 +32198: join 18 2 3 0,2,2 +32198: meet 19 2 5 0,2 +% SZS status Timeout for LAT053-1.p +NO CLASH, using fixed ground order +32222: Facts: +32222: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32222: Goal: +32222: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2 +32222: Order: +32222: nrkbo +32222: Leaf order: +32222: a 2 0 2 1,2 +32222: b 2 0 2 2,2 +32222: join 20 2 0 +32222: meet 20 2 2 0,2 +NO CLASH, using fixed ground order +32223: Facts: +32223: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32223: Goal: +32223: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2 +32223: Order: +32223: kbo +32223: Leaf order: +32223: a 2 0 2 1,2 +32223: b 2 0 2 2,2 +32223: join 20 2 0 +32223: meet 20 2 2 0,2 +NO CLASH, using fixed ground order +32224: Facts: +32224: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32224: Goal: +32224: Id : 1, {_}: meet a b =<= meet b a [] by prove_normal_axioms_2 +32224: Order: +32224: lpo +32224: Leaf order: +32224: a 2 0 2 1,2 +32224: b 2 0 2 2,2 +32224: join 20 2 0 +32224: meet 20 2 2 0,2 +% SZS status Timeout for LAT081-1.p +NO CLASH, using fixed ground order +32257: Facts: +32257: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32257: Goal: +32257: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5 +32257: Order: +32257: nrkbo +32257: Leaf order: +32257: a 2 0 2 1,2 +32257: b 2 0 2 2,2 +32257: meet 18 2 0 +32257: join 22 2 2 0,2 +NO CLASH, using fixed ground order +32258: Facts: +32258: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32258: Goal: +32258: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5 +32258: Order: +32258: kbo +32258: Leaf order: +32258: a 2 0 2 1,2 +32258: b 2 0 2 2,2 +32258: meet 18 2 0 +32258: join 22 2 2 0,2 +NO CLASH, using fixed ground order +32259: Facts: +32259: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32259: Goal: +32259: Id : 1, {_}: join a b =<= join b a [] by prove_normal_axioms_5 +32259: Order: +32259: lpo +32259: Leaf order: +32259: a 2 0 2 1,2 +32259: b 2 0 2 2,2 +32259: meet 18 2 0 +32259: join 22 2 2 0,2 +% SZS status Timeout for LAT084-1.p +NO CLASH, using fixed ground order +32283: Facts: +32283: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32283: Goal: +32283: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7 +32283: Order: +32283: nrkbo +32283: Leaf order: +32283: b 1 0 1 2,2,2 +32283: a 3 0 3 1,2 +32283: meet 19 2 1 0,2 +32283: join 21 2 1 0,2,2 +NO CLASH, using fixed ground order +32284: Facts: +32284: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32284: Goal: +32284: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7 +32284: Order: +32284: kbo +32284: Leaf order: +32284: b 1 0 1 2,2,2 +32284: a 3 0 3 1,2 +32284: meet 19 2 1 0,2 +32284: join 21 2 1 0,2,2 +NO CLASH, using fixed ground order +32285: Facts: +32285: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32285: Goal: +32285: Id : 1, {_}: meet a (join a b) =>= a [] by prove_normal_axioms_7 +32285: Order: +32285: lpo +32285: Leaf order: +32285: b 1 0 1 2,2,2 +32285: a 3 0 3 1,2 +32285: meet 19 2 1 0,2 +32285: join 21 2 1 0,2,2 +% SZS status Timeout for LAT086-1.p +NO CLASH, using fixed ground order +32311: Facts: +32311: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32311: Goal: +32311: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8 +32311: Order: +32311: nrkbo +32311: Leaf order: +32311: b 1 0 1 2,2,2 +32311: a 3 0 3 1,2 +32311: meet 19 2 1 0,2,2 +32311: join 21 2 1 0,2 +NO CLASH, using fixed ground order +32312: Facts: +32312: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32312: Goal: +32312: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8 +32312: Order: +32312: kbo +32312: Leaf order: +32312: b 1 0 1 2,2,2 +32312: a 3 0 3 1,2 +32312: meet 19 2 1 0,2,2 +32312: join 21 2 1 0,2 +NO CLASH, using fixed ground order +32313: Facts: +32313: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +32313: Goal: +32313: Id : 1, {_}: join a (meet a b) =>= a [] by prove_normal_axioms_8 +32313: Order: +32313: lpo +32313: Leaf order: +32313: b 1 0 1 2,2,2 +32313: a 3 0 3 1,2 +32313: meet 19 2 1 0,2,2 +32313: join 21 2 1 0,2 +% SZS status Timeout for LAT087-1.p +NO CLASH, using fixed ground order +32355: Facts: +32355: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32355: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32355: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32355: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32355: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32355: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32355: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32355: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32355: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H3 ?26 ?27 ?28 +32355: Goal: +32355: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +32355: Order: +32355: nrkbo +32355: Leaf order: +32355: a 4 0 4 1,2 +32355: b 4 0 4 1,2,2 +32355: c 4 0 4 2,2,2,2 +32355: join 17 2 4 0,2,2 +32355: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +32356: Facts: +32356: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32356: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32356: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32356: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32356: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32356: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32356: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32356: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32356: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H3 ?26 ?27 ?28 +32356: Goal: +32356: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +32356: Order: +32356: kbo +32356: Leaf order: +32356: a 4 0 4 1,2 +32356: b 4 0 4 1,2,2 +32356: c 4 0 4 2,2,2,2 +32356: join 17 2 4 0,2,2 +32356: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +32357: Facts: +32357: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32357: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32357: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32357: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32357: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32357: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32357: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32357: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32357: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H3 ?26 ?27 ?28 +32357: Goal: +32357: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +32357: Order: +32357: lpo +32357: Leaf order: +32357: a 4 0 4 1,2 +32357: b 4 0 4 1,2,2 +32357: c 4 0 4 2,2,2,2 +32357: join 17 2 4 0,2,2 +32357: meet 21 2 6 0,2 +% SZS status Timeout for LAT099-1.p +NO CLASH, using fixed ground order +32378: Facts: +32378: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32378: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32378: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32378: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32378: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32378: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32378: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32378: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32378: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +32378: Goal: +32378: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +32378: Order: +32378: nrkbo +32378: Leaf order: +32378: d 2 0 2 2,2,2,2,2 +32378: b 3 0 3 1,2,2 +32378: c 3 0 3 1,2,2,2 +32378: a 4 0 4 1,2 +32378: meet 19 2 5 0,2 +32378: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +32379: Facts: +32379: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32379: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32379: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32379: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32379: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32379: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32379: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32379: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32379: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +32379: Goal: +32379: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +32379: Order: +32379: kbo +32379: Leaf order: +32379: d 2 0 2 2,2,2,2,2 +32379: b 3 0 3 1,2,2 +32379: c 3 0 3 1,2,2,2 +32379: a 4 0 4 1,2 +32379: meet 19 2 5 0,2 +32379: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +32380: Facts: +32380: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32380: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32380: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32380: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32380: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32380: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32380: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32380: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32380: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +32380: Goal: +32380: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +32380: Order: +32380: lpo +32380: Leaf order: +32380: d 2 0 2 2,2,2,2,2 +32380: b 3 0 3 1,2,2 +32380: c 3 0 3 1,2,2,2 +32380: a 4 0 4 1,2 +32380: meet 19 2 5 0,2 +32380: join 19 2 5 0,2,2 +% SZS status Timeout for LAT110-1.p +NO CLASH, using fixed ground order +32414: Facts: +32414: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32414: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32414: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32414: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32414: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32414: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32414: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32414: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32414: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29)) + [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29 +32414: Goal: +32414: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +32414: Order: +32414: nrkbo +32414: Leaf order: +32414: b 3 0 3 1,2,2 +32414: c 3 0 3 2,2,2 +32414: a 5 0 5 1,2 +32414: join 17 2 4 0,2,2 +32414: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +32415: Facts: +32415: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32415: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32415: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32415: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32415: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32415: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32415: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32415: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32415: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29)) + [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29 +32415: Goal: +32415: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +32415: Order: +32415: kbo +32415: Leaf order: +32415: b 3 0 3 1,2,2 +32415: c 3 0 3 2,2,2 +32415: a 5 0 5 1,2 +32415: join 17 2 4 0,2,2 +32415: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +32416: Facts: +32416: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32416: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32416: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32416: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32416: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32416: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32416: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32416: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32416: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join (meet ?26 (join ?27 (meet ?26 ?28))) (meet ?28 ?29)) + [29, 28, 27, 26] by equation_H79 ?26 ?27 ?28 ?29 +32416: Goal: +32416: Id : 1, {_}: + meet a (join b c) + =<= + join (meet a (join c (meet a b))) (meet a (join b (meet a c))) + [] by prove_H69 +32416: Order: +32416: lpo +32416: Leaf order: +32416: b 3 0 3 1,2,2 +32416: c 3 0 3 2,2,2 +32416: a 5 0 5 1,2 +32416: join 17 2 4 0,2,2 +32416: meet 20 2 5 0,2 +% SZS status Timeout for LAT118-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +32445: Facts: +32445: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32445: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32445: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32445: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32445: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32445: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32445: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32445: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32445: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +32445: Goal: +32445: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +32445: Order: +32445: kbo +32445: Leaf order: +32445: b 3 0 3 1,2,2 +32445: c 3 0 3 2,2,2,2 +32445: a 6 0 6 1,2 +32445: join 17 2 4 0,2,2 +32445: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +32446: Facts: +32446: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32446: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32446: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32446: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32446: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32446: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32446: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32446: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32446: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +32446: Goal: +32446: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +32446: Order: +32446: lpo +32446: Leaf order: +32446: b 3 0 3 1,2,2 +32446: c 3 0 3 2,2,2,2 +32446: a 6 0 6 1,2 +32446: join 17 2 4 0,2,2 +32446: meet 21 2 6 0,2 +32444: Facts: +32444: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32444: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32444: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32444: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32444: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32444: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32444: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32444: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32444: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?28 (meet ?26 ?27))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H22 ?26 ?27 ?28 +32444: Goal: +32444: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +32444: Order: +32444: nrkbo +32444: Leaf order: +32444: b 3 0 3 1,2,2 +32444: c 3 0 3 2,2,2,2 +32444: a 6 0 6 1,2 +32444: join 17 2 4 0,2,2 +32444: meet 21 2 6 0,2 +% SZS status Timeout for LAT142-1.p +NO CLASH, using fixed ground order +32541: Facts: +32541: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32541: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32541: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32541: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32541: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32541: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32541: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32541: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32541: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +32541: Goal: +32541: Id : 1, {_}: + meet a (meet b (join c (meet a d))) + =<= + meet a (meet b (join c (meet d (join a (meet b c))))) + [] by prove_H45 +32541: Order: +32541: nrkbo +32541: Leaf order: +32541: d 2 0 2 2,2,2,2,2 +32541: b 3 0 3 1,2,2 +32541: c 3 0 3 1,2,2,2 +32541: a 4 0 4 1,2 +32541: join 16 2 3 0,2,2,2 +32541: meet 21 2 7 0,2 +NO CLASH, using fixed ground order +32542: Facts: +32542: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32542: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32542: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32542: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32542: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32542: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32542: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32542: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32542: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +32542: Goal: +32542: Id : 1, {_}: + meet a (meet b (join c (meet a d))) + =<= + meet a (meet b (join c (meet d (join a (meet b c))))) + [] by prove_H45 +32542: Order: +32542: kbo +32542: Leaf order: +32542: d 2 0 2 2,2,2,2,2 +32542: b 3 0 3 1,2,2 +32542: c 3 0 3 1,2,2,2 +32542: a 4 0 4 1,2 +32542: join 16 2 3 0,2,2,2 +32542: meet 21 2 7 0,2 +NO CLASH, using fixed ground order +32543: Facts: +32543: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32543: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32543: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32543: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32543: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32543: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32543: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32543: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32543: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 ?29)) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (meet ?29 (join ?27 ?28))))) + [29, 28, 27, 26] by equation_H34 ?26 ?27 ?28 ?29 +32543: Goal: +32543: Id : 1, {_}: + meet a (meet b (join c (meet a d))) + =>= + meet a (meet b (join c (meet d (join a (meet b c))))) + [] by prove_H45 +32543: Order: +32543: lpo +32543: Leaf order: +32543: d 2 0 2 2,2,2,2,2 +32543: b 3 0 3 1,2,2 +32543: c 3 0 3 1,2,2,2 +32543: a 4 0 4 1,2 +32543: join 16 2 3 0,2,2,2 +32543: meet 21 2 7 0,2 +% SZS status Timeout for LAT147-1.p +NO CLASH, using fixed ground order +32564: Facts: +32564: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32564: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32564: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32564: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32564: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32564: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32564: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32564: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32564: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29 +32564: Goal: +32564: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +32564: Order: +32564: nrkbo +32564: Leaf order: +32564: b 3 0 3 1,2,2 +32564: c 3 0 3 2,2,2,2 +32564: a 6 0 6 1,2 +32564: join 18 2 4 0,2,2 +32564: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +32565: Facts: +32565: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32565: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32565: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32565: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32565: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32565: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32565: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32565: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32565: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29 +32565: Goal: +32565: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +32565: Order: +32565: kbo +32565: Leaf order: +32565: b 3 0 3 1,2,2 +32565: c 3 0 3 2,2,2,2 +32565: a 6 0 6 1,2 +32565: join 18 2 4 0,2,2 +32565: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +32566: Facts: +32566: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32566: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32566: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32566: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32566: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32566: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32566: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32566: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32566: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?27 (join ?29 (meet ?26 ?28))))) + [29, 28, 27, 26] by equation_H42 ?26 ?27 ?28 ?29 +32566: Goal: +32566: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +32566: Order: +32566: lpo +32566: Leaf order: +32566: b 3 0 3 1,2,2 +32566: c 3 0 3 2,2,2,2 +32566: a 6 0 6 1,2 +32566: join 18 2 4 0,2,2 +32566: meet 20 2 6 0,2 +% SZS status Timeout for LAT154-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +32589: Facts: +32589: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32589: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32589: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32589: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32589: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32589: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32589: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32589: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32589: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +32589: Goal: +32589: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +32589: Order: +32589: kbo +32589: Leaf order: +32589: a 4 0 4 1,2 +32589: b 4 0 4 1,2,2 +32589: c 4 0 4 2,2,2,2 +32589: join 18 2 4 0,2,2 +32589: meet 20 2 6 0,2 +32588: Facts: +32588: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32588: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32588: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32588: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32588: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32588: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32588: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32588: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32588: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +32588: Goal: +32588: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +32588: Order: +32588: nrkbo +32588: Leaf order: +32588: a 4 0 4 1,2 +32588: b 4 0 4 1,2,2 +32588: c 4 0 4 2,2,2,2 +32588: join 18 2 4 0,2,2 +32588: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +32590: Facts: +32590: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32590: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32590: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32590: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32590: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32590: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32590: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32590: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32590: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (join (meet ?26 ?28) (meet ?28 (join ?27 ?29)))) + [29, 28, 27, 26] by equation_H49 ?26 ?27 ?28 ?29 +32590: Goal: +32590: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +32590: Order: +32590: lpo +32590: Leaf order: +32590: a 4 0 4 1,2 +32590: b 4 0 4 1,2,2 +32590: c 4 0 4 2,2,2,2 +32590: join 18 2 4 0,2,2 +32590: meet 20 2 6 0,2 +% SZS status Timeout for LAT155-1.p +NO CLASH, using fixed ground order +32615: Facts: +32615: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32615: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32615: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32615: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32615: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32615: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32615: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32615: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32615: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29 +32615: Goal: +32615: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +32615: Order: +32615: nrkbo +32615: Leaf order: +32615: c 2 0 2 2,2,2 +32615: a 4 0 4 1,2 +32615: b 4 0 4 1,2,2 +32615: meet 18 2 4 0,2 +32615: join 18 2 4 0,2,2 +NO CLASH, using fixed ground order +32616: Facts: +32616: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32616: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32616: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32616: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32616: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32616: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32616: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32616: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32616: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29 +32616: Goal: +32616: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +32616: Order: +32616: kbo +32616: Leaf order: +32616: c 2 0 2 2,2,2 +32616: a 4 0 4 1,2 +32616: b 4 0 4 1,2,2 +32616: meet 18 2 4 0,2 +32616: join 18 2 4 0,2,2 +NO CLASH, using fixed ground order +32617: Facts: +32617: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +32617: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +32617: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +32617: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +32617: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +32617: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +32617: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +32617: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +32617: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + join ?26 (meet ?27 (meet (join ?26 ?28) (join ?28 (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H49_dual ?26 ?27 ?28 ?29 +32617: Goal: +32617: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +32617: Order: +32617: lpo +32617: Leaf order: +32617: c 2 0 2 2,2,2 +32617: a 4 0 4 1,2 +32617: b 4 0 4 1,2,2 +32617: meet 18 2 4 0,2 +32617: join 18 2 4 0,2,2 +% SZS status Timeout for LAT170-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +32640: Facts: +32640: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +32640: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +32640: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +32640: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +32640: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +32640: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +32640: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +32640: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +32640: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +32640: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +32640: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +32640: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +32640: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +NO CLASH, using fixed ground order +32641: Facts: +32641: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +32641: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +32641: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +32641: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +32641: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +32641: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +32641: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +32641: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +32641: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +32641: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +32641: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +32641: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +32641: Id : 14, {_}: + associator ?34 ?35 ?36 + =>= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +32641: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +32641: Goal: +32641: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +32641: Order: +32641: lpo +32641: Leaf order: +32641: y 4 0 4 3,1,1,1,2 +32641: additive_identity 9 0 1 3 +32641: x 9 0 9 1,1,1,1,2 +32641: additive_inverse 6 1 0 +32641: commutator 1 2 0 +32641: add 16 2 0 +32641: multiply 22 2 4 0,2 +32641: associator 5 3 4 0,1,1,1,2 +32639: Facts: +32639: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +32639: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +32639: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +32639: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +32639: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +32639: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +32639: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +32639: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +32639: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +32639: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +32639: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +32639: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +32639: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +32639: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +32639: Goal: +32639: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +32639: Order: +32639: nrkbo +32639: Leaf order: +32639: y 4 0 4 3,1,1,1,2 +32639: additive_identity 9 0 1 3 +32639: x 9 0 9 1,1,1,1,2 +32639: additive_inverse 6 1 0 +32639: commutator 1 2 0 +32639: add 16 2 0 +32639: multiply 22 2 4 0,2 +32639: associator 5 3 4 0,1,1,1,2 +32640: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +32640: Goal: +32640: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +32640: Order: +32640: kbo +32640: Leaf order: +32640: y 4 0 4 3,1,1,1,2 +32640: additive_identity 9 0 1 3 +32640: x 9 0 9 1,1,1,1,2 +32640: additive_inverse 6 1 0 +32640: commutator 1 2 0 +32640: add 16 2 0 +32640: multiply 22 2 4 0,2 +32640: associator 5 3 4 0,1,1,1,2 +% SZS status Timeout for RNG031-6.p +NO CLASH, using fixed ground order +32666: Facts: +32666: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +32666: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +32666: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +32666: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +32666: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +32666: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +32666: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +32666: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +32666: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +32666: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +32666: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +32666: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +32666: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +32666: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +32666: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +32666: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +32666: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +32666: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +32666: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +32666: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +32666: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +32666: Goal: +32666: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +32666: Order: +32666: nrkbo +32666: Leaf order: +32666: y 4 0 4 3,1,1,1,2 +32666: additive_identity 9 0 1 3 +32666: x 9 0 9 1,1,1,1,2 +32666: additive_inverse 22 1 0 +32666: commutator 1 2 0 +32666: add 24 2 0 +32666: multiply 40 2 4 0,2add +32666: associator 5 3 4 0,1,1,1,2 +NO CLASH, using fixed ground order +32667: Facts: +32667: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +32667: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +32667: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +32667: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +32667: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +32667: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +32667: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +32667: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +32667: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +32667: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +32667: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +32667: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +32667: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +32667: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +32667: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +32667: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +32667: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +32667: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +32667: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +32667: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +32667: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +32667: Goal: +32667: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +32667: Order: +32667: kbo +32667: Leaf order: +32667: y 4 0 4 3,1,1,1,2 +32667: additive_identity 9 0 1 3 +32667: x 9 0 9 1,1,1,1,2 +32667: additive_inverse 22 1 0 +32667: commutator 1 2 0 +32667: add 24 2 0 +32667: multiply 40 2 4 0,2add +32667: associator 5 3 4 0,1,1,1,2 +NO CLASH, using fixed ground order +32668: Facts: +32668: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +32668: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +32668: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +32668: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +32668: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +32668: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +32668: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +32668: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +32668: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +32668: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +32668: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +32668: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +32668: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +32668: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +32668: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +32668: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +32668: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +32668: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +32668: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +32668: Id : 21, {_}: + associator ?59 ?60 ?61 + =>= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +32668: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +32668: Goal: +32668: Id : 1, {_}: + multiply + (multiply (multiply (associator x x y) (associator x x y)) x) + (multiply (associator x x y) (associator x x y)) + =>= + additive_identity + [] by prove_conjecture_2 +32668: Order: +32668: lpo +32668: Leaf order: +32668: y 4 0 4 3,1,1,1,2 +32668: additive_identity 9 0 1 3 +32668: x 9 0 9 1,1,1,1,2 +32668: additive_inverse 22 1 0 +32668: commutator 1 2 0 +32668: add 24 2 0 +32668: multiply 40 2 4 0,2add +32668: associator 5 3 4 0,1,1,1,2 +% SZS status Timeout for RNG031-7.p +NO CLASH, using fixed ground order +32691: Facts: +32691: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3 +32691: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5 +32691: Goal: +32691: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1 +32691: Order: +32691: nrkbo +32691: Leaf order: +32691: f 2 1 0 +32691: g1 2 1 1 0,2 +32691: g2 2 1 1 0,3 +NO CLASH, using fixed ground order +32692: Facts: +32692: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3 +32692: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5 +32692: Goal: +32692: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1 +32692: Order: +32692: kbo +32692: Leaf order: +32692: f 2 1 0 +32692: g1 2 1 1 0,2 +32692: g2 2 1 1 0,3 +NO CLASH, using fixed ground order +32693: Facts: +32693: Id : 2, {_}: f (g1 ?3) =>= ?3 [3] by clause1 ?3 +32693: Id : 3, {_}: f (g2 ?5) =>= ?5 [5] by clause2 ?5 +32693: Goal: +32693: Id : 1, {_}: g1 ?1 =<= g2 ?1 [1] by clause3 ?1 +32693: Order: +32693: lpo +32693: Leaf order: +32693: f 2 1 0 +32693: g1 2 1 1 0,2 +32693: g2 2 1 1 0,3 +32691: status GaveUp for SYN305-1.p +32693: status GaveUp for SYN305-1.p +32692: status GaveUp for SYN305-1.p +% SZS status Timeout for SYN305-1.p +CLASH, statistics insufficient +32698: Facts: +32698: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32698: Id : 3, {_}: + apply (apply (apply h ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?8) ?9) ?8 + [9, 8, 7] by h_definition ?7 ?8 ?9 +32698: Goal: +32698: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +32698: Order: +32698: nrkbo +32698: Leaf order: +32698: b 1 0 0 +32698: h 1 0 0 +32698: f 3 1 3 0,2,2 +32698: apply 14 2 3 0,2 +CLASH, statistics insufficient +32699: Facts: +32699: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32699: Id : 3, {_}: + apply (apply (apply h ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?8) ?9) ?8 + [9, 8, 7] by h_definition ?7 ?8 ?9 +32699: Goal: +32699: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +32699: Order: +32699: kbo +32699: Leaf order: +32699: b 1 0 0 +32699: h 1 0 0 +32699: f 3 1 3 0,2,2 +32699: apply 14 2 3 0,2 +CLASH, statistics insufficient +32700: Facts: +32700: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32700: Id : 3, {_}: + apply (apply (apply h ?7) ?8) ?9 + =?= + apply (apply (apply ?7 ?8) ?9) ?8 + [9, 8, 7] by h_definition ?7 ?8 ?9 +32700: Goal: +32700: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +32700: Order: +32700: lpo +32700: Leaf order: +32700: b 1 0 0 +32700: h 1 0 0 +32700: f 3 1 3 0,2,2 +32700: apply 14 2 3 0,2 +% SZS status Timeout for COL043-1.p +CLASH, statistics insufficient +32721: Facts: +32721: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32721: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +32721: Id : 4, {_}: + apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12 + [12, 11] by w_definition ?11 ?12 +32721: Goal: +32721: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1) + =<= + apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1)) + [1] by prove_p_combinator ?1 +32721: Order: +32721: nrkbo +32721: Leaf order: +32721: b 1 0 0 +32721: q 1 0 0 +32721: w 1 0 0 +32721: h 2 1 2 0,2,2 +32721: f 3 1 3 0,2,1,1,1,2 +32721: g 4 1 4 0,2,1,1,2 +32721: apply 22 2 8 0,2 +CLASH, statistics insufficient +32722: Facts: +32722: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32722: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +32722: Id : 4, {_}: + apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12 + [12, 11] by w_definition ?11 ?12 +32722: Goal: +32722: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1) + =<= + apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1)) + [1] by prove_p_combinator ?1 +32722: Order: +32722: kbo +32722: Leaf order: +32722: b 1 0 0 +32722: q 1 0 0 +32722: w 1 0 0 +32722: h 2 1 2 0,2,2 +32722: f 3 1 3 0,2,1,1,1,2 +32722: g 4 1 4 0,2,1,1,2 +32722: apply 22 2 8 0,2 +CLASH, statistics insufficient +32723: Facts: +32723: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +32723: Id : 3, {_}: + apply (apply (apply q ?7) ?8) ?9 =>= apply ?8 (apply ?7 ?9) + [9, 8, 7] by q_definition ?7 ?8 ?9 +32723: Id : 4, {_}: + apply (apply w ?11) ?12 =?= apply (apply ?11 ?12) ?12 + [12, 11] by w_definition ?11 ?12 +32723: Goal: +32723: Id : 1, {_}: + apply (apply (apply (apply ?1 (f ?1)) (g ?1)) (g ?1)) (h ?1) + =>= + apply (apply (f ?1) (g ?1)) (apply (apply (f ?1) (g ?1)) (h ?1)) + [1] by prove_p_combinator ?1 +32723: Order: +32723: lpo +32723: Leaf order: +32723: b 1 0 0 +32723: q 1 0 0 +32723: w 1 0 0 +32723: h 2 1 2 0,2,2 +32723: f 3 1 3 0,2,1,1,1,2 +32723: g 4 1 4 0,2,1,1,2 +32723: apply 22 2 8 0,2 +% SZS status Timeout for COL066-1.p +NO CLASH, using fixed ground order +32745: Facts: +32745: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +32745: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +32745: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +32745: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +32745: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +32745: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =?= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +32745: Id : 8, {_}: + join (join ?19 ?20) ?21 =?= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +32745: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +32745: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +32745: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +32745: Goal: +32745: Id : 1, {_}: + join + (complement + (join + (join (meet (complement a) b) + (meet (complement a) (complement b))) + (meet a (join (complement a) b)))) (join (complement a) b) + =>= + n1 + [] by prove_e3 +32745: Order: +32745: nrkbo +32745: Leaf order: +32745: n0 1 0 0 +32745: n1 2 0 1 3 +32745: b 4 0 4 2,1,1,1,1,2 +32745: a 5 0 5 1,1,1,1,1,1,2 +32745: complement 15 1 6 0,1,2 +32745: meet 12 2 3 0,1,1,1,1,2 +32745: join 17 2 5 0,2 +NO CLASH, using fixed ground order +32746: Facts: +32746: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +32746: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +32746: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +32746: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +32746: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +32746: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +32746: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +32746: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +32746: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +NO CLASH, using fixed ground order +32747: Facts: +32747: Id : 2, {_}: join (complement ?2) ?2 =>= n1 [2] by top ?2 +32747: Id : 3, {_}: meet (complement ?4) ?4 =>= n0 [4] by bottom ?4 +32747: Id : 4, {_}: join ?6 (meet ?6 ?7) =>= ?6 [7, 6] by absorption2 ?6 ?7 +32747: Id : 5, {_}: + meet ?9 ?10 =?= meet ?10 ?9 + [10, 9] by commutativity_of_meet ?9 ?10 +32747: Id : 6, {_}: + join ?12 ?13 =?= join ?13 ?12 + [13, 12] by commutativity_of_join ?12 ?13 +32747: Id : 7, {_}: + meet (meet ?15 ?16) ?17 =>= meet ?15 (meet ?16 ?17) + [17, 16, 15] by associativity_of_meet ?15 ?16 ?17 +32747: Id : 8, {_}: + join (join ?19 ?20) ?21 =>= join ?19 (join ?20 ?21) + [21, 20, 19] by associativity_of_join ?19 ?20 ?21 +32747: Id : 9, {_}: + complement (complement ?23) =>= ?23 + [23] by complement_involution ?23 +32747: Id : 10, {_}: + join ?25 (join ?26 (complement ?26)) =>= join ?26 (complement ?26) + [26, 25] by join_complement ?25 ?26 +32747: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +32747: Goal: +32747: Id : 1, {_}: + join + (complement + (join + (join (meet (complement a) b) + (meet (complement a) (complement b))) + (meet a (join (complement a) b)))) (join (complement a) b) + =>= + n1 + [] by prove_e3 +32747: Order: +32747: lpo +32747: Leaf order: +32747: n0 1 0 0 +32747: n1 2 0 1 3 +32747: b 4 0 4 2,1,1,1,1,2 +32747: a 5 0 5 1,1,1,1,1,1,2 +32747: complement 15 1 6 0,1,2 +32747: meet 12 2 3 0,1,1,1,1,2 +32747: join 17 2 5 0,2 +32746: Id : 11, {_}: + meet ?28 ?29 =<= complement (join (complement ?28) (complement ?29)) + [29, 28] by meet_complement ?28 ?29 +32746: Goal: +32746: Id : 1, {_}: + join + (complement + (join + (join (meet (complement a) b) + (meet (complement a) (complement b))) + (meet a (join (complement a) b)))) (join (complement a) b) + =>= + n1 + [] by prove_e3 +32746: Order: +32746: kbo +32746: Leaf order: +32746: n0 1 0 0 +32746: n1 2 0 1 3 +32746: b 4 0 4 2,1,1,1,1,2 +32746: a 5 0 5 1,1,1,1,1,1,2 +32746: complement 15 1 6 0,1,2 +32746: meet 12 2 3 0,1,1,1,1,2 +32746: join 17 2 5 0,2 +% SZS status Timeout for LAT018-1.p +NO CLASH, using fixed ground order +301: Facts: +301: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +301: Goal: +301: Id : 1, {_}: + meet (meet a b) c =>= meet a (meet b c) + [] by prove_normal_axioms_3 +301: Order: +301: nrkbo +301: Leaf order: +301: a 2 0 2 1,1,2 +301: b 2 0 2 2,1,2 +301: c 2 0 2 2,2 +301: join 20 2 0 +301: meet 22 2 4 0,2 +NO CLASH, using fixed ground order +302: Facts: +302: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +302: Goal: +302: Id : 1, {_}: + meet (meet a b) c =>= meet a (meet b c) + [] by prove_normal_axioms_3 +302: Order: +302: kbo +302: Leaf order: +302: a 2 0 2 1,1,2 +302: b 2 0 2 2,1,2 +302: c 2 0 2 2,2 +302: join 20 2 0 +302: meet 22 2 4 0,2 +NO CLASH, using fixed ground order +303: Facts: +303: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +303: Goal: +303: Id : 1, {_}: + meet (meet a b) c =>= meet a (meet b c) + [] by prove_normal_axioms_3 +303: Order: +303: lpo +303: Leaf order: +303: a 2 0 2 1,1,2 +303: b 2 0 2 2,1,2 +303: c 2 0 2 2,2 +303: join 20 2 0 +303: meet 22 2 4 0,2 +% SZS status Timeout for LAT082-1.p +NO CLASH, using fixed ground order +337: Facts: +337: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +337: Goal: +337: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_normal_axioms_6 +337: Order: +337: nrkbo +337: Leaf order: +337: a 2 0 2 1,1,2 +337: b 2 0 2 2,1,2 +337: c 2 0 2 2,2 +337: meet 18 2 0 +337: join 24 2 4 0,2 +NO CLASH, using fixed ground order +338: Facts: +338: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +338: Goal: +338: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_normal_axioms_6 +338: Order: +338: kbo +338: Leaf order: +338: a 2 0 2 1,1,2 +338: b 2 0 2 2,1,2 +338: c 2 0 2 2,2 +338: meet 18 2 0 +338: join 24 2 4 0,2 +NO CLASH, using fixed ground order +339: Facts: +339: Id : 2, {_}: + join (meet (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4) + (meet + (join (meet ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)) + (meet + (join + (meet ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)) + (meet ?8 + (join ?3 + (meet (meet (join ?5 (join ?3 ?6)) (join ?7 ?3)) ?3)))) + (join ?2 (join (join (meet ?5 ?3) (meet ?3 ?6)) ?3)))) + (join (join (meet ?2 ?3) (meet ?3 (join ?2 ?3))) ?4)) + =>= + ?3 + [8, 7, 6, 5, 4, 3, 2] by single_axiom ?2 ?3 ?4 ?5 ?6 ?7 ?8 +339: Goal: +339: Id : 1, {_}: + join (join a b) c =>= join a (join b c) + [] by prove_normal_axioms_6 +339: Order: +339: lpo +339: Leaf order: +339: a 2 0 2 1,1,2 +339: b 2 0 2 2,1,2 +339: c 2 0 2 2,2 +339: meet 18 2 0 +339: join 24 2 4 0,2 +% SZS status Timeout for LAT085-1.p +NO CLASH, using fixed ground order +1422: Facts: +1422: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +1422: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +1422: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +1422: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +1422: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +1422: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +1422: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +1422: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +1422: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +1422: Goal: +1422: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +1422: Order: +1422: nrkbo +1422: Leaf order: +1422: a 4 0 4 1,2 +1422: b 4 0 4 1,2,2 +1422: c 4 0 4 2,2,2,2 +1422: join 16 2 4 0,2,2 +1422: meet 22 2 6 0,2 +NO CLASH, using fixed ground order +1423: Facts: +1423: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +1423: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +1423: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +1423: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +1423: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +1423: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +1423: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +1423: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +1423: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +1423: Goal: +1423: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +1423: Order: +1423: kbo +1423: Leaf order: +1423: a 4 0 4 1,2 +1423: b 4 0 4 1,2,2 +1423: c 4 0 4 2,2,2,2 +1423: join 16 2 4 0,2,2 +1423: meet 22 2 6 0,2 +NO CLASH, using fixed ground order +1424: Facts: +1424: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +1424: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +1424: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +1424: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +1424: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +1424: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +1424: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +1424: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +1424: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +1424: Goal: +1424: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +1424: Order: +1424: lpo +1424: Leaf order: +1424: a 4 0 4 1,2 +1424: b 4 0 4 1,2,2 +1424: c 4 0 4 2,2,2,2 +1424: join 16 2 4 0,2,2 +1424: meet 22 2 6 0,2 +% SZS status Timeout for LAT144-1.p +NO CLASH, using fixed ground order +1797: Facts: +1797: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +1797: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +1797: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +1797: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +1797: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +1797: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +1797: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +1797: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +1797: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +1797: Goal: +1797: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +1797: Order: +1797: nrkbo +1797: Leaf order: +1797: d 2 0 2 2,2,2,2,2 +1797: b 3 0 3 1,2,2 +1797: c 3 0 3 1,2,2,2 +1797: a 4 0 4 1,2 +1797: join 18 2 5 0,2,2 +1797: meet 19 2 5 0,2 +NO CLASH, using fixed ground order +1798: Facts: +1798: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +1798: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +1798: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +1798: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +1798: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +1798: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +1798: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +1798: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +1798: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +1798: Goal: +1798: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +1798: Order: +1798: kbo +1798: Leaf order: +1798: d 2 0 2 2,2,2,2,2 +1798: b 3 0 3 1,2,2 +1798: c 3 0 3 1,2,2,2 +1798: a 4 0 4 1,2 +1798: join 18 2 5 0,2,2 +1798: meet 19 2 5 0,2 +NO CLASH, using fixed ground order +1799: Facts: +1799: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +1799: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +1799: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +1799: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +1799: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +1799: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +1799: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +1799: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +1799: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +1799: Goal: +1799: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +1799: Order: +1799: lpo +1799: Leaf order: +1799: d 2 0 2 2,2,2,2,2 +1799: b 3 0 3 1,2,2 +1799: c 3 0 3 1,2,2,2 +1799: a 4 0 4 1,2 +1799: join 18 2 5 0,2,2 +1799: meet 19 2 5 0,2 +% SZS status Timeout for LAT150-1.p +NO CLASH, using fixed ground order +3353: Facts: +3353: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +3353: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +3353: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +3353: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +3353: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +3353: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +3353: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +3353: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +3353: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +3353: Goal: +3353: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +3353: Order: +3353: nrkbo +3353: Leaf order: +3353: d 2 0 2 2,2,2,2,2 +3353: b 3 0 3 1,2,2 +3353: c 3 0 3 1,2,2,2 +3353: a 4 0 4 1,2 +3353: join 18 2 5 0,2,2 +3353: meet 19 2 5 0,2 +NO CLASH, using fixed ground order +3358: Facts: +3358: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +3358: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +3358: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +3358: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +3358: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +3358: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +3358: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +3358: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +3358: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +3358: Goal: +3358: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +3358: Order: +3358: kbo +3358: Leaf order: +3358: d 2 0 2 2,2,2,2,2 +3358: b 3 0 3 1,2,2 +3358: c 3 0 3 1,2,2,2 +3358: a 4 0 4 1,2 +3358: join 18 2 5 0,2,2 +3358: meet 19 2 5 0,2 +NO CLASH, using fixed ground order +3361: Facts: +3361: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +3361: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +3361: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +3361: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +3361: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +3361: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +3361: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +3361: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +3361: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?28)))) + [29, 28, 27, 26] by equation_H39 ?26 ?27 ?28 ?29 +3361: Goal: +3361: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +3361: Order: +3361: lpo +3361: Leaf order: +3361: d 2 0 2 2,2,2,2,2 +3361: b 3 0 3 1,2,2 +3361: c 3 0 3 1,2,2,2 +3361: a 4 0 4 1,2 +3361: join 18 2 5 0,2,2 +3361: meet 19 2 5 0,2 +% SZS status Timeout for LAT151-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +4534: Facts: +4534: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +4534: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +4534: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +4534: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +4534: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +4534: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +4534: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +4534: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +4534: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +4534: Goal: +4534: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +4534: Order: +4534: kbo +4534: Leaf order: +4534: b 3 0 3 1,2,2 +4534: c 3 0 3 2,2,2,2 +4534: a 6 0 6 1,2 +4534: join 18 2 4 0,2,2 +4534: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +4537: Facts: +4537: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +4537: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +4537: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +4537: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +4537: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +4537: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +4537: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +4537: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +4537: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +4537: Goal: +4537: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +4537: Order: +4537: lpo +4537: Leaf order: +4537: b 3 0 3 1,2,2 +4537: c 3 0 3 2,2,2,2 +4537: a 6 0 6 1,2 +4537: join 18 2 4 0,2,2 +4537: meet 20 2 6 0,2 +4533: Facts: +4533: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +4533: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +4533: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +4533: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +4533: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +4533: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +4533: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +4533: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +4533: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +4533: Goal: +4533: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +4533: Order: +4533: nrkbo +4533: Leaf order: +4533: b 3 0 3 1,2,2 +4533: c 3 0 3 2,2,2,2 +4533: a 6 0 6 1,2 +4533: join 18 2 4 0,2,2 +4533: meet 20 2 6 0,2 +% SZS status Timeout for LAT152-1.p +NO CLASH, using fixed ground order +5952: Facts: +5952: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +5952: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +5952: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +5952: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +5952: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +5952: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +5952: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +5952: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +5952: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +5952: Goal: +5952: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +5952: Order: +5952: nrkbo +5952: Leaf order: +5952: c 2 0 2 2,2,2,2 +5952: b 4 0 4 1,2,2 +5952: a 6 0 6 1,2 +5952: join 18 2 4 0,2,2 +5952: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +5958: Facts: +5958: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +5958: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +5958: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +5958: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +5958: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +5958: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +5958: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +5958: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +5958: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +5958: Goal: +5958: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +5958: Order: +5958: kbo +5958: Leaf order: +5958: c 2 0 2 2,2,2,2 +5958: b 4 0 4 1,2,2 +5958: a 6 0 6 1,2 +5958: join 18 2 4 0,2,2 +5958: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +5959: Facts: +5959: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +5959: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +5959: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +5959: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +5959: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +5959: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +5959: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +5959: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +5959: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +5959: Goal: +5959: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +5959: Order: +5959: lpo +5959: Leaf order: +5959: c 2 0 2 2,2,2,2 +5959: b 4 0 4 1,2,2 +5959: a 6 0 6 1,2 +5959: join 18 2 4 0,2,2 +5959: meet 20 2 6 0,2 +% SZS status Timeout for LAT159-1.p +NO CLASH, using fixed ground order +7548: Facts: +7548: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +7548: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +7548: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +7548: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +7548: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +7548: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +7548: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +7548: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +7548: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +7548: Goal: +7548: Id : 1, {_}: + meet a (meet b (join c d)) + =<= + meet a (meet b (join c (meet a (join d (meet b c))))) + [] by prove_H73 +7548: Order: +7548: nrkbo +7548: Leaf order: +7548: d 2 0 2 2,2,2,2 +7548: a 3 0 3 1,2 +7548: b 3 0 3 1,2,2 +7548: c 3 0 3 1,2,2,2 +7548: join 15 2 3 0,2,2,2 +7548: meet 19 2 6 0,2 +NO CLASH, using fixed ground order +7549: Facts: +7549: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +7549: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +7549: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +7549: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +7549: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +7549: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +7549: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +7549: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +7549: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +7549: Goal: +7549: Id : 1, {_}: + meet a (meet b (join c d)) + =<= + meet a (meet b (join c (meet a (join d (meet b c))))) + [] by prove_H73 +7549: Order: +7549: kbo +7549: Leaf order: +7549: d 2 0 2 2,2,2,2 +7549: a 3 0 3 1,2 +7549: b 3 0 3 1,2,2 +7549: c 3 0 3 1,2,2,2 +7549: join 15 2 3 0,2,2,2 +7549: meet 19 2 6 0,2 +NO CLASH, using fixed ground order +7552: Facts: +7552: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +7552: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +7552: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +7552: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +7552: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +7552: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +7552: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +7552: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +7552: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet ?26 (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H68 ?26 ?27 ?28 +7552: Goal: +7552: Id : 1, {_}: + meet a (meet b (join c d)) + =<= + meet a (meet b (join c (meet a (join d (meet b c))))) + [] by prove_H73 +7552: Order: +7552: lpo +7552: Leaf order: +7552: d 2 0 2 2,2,2,2 +7552: a 3 0 3 1,2 +7552: b 3 0 3 1,2,2 +7552: c 3 0 3 1,2,2,2 +7552: join 15 2 3 0,2,2,2 +7552: meet 19 2 6 0,2 +% SZS status Timeout for LAT162-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +8627: Facts: +8627: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +8627: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +8627: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +8627: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +8627: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +8627: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +8627: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +8627: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +8627: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +8627: Goal: +8627: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +8627: Order: +8627: kbo +8627: Leaf order: +8627: b 3 0 3 1,2,2 +8627: c 3 0 3 2,2,2,2 +8627: a 6 0 6 1,2 +8627: join 17 2 4 0,2,2 +8627: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +8628: Facts: +8628: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +8628: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +8628: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +8628: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +8628: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +8628: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +8628: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +8628: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +8628: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +8628: Goal: +8628: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +8628: Order: +8628: lpo +8628: Leaf order: +8628: b 3 0 3 1,2,2 +8628: c 3 0 3 2,2,2,2 +8628: a 6 0 6 1,2 +8628: join 17 2 4 0,2,2 +8628: meet 20 2 6 0,2 +8626: Facts: +8626: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +8626: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +8626: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +8626: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +8626: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +8626: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +8626: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +8626: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +8626: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +8626: Goal: +8626: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +8626: Order: +8626: nrkbo +8626: Leaf order: +8626: b 3 0 3 1,2,2 +8626: c 3 0 3 2,2,2,2 +8626: a 6 0 6 1,2 +8626: join 17 2 4 0,2,2 +8626: meet 20 2 6 0,2 +% SZS status Timeout for LAT164-1.p +NO CLASH, using fixed ground order +10913: Facts: +10913: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +10913: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +10913: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +10913: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +10913: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +10913: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +10913: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +10913: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +10913: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +10913: Goal: +10913: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +10913: Order: +10913: nrkbo +10913: Leaf order: +10913: c 2 0 2 2,2,2 +10913: a 4 0 4 1,2 +10913: b 4 0 4 1,2,2 +10913: meet 17 2 4 0,2 +10913: join 19 2 4 0,2,2 +NO CLASH, using fixed ground order +10920: Facts: +10920: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +10920: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +10920: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +10920: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +10920: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +10920: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +10920: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +10920: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +10920: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +10920: Goal: +10920: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +10920: Order: +10920: kbo +10920: Leaf order: +10920: c 2 0 2 2,2,2 +10920: a 4 0 4 1,2 +10920: b 4 0 4 1,2,2 +10920: meet 17 2 4 0,2 +10920: join 19 2 4 0,2,2 +NO CLASH, using fixed ground order +10926: Facts: +10926: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +10926: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +10926: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +10926: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +10926: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +10926: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +10926: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +10926: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +10926: Id : 10, {_}: + meet (join ?26 ?27) (join ?26 ?28) + =<= + join ?26 + (meet (join ?27 (meet ?26 (join ?27 ?28))) + (join ?28 (meet ?26 ?27))) + [28, 27, 26] by equation_H21_dual ?26 ?27 ?28 +10926: Goal: +10926: Id : 1, {_}: + meet a (join b c) + =<= + meet a (join b (meet (join a b) (join c (meet a b)))) + [] by prove_H58 +10926: Order: +10926: lpo +10926: Leaf order: +10926: c 2 0 2 2,2,2 +10926: a 4 0 4 1,2 +10926: b 4 0 4 1,2,2 +10926: meet 17 2 4 0,2 +10926: join 19 2 4 0,2,2 +% SZS status Timeout for LAT169-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +11323: Facts: +11323: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11323: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11323: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11323: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11323: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11323: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11323: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11323: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11323: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +11323: Goal: +11323: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +11323: Order: +11323: kbo +11323: Leaf order: +11323: b 3 0 3 1,2,2 +11323: c 3 0 3 2,2,2,2 +11323: a 6 0 6 1,2 +11323: join 18 2 4 0,2,2 +11323: meet 19 2 6 0,2 +NO CLASH, using fixed ground order +11324: Facts: +11324: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11324: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11324: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11324: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11324: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11324: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11324: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11324: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11324: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +11324: Goal: +11324: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +11324: Order: +11324: lpo +11324: Leaf order: +11324: b 3 0 3 1,2,2 +11324: c 3 0 3 2,2,2,2 +11324: a 6 0 6 1,2 +11324: join 18 2 4 0,2,2 +11324: meet 19 2 6 0,2 +11322: Facts: +11322: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11322: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11322: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11322: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11322: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11322: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11322: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11322: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11322: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +11322: Goal: +11322: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +11322: Order: +11322: nrkbo +11322: Leaf order: +11322: b 3 0 3 1,2,2 +11322: c 3 0 3 2,2,2,2 +11322: a 6 0 6 1,2 +11322: join 18 2 4 0,2,2 +11322: meet 19 2 6 0,2 +% SZS status Timeout for LAT174-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +11474: Facts: +11474: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11474: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11474: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11474: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11474: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11474: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11474: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11474: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11474: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11474: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11474: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11474: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11474: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11474: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11474: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11474: Goal: +11474: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +11474: Order: +11474: kbo +11474: Leaf order: +11474: cz 2 0 2 1,2 +11474: cy 2 0 2 1,2,2,2 +11474: cx 4 0 4 1,2,2 +11474: additive_identity 8 0 0 +11474: additive_inverse 6 1 0 +11474: commutator 1 2 0 +11474: add 16 2 0 +11474: multiply 28 2 6 0,2 +11474: associator 1 3 0 +NO CLASH, using fixed ground order +11475: Facts: +11475: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11475: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11475: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11475: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11475: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11475: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11475: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11475: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11475: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11475: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11475: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11475: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11475: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11475: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11475: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11475: Goal: +11475: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +11475: Order: +11475: lpo +11475: Leaf order: +11475: cz 2 0 2 1,2 +11475: cy 2 0 2 1,2,2,2 +11475: cx 4 0 4 1,2,2 +11475: additive_identity 8 0 0 +11475: additive_inverse 6 1 0 +11475: commutator 1 2 0 +11475: add 16 2 0 +11475: multiply 28 2 6 0,2 +11475: associator 1 3 0 +11473: Facts: +11473: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +11473: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +11473: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +11473: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +11473: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +11473: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +11473: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +11473: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +11473: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +11473: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +11473: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +11473: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +11473: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +11473: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +11473: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +11473: Goal: +11473: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +11473: Order: +11473: nrkbo +11473: Leaf order: +11473: cz 2 0 2 1,2 +11473: cy 2 0 2 1,2,2,2 +11473: cx 4 0 4 1,2,2 +11473: additive_identity 8 0 0 +11473: additive_inverse 6 1 0 +11473: commutator 1 2 0 +11473: add 16 2 0 +11473: multiply 28 2 6 0,2 +11473: associator 1 3 0 +% SZS status Timeout for RNG027-5.p +NO CLASH, using fixed ground order +12546: Facts: +12546: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +12546: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +12546: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +12546: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +12546: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +12546: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +12546: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +12546: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +12546: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +12546: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +12546: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +12546: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +12546: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +12546: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +NO CLASH, using fixed ground order +12546: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +12546: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +12546: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +12546: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +12546: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +12546: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +12547: Facts: +12546: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +12546: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +12546: Goal: +12546: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +12546: Order: +12546: nrkbo +12546: Leaf order: +12546: cz 2 0 2 1,2 +12546: cy 2 0 2 1,2,2,2 +12546: cx 4 0 4 1,2,2 +12546: additive_identity 8 0 0 +12546: additive_inverse 22 1 0 +12546: commutator 1 2 0 +12546: add 24 2 0 +12546: multiply 46 2 6 0,2 +12547: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +12547: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +12547: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +12547: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +12547: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +12547: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +12547: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +12546: associator 1 3 0 +12547: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +12547: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +12547: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +12547: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +12547: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +12547: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +12547: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +12547: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +12547: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +12547: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +12547: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +12547: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +12547: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +12547: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +12547: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +12547: Goal: +12547: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +12547: Order: +12547: kbo +12547: Leaf order: +12547: cz 2 0 2 1,2 +12547: cy 2 0 2 1,2,2,2 +12547: cx 4 0 4 1,2,2 +12547: additive_identity 8 0 0 +12547: additive_inverse 22 1 0 +12547: commutator 1 2 0 +12547: add 24 2 0 +12547: multiply 46 2 6 0,2 +12547: associator 1 3 0 +NO CLASH, using fixed ground order +12548: Facts: +12548: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +12548: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +12548: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +12548: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +12548: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +12548: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +12548: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +12548: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +12548: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +12548: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +12548: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +12548: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +12548: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +12548: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +12548: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +12548: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +12548: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +12548: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +12548: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +12548: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +12548: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +12548: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +12548: Goal: +12548: Id : 1, {_}: + multiply cz (multiply cx (multiply cy cx)) + =<= + multiply (multiply (multiply cz cx) cy) cx + [] by prove_right_moufang +12548: Order: +12548: lpo +12548: Leaf order: +12548: cz 2 0 2 1,2 +12548: cy 2 0 2 1,2,2,2 +12548: cx 4 0 4 1,2,2 +12548: additive_identity 8 0 0 +12548: additive_inverse 22 1 0 +12548: commutator 1 2 0 +12548: add 24 2 0 +12548: multiply 46 2 6 0,2 +12548: associator 1 3 0 +% SZS status Timeout for RNG027-7.p +NO CLASH, using fixed ground order +14022: Facts: +14022: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +14022: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +14022: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +14022: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +14022: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +14022: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +14022: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +14022: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +NO CLASH, using fixed ground order +14022: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +14022: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +14022: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +14022: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +14022: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +14022: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +14022: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +14022: Goal: +14022: Id : 1, {_}: + associator x (multiply x y) z =>= multiply (associator x y z) x + [] by prove_right_moufang +14022: Order: +14022: nrkbo +14022: Leaf order: +14022: y 2 0 2 2,2,2 +14022: z 2 0 2 3,2 +14022: x 4 0 4 1,2 +14022: additive_identity 8 0 0 +14022: additive_inverse 6 1 0 +14022: commutator 1 2 0 +14022: add 16 2 0 +14022: multiply 24 2 2 0,2,2 +14022: associator 3 3 2 0,2 +14023: Facts: +14023: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +14023: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +14023: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +14023: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +14023: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +14023: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +14023: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +14023: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +14023: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +14023: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +14023: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +14023: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +14023: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +14023: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +14023: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +14023: Goal: +14023: Id : 1, {_}: + associator x (multiply x y) z =>= multiply (associator x y z) x + [] by prove_right_moufang +14023: Order: +14023: kbo +14023: Leaf order: +14023: y 2 0 2 2,2,2 +14023: z 2 0 2 3,2 +14023: x 4 0 4 1,2 +14023: additive_identity 8 0 0 +14023: additive_inverse 6 1 0 +14023: commutator 1 2 0 +14023: add 16 2 0 +14023: multiply 24 2 2 0,2,2 +14023: associator 3 3 2 0,2 +NO CLASH, using fixed ground order +14025: Facts: +14025: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +14025: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +14025: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +14025: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +14025: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +14025: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +14025: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +14025: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +14025: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +14025: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +14025: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +14025: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +14025: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +14025: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +14025: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +14025: Goal: +14025: Id : 1, {_}: + associator x (multiply x y) z =>= multiply (associator x y z) x + [] by prove_right_moufang +14025: Order: +14025: lpo +14025: Leaf order: +14025: y 2 0 2 2,2,2 +14025: z 2 0 2 3,2 +14025: x 4 0 4 1,2 +14025: additive_identity 8 0 0 +14025: additive_inverse 6 1 0 +14025: commutator 1 2 0 +14025: add 16 2 0 +14025: multiply 24 2 2 0,2,2 +14025: associator 3 3 2 0,2 +% SZS status Timeout for RNG027-8.p +NO CLASH, using fixed ground order +15720: Facts: +15720: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +15720: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +15720: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +15720: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +15720: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +15720: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +15720: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +15720: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +15720: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +15720: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +15720: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +15720: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +15720: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +15720: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +15720: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +15720: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +15720: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +15720: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +15720: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +15720: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +15720: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +15720: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +15720: Goal: +15720: Id : 1, {_}: + associator x (multiply x y) z =>= multiply (associator x y z) x + [] by prove_right_moufang +15720: Order: +15720: nrkbo +15720: Leaf order: +15720: y 2 0 2 2,2,2 +15720: z 2 0 2 3,2 +15720: x 4 0 4 1,2 +15720: additive_identity 8 0 0 +15720: additive_inverse 22 1 0 +15720: commutator 1 2 0 +15720: add 24 2 0 +15720: multiply 42 2 2 0,2,2 +15720: associator 3 3 2 0,2 +NO CLASH, using fixed ground order +15721: Facts: +15721: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +15721: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +15721: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +15721: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +15721: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +15721: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +15721: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +15721: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +15721: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +15721: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +15721: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +15721: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +15721: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +15721: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +15721: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +15721: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +15721: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +15721: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +15721: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +15721: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +15721: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +15721: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +15721: Goal: +15721: Id : 1, {_}: + associator x (multiply x y) z =>= multiply (associator x y z) x + [] by prove_right_moufang +15721: Order: +15721: kbo +15721: Leaf order: +15721: y 2 0 2 2,2,2 +15721: z 2 0 2 3,2 +15721: x 4 0 4 1,2 +15721: additive_identity 8 0 0 +15721: additive_inverse 22 1 0 +15721: commutator 1 2 0 +15721: add 24 2 0 +15721: multiply 42 2 2 0,2,2 +15721: associator 3 3 2 0,2 +NO CLASH, using fixed ground order +15722: Facts: +15722: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +15722: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +15722: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +15722: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +15722: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +15722: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +15722: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +15722: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +15722: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +15722: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +15722: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +15722: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +15722: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +15722: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +15722: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +15722: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +15722: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +15722: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +15722: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +15722: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +15722: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +15722: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +15722: Goal: +15722: Id : 1, {_}: + associator x (multiply x y) z =>= multiply (associator x y z) x + [] by prove_right_moufang +15722: Order: +15722: lpo +15722: Leaf order: +15722: y 2 0 2 2,2,2 +15722: z 2 0 2 3,2 +15722: x 4 0 4 1,2 +15722: additive_identity 8 0 0 +15722: additive_inverse 22 1 0 +15722: commutator 1 2 0 +15722: add 24 2 0 +15722: multiply 42 2 2 0,2,2 +15722: associator 3 3 2 0,2 +% SZS status Timeout for RNG027-9.p +NO CLASH, using fixed ground order +16372: Facts: +16372: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +16372: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +16372: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +16372: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +16372: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +16372: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +16372: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +16372: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +16372: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +16372: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +16372: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +16372: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +16372: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +16372: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +16372: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +16372: Goal: +16372: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +16372: Order: +16372: nrkbo +16372: Leaf order: +16372: cy 2 0 2 1,2,1,2 +16372: cz 2 0 2 2,2 +16372: cx 4 0 4 1,1,2 +16372: additive_identity 8 0 0 +16372: additive_inverse 6 1 0 +16372: commutator 1 2 0 +16372: add 16 2 0 +16372: multiply 28 2 6 0,2 +16372: associator 1 3 0 +NO CLASH, using fixed ground order +16373: Facts: +16373: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +16373: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +16373: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +16373: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +16373: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +16373: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +16373: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +16373: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +16373: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +NO CLASH, using fixed ground order +16374: Facts: +16374: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +16374: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +16374: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +16374: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +16374: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +16374: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +16374: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +16374: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +16374: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +16373: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +16373: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +16373: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +16373: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +16373: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +16373: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +16373: Goal: +16373: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +16373: Order: +16373: kbo +16373: Leaf order: +16373: cy 2 0 2 1,2,1,2 +16373: cz 2 0 2 2,2 +16373: cx 4 0 4 1,1,2 +16373: additive_identity 8 0 0 +16373: additive_inverse 6 1 0 +16373: commutator 1 2 0 +16373: add 16 2 0 +16373: multiply 28 2 6 0,2 +16373: associator 1 3 0 +16374: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +16374: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +16374: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +16374: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +16374: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +16374: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +16374: Goal: +16374: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +16374: Order: +16374: lpo +16374: Leaf order: +16374: cy 2 0 2 1,2,1,2 +16374: cz 2 0 2 2,2 +16374: cx 4 0 4 1,1,2 +16374: additive_identity 8 0 0 +16374: additive_inverse 6 1 0 +16374: commutator 1 2 0 +16374: add 16 2 0 +16374: multiply 28 2 6 0,2 +16374: associator 1 3 0 +% SZS status Timeout for RNG028-5.p +NO CLASH, using fixed ground order +18637: Facts: +18637: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +18637: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +18637: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +18637: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +18637: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +18637: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +18637: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +18637: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +18637: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +18637: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +18637: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +18637: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +18637: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +18637: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +18637: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +18637: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +18637: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +18637: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +18637: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +18637: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +18637: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +18637: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +18637: Goal: +18637: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +18637: Order: +18637: nrkbo +18637: Leaf order: +18637: cy 2 0 2 1,2,1,2 +18637: cz 2 0 2 2,2 +18637: cx 4 0 4 1,1,2 +18637: additive_identity 8 0 0 +18637: additive_inverse 22 1 0 +18637: commutator 1 2 0 +18637: add 24 2 0 +18637: multiply 46 2 6 0,2 +18637: associator 1 3 0 +NO CLASH, using fixed ground order +18660: Facts: +18660: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +18660: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +18660: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +18660: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +18660: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +18660: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +18660: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +18660: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +18660: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +18660: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +18660: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +18660: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +18660: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +18660: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +18660: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +18660: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +18660: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +18660: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +18660: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +18660: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +18660: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +18660: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +18660: Goal: +18660: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +18660: Order: +18660: kbo +18660: Leaf order: +18660: cy 2 0 2 1,2,1,2 +18660: cz 2 0 2 2,2 +18660: cx 4 0 4 1,1,2 +18660: additive_identity 8 0 0 +18660: additive_inverse 22 1 0 +18660: commutator 1 2 0 +18660: add 24 2 0 +18660: multiply 46 2 6 0,2 +18660: associator 1 3 0 +NO CLASH, using fixed ground order +18670: Facts: +18670: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +18670: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +18670: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +18670: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +18670: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +18670: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +18670: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +18670: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +18670: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +18670: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +18670: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +18670: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +18670: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +18670: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +18670: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +18670: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +18670: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +18670: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +18670: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +18670: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +18670: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +18670: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +18670: Goal: +18670: Id : 1, {_}: + multiply (multiply cx (multiply cy cx)) cz + =>= + multiply cx (multiply cy (multiply cx cz)) + [] by prove_left_moufang +18670: Order: +18670: lpo +18670: Leaf order: +18670: cy 2 0 2 1,2,1,2 +18670: cz 2 0 2 2,2 +18670: cx 4 0 4 1,1,2 +18670: additive_identity 8 0 0 +18670: additive_inverse 22 1 0 +18670: commutator 1 2 0 +18670: add 24 2 0 +18670: multiply 46 2 6 0,2 +18670: associator 1 3 0 +% SZS status Timeout for RNG028-7.p +NO CLASH, using fixed ground order +20636: Facts: +20636: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20636: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20636: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20636: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20636: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20636: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20636: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20636: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20636: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20636: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20636: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20636: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20636: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20636: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20636: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20636: Goal: +20636: Id : 1, {_}: + associator x (multiply y x) z =>= multiply x (associator x y z) + [] by prove_left_moufang +20636: Order: +20636: nrkbo +20636: Leaf order: +20636: y 2 0 2 1,2,2 +20636: z 2 0 2 3,2 +20636: x 4 0 4 1,2 +20636: additive_identity 8 0 0 +20636: additive_inverse 6 1 0 +20636: commutator 1 2 0 +20636: add 16 2 0 +20636: multiply 24 2 2 0,2,2 +20636: associator 3 3 2 0,2 +NO CLASH, using fixed ground order +20637: Facts: +20637: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20637: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20637: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20637: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20637: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20637: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20637: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20637: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20637: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20637: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20637: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20637: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20637: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20637: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20637: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20637: Goal: +20637: Id : 1, {_}: + associator x (multiply y x) z =>= multiply x (associator x y z) + [] by prove_left_moufang +20637: Order: +20637: kbo +20637: Leaf order: +20637: y 2 0 2 1,2,2 +20637: z 2 0 2 3,2 +20637: x 4 0 4 1,2 +20637: additive_identity 8 0 0 +20637: additive_inverse 6 1 0 +20637: commutator 1 2 0 +20637: add 16 2 0 +20637: multiply 24 2 2 0,2,2 +20637: associator 3 3 2 0,2 +NO CLASH, using fixed ground order +20638: Facts: +20638: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +20638: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +20638: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +20638: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +20638: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +20638: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +20638: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +20638: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +20638: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +20638: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +20638: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +20638: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +20638: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +20638: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +20638: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +20638: Goal: +20638: Id : 1, {_}: + associator x (multiply y x) z =>= multiply x (associator x y z) + [] by prove_left_moufang +20638: Order: +20638: lpo +20638: Leaf order: +20638: y 2 0 2 1,2,2 +20638: z 2 0 2 3,2 +20638: x 4 0 4 1,2 +20638: additive_identity 8 0 0 +20638: additive_inverse 6 1 0 +20638: commutator 1 2 0 +20638: add 16 2 0 +20638: multiply 24 2 2 0,2,2 +20638: associator 3 3 2 0,2 +% SZS status Timeout for RNG028-8.p +NO CLASH, using fixed ground order +22095: Facts: +22095: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22095: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22095: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22095: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22095: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22095: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22095: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22095: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22095: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22095: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22095: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22095: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22095: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22095: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22095: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22095: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +22095: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +22095: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +22095: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +22095: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +22095: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +22095: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +22095: Goal: +22095: Id : 1, {_}: + associator x (multiply y x) z =>= multiply x (associator x y z) + [] by prove_left_moufang +22095: Order: +22095: nrkbo +22095: Leaf order: +22095: y 2 0 2 1,2,2 +22095: z 2 0 2 3,2 +22095: x 4 0 4 1,2 +22095: additive_identity 8 0 0 +22095: additive_inverse 22 1 0 +22095: commutator 1 2 0 +22095: add 24 2 0 +22095: multiply 42 2 2 0,2,2 +22095: associator 3 3 2 0,2 +NO CLASH, using fixed ground order +22098: Facts: +NO CLASH, using fixed ground order +22098: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22098: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22098: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22098: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22098: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22098: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22098: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22098: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22098: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22098: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22098: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22098: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22098: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22098: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22098: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22098: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +22098: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +22098: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +22098: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +22098: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +22098: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +22098: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +22098: Goal: +22098: Id : 1, {_}: + associator x (multiply y x) z =>= multiply x (associator x y z) + [] by prove_left_moufang +22098: Order: +22098: kbo +22098: Leaf order: +22098: y 2 0 2 1,2,2 +22098: z 2 0 2 3,2 +22098: x 4 0 4 1,2 +22098: additive_identity 8 0 0 +22098: additive_inverse 22 1 0 +22098: commutator 1 2 0 +22098: add 24 2 0 +22098: multiply 42 2 2 0,2,2 +22098: associator 3 3 2 0,2 +22100: Facts: +22100: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +22100: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +22100: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +22100: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +22100: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +22100: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +22100: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +22100: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +22100: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +22100: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +22100: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +22100: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +22100: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +22100: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +22100: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +22100: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +22100: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +22100: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +22100: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +22100: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +22100: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +22100: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +22100: Goal: +22100: Id : 1, {_}: + associator x (multiply y x) z =>= multiply x (associator x y z) + [] by prove_left_moufang +22100: Order: +22100: lpo +22100: Leaf order: +22100: y 2 0 2 1,2,2 +22100: z 2 0 2 3,2 +22100: x 4 0 4 1,2 +22100: additive_identity 8 0 0 +22100: additive_inverse 22 1 0 +22100: commutator 1 2 0 +22100: add 24 2 0 +22100: multiply 42 2 2 0,2,2 +22100: associator 3 3 2 0,2 +% SZS status Timeout for RNG028-9.p +NO CLASH, using fixed ground order +23750: Facts: +23750: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +23750: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +23750: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +23750: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +23750: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +23750: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +23750: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +23750: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +23750: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +23750: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +23750: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +23750: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +23750: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +23750: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +23750: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +23750: Goal: +23750: Id : 1, {_}: + multiply (multiply cx cy) (multiply cz cx) + =>= + multiply cx (multiply (multiply cy cz) cx) + [] by prove_middle_law +23750: Order: +23750: nrkbo +23750: Leaf order: +23750: cz 2 0 2 1,2,2 +23750: cy 2 0 2 2,1,2 +23750: cx 4 0 4 1,1,2 +23750: additive_identity 8 0 0 +23750: additive_inverse 6 1 0 +23750: commutator 1 2 0 +23750: add 16 2 0 +23750: multiply 28 2 6 0,2 +23750: associator 1 3 0 +NO CLASH, using fixed ground order +23751: Facts: +23751: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +23751: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +23751: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +23751: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +23751: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +23751: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +23751: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +23751: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +23751: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +23751: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +23751: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +23751: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +23751: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +23751: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +23751: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +23751: Goal: +23751: Id : 1, {_}: + multiply (multiply cx cy) (multiply cz cx) + =>= + multiply cx (multiply (multiply cy cz) cx) + [] by prove_middle_law +23751: Order: +23751: kbo +23751: Leaf order: +23751: cz 2 0 2 1,2,2 +23751: cy 2 0 2 2,1,2 +23751: cx 4 0 4 1,1,2 +23751: additive_identity 8 0 0 +23751: additive_inverse 6 1 0 +23751: commutator 1 2 0 +23751: add 16 2 0 +23751: multiply 28 2 6 0,2 +23751: associator 1 3 0 +NO CLASH, using fixed ground order +23752: Facts: +23752: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +23752: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +23752: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +23752: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +23752: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +23752: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +23752: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +23752: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +23752: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +23752: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +23752: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +23752: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +23752: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +23752: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +23752: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +23752: Goal: +23752: Id : 1, {_}: + multiply (multiply cx cy) (multiply cz cx) + =>= + multiply cx (multiply (multiply cy cz) cx) + [] by prove_middle_law +23752: Order: +23752: lpo +23752: Leaf order: +23752: cz 2 0 2 1,2,2 +23752: cy 2 0 2 2,1,2 +23752: cx 4 0 4 1,1,2 +23752: additive_identity 8 0 0 +23752: additive_inverse 6 1 0 +23752: commutator 1 2 0 +23752: add 16 2 0 +23752: multiply 28 2 6 0,2 +23752: associator 1 3 0 +% SZS status Timeout for RNG029-5.p +NO CLASH, using fixed ground order +24862: Facts: +24862: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24862: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24862: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24862: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24862: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24862: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24862: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24862: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24862: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24862: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24862: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24862: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24862: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24862: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24862: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24862: Goal: +24862: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +24862: Order: +24862: nrkbo +24862: Leaf order: +24862: z 2 0 2 1,2,2 +24862: y 2 0 2 2,1,2 +24862: x 4 0 4 1,1,2 +24862: additive_identity 8 0 0 +24862: additive_inverse 6 1 0 +24862: commutator 1 2 0 +24862: add 16 2 0 +24862: multiply 28 2 6 0,2 +24862: associator 1 3 0 +NO CLASH, using fixed ground order +24863: Facts: +24863: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24863: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24863: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24863: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24863: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24863: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24863: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24863: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24863: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24863: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24863: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24863: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24863: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24863: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24863: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24863: Goal: +24863: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +24863: Order: +24863: kbo +24863: Leaf order: +24863: z 2 0 2 1,2,2 +24863: y 2 0 2 2,1,2 +24863: x 4 0 4 1,1,2 +24863: additive_identity 8 0 0 +24863: additive_inverse 6 1 0 +24863: commutator 1 2 0 +24863: add 16 2 0 +24863: multiply 28 2 6 0,2 +24863: associator 1 3 0 +NO CLASH, using fixed ground order +24864: Facts: +24864: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +24864: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +24864: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +24864: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +24864: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +24864: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +24864: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +24864: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +24864: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +24864: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +24864: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +24864: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +24864: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +24864: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +24864: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +24864: Goal: +24864: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +24864: Order: +24864: lpo +24864: Leaf order: +24864: z 2 0 2 1,2,2 +24864: y 2 0 2 2,1,2 +24864: x 4 0 4 1,1,2 +24864: additive_identity 8 0 0 +24864: additive_inverse 6 1 0 +24864: commutator 1 2 0 +24864: add 16 2 0 +24864: multiply 28 2 6 0,2 +24864: associator 1 3 0 +% SZS status Timeout for RNG029-6.p +NO CLASH, using fixed ground order +26436: Facts: +26436: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26436: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26436: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26436: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26436: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26436: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26436: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26436: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26436: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26436: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26436: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26436: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26436: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26436: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26436: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26436: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26436: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26436: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26436: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26436: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26436: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26436: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26436: Goal: +26436: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +26436: Order: +26436: nrkbo +26436: Leaf order: +26436: z 2 0 2 1,2,2 +26436: y 2 0 2 2,1,2 +26436: x 4 0 4 1,1,2 +26436: additive_identity 8 0 0 +26436: additive_inverse 22 1 0 +26436: commutator 1 2 0 +26436: add 24 2 0 +26436: multiply 46 2 6 0,2 +26436: associator 1 3 0 +NO CLASH, using fixed ground order +26437: Facts: +26437: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26437: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26437: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26437: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26437: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26437: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +NO CLASH, using fixed ground order +26438: Facts: +26438: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26438: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26438: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26438: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26438: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26438: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26438: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26438: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26438: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26438: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26438: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26438: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26438: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26438: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26438: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26438: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26438: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26438: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26438: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26438: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26438: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26438: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26438: Goal: +26438: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +26438: Order: +26438: lpo +26438: Leaf order: +26438: z 2 0 2 1,2,2 +26438: y 2 0 2 2,1,2 +26438: x 4 0 4 1,1,2 +26438: additive_identity 8 0 0 +26438: additive_inverse 22 1 0 +26438: commutator 1 2 0 +26438: add 24 2 0 +26438: multiply 46 2 6 0,2 +26438: associator 1 3 0 +26437: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26437: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26437: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26437: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26437: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26437: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26437: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26437: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26437: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26437: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26437: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26437: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26437: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26437: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26437: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26437: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26437: Goal: +26437: Id : 1, {_}: + multiply (multiply x y) (multiply z x) + =<= + multiply (multiply x (multiply y z)) x + [] by prove_middle_moufang +26437: Order: +26437: kbo +26437: Leaf order: +26437: z 2 0 2 1,2,2 +26437: y 2 0 2 2,1,2 +26437: x 4 0 4 1,1,2 +26437: additive_identity 8 0 0 +26437: additive_inverse 22 1 0 +26437: commutator 1 2 0 +26437: add 24 2 0 +26437: multiply 46 2 6 0,2 +26437: associator 1 3 0 +% SZS status Timeout for RNG029-7.p +NO CLASH, using fixed ground order +28162: Facts: +28162: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +28162: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +28162: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +28162: Id : 5, {_}: add c d =>= d [] by absorbtion +28162: Goal: +28162: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +28162: Order: +28162: nrkbo +28162: Leaf order: +28162: c 1 0 0 +28162: d 2 0 0 +28162: a 2 0 2 1,1,1,2 +28162: b 3 0 3 1,2,1,1,2 +28162: negate 9 1 5 0,1,2 +28162: add 13 2 3 0,2 +NO CLASH, using fixed ground order +28167: Facts: +28167: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +28167: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +28167: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +28167: Id : 5, {_}: add c d =>= d [] by absorbtion +28167: Goal: +28167: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +28167: Order: +28167: kbo +28167: Leaf order: +28167: c 1 0 0 +28167: d 2 0 0 +28167: a 2 0 2 1,1,1,2 +28167: b 3 0 3 1,2,1,1,2 +28167: negate 9 1 5 0,1,2 +28167: add 13 2 3 0,2 +NO CLASH, using fixed ground order +28168: Facts: +28168: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +28168: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +28168: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +28168: Id : 5, {_}: add c d =>= d [] by absorbtion +28168: Goal: +28168: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +28168: Order: +28168: lpo +28168: Leaf order: +28168: c 1 0 0 +28168: d 2 0 0 +28168: a 2 0 2 1,1,1,2 +28168: b 3 0 3 1,2,1,1,2 +28168: negate 9 1 5 0,1,2 +28168: add 13 2 3 0,2 +% SZS status Timeout for ROB006-1.p +NO CLASH, using fixed ground order +30020: Facts: +30020: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30020: Id : 3, {_}: + add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30020: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30020: Id : 5, {_}: add c d =>= d [] by absorbtion +30020: Goal: +30020: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30020: Order: +30020: nrkbo +30020: Leaf order: +30020: c 1 0 0 +30020: d 2 0 0 +30020: negate 4 1 0 +30020: add 11 2 1 0,2 +NO CLASH, using fixed ground order +30021: Facts: +30021: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30021: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30021: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30021: Id : 5, {_}: add c d =>= d [] by absorbtion +30021: Goal: +30021: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30021: Order: +30021: kbo +30021: Leaf order: +30021: c 1 0 0 +30021: d 2 0 0 +30021: negate 4 1 0 +30021: add 11 2 1 0,2 +NO CLASH, using fixed ground order +30022: Facts: +30022: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +30022: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +30022: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +30022: Id : 5, {_}: add c d =>= d [] by absorbtion +30022: Goal: +30022: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +30022: Order: +30022: lpo +30022: Leaf order: +30022: c 1 0 0 +30022: d 2 0 0 +30022: negate 4 1 0 +30022: add 11 2 1 0,2 +% SZS status Timeout for ROB006-2.p +NO CLASH, using fixed ground order +31074: Facts: +31074: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +31074: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +31074: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +31074: Id : 5, {_}: add c d =>= c [] by identity_constant +31074: Goal: +31074: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +31074: Order: +31074: nrkbo +31074: Leaf order: +31074: d 1 0 0 +31074: c 2 0 0 +31074: a 2 0 2 1,1,1,2 +31074: b 3 0 3 1,2,1,1,2 +31074: negate 9 1 5 0,1,2 +31074: add 13 2 3 0,2 +NO CLASH, using fixed ground order +31075: Facts: +31075: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +31075: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +31075: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +31075: Id : 5, {_}: add c d =>= c [] by identity_constant +31075: Goal: +31075: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +31075: Order: +31075: kbo +31075: Leaf order: +31075: d 1 0 0 +31075: c 2 0 0 +31075: a 2 0 2 1,1,1,2 +31075: b 3 0 3 1,2,1,1,2 +31075: negate 9 1 5 0,1,2 +31075: add 13 2 3 0,2 +NO CLASH, using fixed ground order +31076: Facts: +31076: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +31076: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +31076: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +31076: Id : 5, {_}: add c d =>= c [] by identity_constant +31076: Goal: +31076: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +31076: Order: +31076: lpo +31076: Leaf order: +31076: d 1 0 0 +31076: c 2 0 0 +31076: a 2 0 2 1,1,1,2 +31076: b 3 0 3 1,2,1,1,2 +31076: negate 9 1 5 0,1,2 +31076: add 13 2 3 0,2 +% SZS status Timeout for ROB026-1.p +NO CLASH, using fixed ground order +32629: Facts: +32629: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +32629: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +32629: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +32629: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +32629: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +32629: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +32629: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +32629: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +32629: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +32629: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +32629: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +32629: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +32629: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +32629: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +32629: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +32629: Goal: +32629: Id : 1, {_}: + least_upper_bound a (greatest_lower_bound b c) + =<= + greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c) + [] by prove_distrnu +32629: Order: +32629: nrkbo +32629: Leaf order: +32629: identity 2 0 0 +32629: b 2 0 2 1,2,2 +32629: c 2 0 2 2,2,2 +32629: a 3 0 3 1,2 +32629: inverse 1 1 0 +32629: greatest_lower_bound 15 2 2 0,2,2 +32629: least_upper_bound 16 2 3 0,2 +32629: multiply 18 2 0 +NO CLASH, using fixed ground order +32630: Facts: +32630: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +32630: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +32630: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +32630: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +32630: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +32630: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +32630: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +32630: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +32630: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +32630: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +32630: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +32630: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +32630: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +32630: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +32630: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +32630: Goal: +32630: Id : 1, {_}: + least_upper_bound a (greatest_lower_bound b c) + =<= + greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c) + [] by prove_distrnu +32630: Order: +32630: kbo +32630: Leaf order: +32630: identity 2 0 0 +32630: b 2 0 2 1,2,2 +32630: c 2 0 2 2,2,2 +32630: a 3 0 3 1,2 +32630: inverse 1 1 0 +32630: greatest_lower_bound 15 2 2 0,2,2 +32630: least_upper_bound 16 2 3 0,2 +32630: multiply 18 2 0 +NO CLASH, using fixed ground order +32631: Facts: +32631: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +32631: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +32631: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +32631: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +32631: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +32631: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +32631: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +32631: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +32631: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +32631: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +32631: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +32631: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +32631: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +32631: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +32631: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +32631: Goal: +32631: Id : 1, {_}: + least_upper_bound a (greatest_lower_bound b c) + =>= + greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c) + [] by prove_distrnu +32631: Order: +32631: lpo +32631: Leaf order: +32631: identity 2 0 0 +32631: b 2 0 2 1,2,2 +32631: c 2 0 2 2,2,2 +32631: a 3 0 3 1,2 +32631: inverse 1 1 0 +32631: greatest_lower_bound 15 2 2 0,2,2 +32631: least_upper_bound 16 2 3 0,2 +32631: multiply 18 2 0 +% SZS status Timeout for GRP164-1.p +NO CLASH, using fixed ground order +2296: Facts: +2296: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +2296: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +2296: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +2296: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +2296: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +2296: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +2296: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +2296: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +2296: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +2296: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +2296: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +2296: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +2296: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +2296: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +2296: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +2296: Goal: +2296: Id : 1, {_}: + greatest_lower_bound a (least_upper_bound b c) + =<= + least_upper_bound (greatest_lower_bound a b) + (greatest_lower_bound a c) + [] by prove_distrun +2296: Order: +2296: nrkbo +2296: Leaf order: +2296: identity 2 0 0 +2296: b 2 0 2 1,2,2 +2296: c 2 0 2 2,2,2 +2296: a 3 0 3 1,2 +2296: inverse 1 1 0 +2296: least_upper_bound 15 2 2 0,2,2 +2296: greatest_lower_bound 16 2 3 0,2 +2296: multiply 18 2 0 +NO CLASH, using fixed ground order +2305: Facts: +2305: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +2305: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +2305: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +2305: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +2305: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +2305: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +2305: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +2305: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +2305: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +2305: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +2305: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +2305: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +2305: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +2305: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +2305: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +2305: Goal: +2305: Id : 1, {_}: + greatest_lower_bound a (least_upper_bound b c) + =<= + least_upper_bound (greatest_lower_bound a b) + (greatest_lower_bound a c) + [] by prove_distrun +2305: Order: +2305: kbo +2305: Leaf order: +2305: identity 2 0 0 +2305: b 2 0 2 1,2,2 +2305: c 2 0 2 2,2,2 +2305: a 3 0 3 1,2 +2305: inverse 1 1 0 +2305: least_upper_bound 15 2 2 0,2,2 +2305: greatest_lower_bound 16 2 3 0,2 +2305: multiply 18 2 0 +NO CLASH, using fixed ground order +2309: Facts: +2309: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +2309: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +2309: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +2309: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +2309: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +2309: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +2309: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +2309: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +2309: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +2309: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +2309: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +2309: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +2309: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +2309: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +2309: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +2309: Goal: +2309: Id : 1, {_}: + greatest_lower_bound a (least_upper_bound b c) + =>= + least_upper_bound (greatest_lower_bound a b) + (greatest_lower_bound a c) + [] by prove_distrun +2309: Order: +2309: lpo +2309: Leaf order: +2309: identity 2 0 0 +2309: b 2 0 2 1,2,2 +2309: c 2 0 2 2,2,2 +2309: a 3 0 3 1,2 +2309: inverse 1 1 0 +2309: least_upper_bound 15 2 2 0,2,2 +2309: greatest_lower_bound 16 2 3 0,2 +2309: multiply 18 2 0 +% SZS status Timeout for GRP164-2.p +NO CLASH, using fixed ground order +4004: Facts: +4004: Id : 2, {_}: + multiply (multiply ?2 ?3) ?4 =?= multiply ?2 (multiply ?3 ?4) + [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4 +4004: Id : 3, {_}: + multiply ?6 (multiply ?7 (multiply ?7 ?7)) + =?= + multiply ?7 (multiply ?7 (multiply ?7 ?6)) + [7, 6] by condition ?6 ?7 +4004: Goal: +4004: Id : 1, {_}: + multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a (multiply b (multiply a b)))))))))))))))) + =>= + multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b (multiply b (multiply b b)))))))))))))))) + [] by prove_this +4004: Order: +4004: nrkbo +4004: Leaf order: +4004: a 18 0 18 1,2 +4004: b 18 0 18 1,2,2 +4004: multiply 44 2 34 0,2 +NO CLASH, using fixed ground order +4005: Facts: +4005: Id : 2, {_}: + multiply (multiply ?2 ?3) ?4 =>= multiply ?2 (multiply ?3 ?4) + [4, 3, 2] by associativity_of_multiply ?2 ?3 ?4 +4005: Id : 3, {_}: + multiply ?6 (multiply ?7 (multiply ?7 ?7)) + =?= + multiply ?7 (multiply ?7 (multiply ?7 ?6)) + [7, 6] by condition ?6 ?7 +4005: Goal: +4005: Id : 1, {_}: + multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a + (multiply b + (multiply a (multiply b (multiply a b)))))))))))))))) + =?= + multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply a + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b + (multiply b (multiply b (multiply b b)))))))))))))))) + [] by prove_this +4005: Order: +4005: kbo +4005: Leaf order: +4005: a 18 0 18 1,2 +4005: b 18 0 18 1,2,2 +4005: multiply 44 2 34 0,2 +NO CLASH, using fixed ground order +% SZS status Timeout for GRP196-1.p +NO CLASH, using fixed ground order +7093: Facts: +7093: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5 +7093: Goal: +7093: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +7093: Order: +7093: nrkbo +7093: Leaf order: +7093: a 3 0 3 1,2 +7093: c 3 0 3 2,1,2,2 +7093: b 4 0 4 1,1,2,2 +7093: f 18 2 8 0,2 +NO CLASH, using fixed ground order +7104: Facts: +7104: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5 +7104: Goal: +7104: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +7104: Order: +7104: kbo +7104: Leaf order: +7104: a 3 0 3 1,2 +7104: c 3 0 3 2,1,2,2 +7104: b 4 0 4 1,1,2,2 +7104: f 18 2 8 0,2 +NO CLASH, using fixed ground order +7109: Facts: +7109: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?3 (f (f ?2 ?2) ?2)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by ol_23A ?2 ?3 ?4 ?5 +7109: Goal: +7109: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +7109: Order: +7109: lpo +7109: Leaf order: +7109: a 3 0 3 1,2 +7109: c 3 0 3 2,1,2,2 +7109: b 4 0 4 1,1,2,2 +7109: f 18 2 8 0,2 +% SZS status Timeout for LAT070-1.p +NO CLASH, using fixed ground order +9646: Facts: +9646: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +9646: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +9646: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +9646: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +9646: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +9646: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +9646: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +9646: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +9646: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +9646: Goal: +9646: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +9646: Order: +9646: nrkbo +9646: Leaf order: +9646: b 3 0 3 1,2,2 +9646: c 3 0 3 2,2,2,2 +9646: a 6 0 6 1,2 +9646: join 17 2 4 0,2,2 +9646: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +9648: Facts: +9648: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +9648: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +9648: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +9648: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +9648: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +9648: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +9648: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +9648: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +9648: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +9648: Goal: +9648: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +9648: Order: +9648: kbo +9648: Leaf order: +9648: b 3 0 3 1,2,2 +9648: c 3 0 3 2,2,2,2 +9648: a 6 0 6 1,2 +9648: join 17 2 4 0,2,2 +9648: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +9649: Facts: +9649: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +9649: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +9649: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +9649: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +9649: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +9649: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +9649: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +9649: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +9649: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?26 (join (meet ?26 ?27) (meet ?28 (join ?26 ?27))))) + [28, 27, 26] by equation_H7 ?26 ?27 ?28 +9649: Goal: +9649: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +9649: Order: +9649: lpo +9649: Leaf order: +9649: b 3 0 3 1,2,2 +9649: c 3 0 3 2,2,2,2 +9649: a 6 0 6 1,2 +9649: join 17 2 4 0,2,2 +9649: meet 21 2 6 0,2 +% SZS status Timeout for LAT138-1.p +NO CLASH, using fixed ground order +11119: Facts: +11119: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11119: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11119: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11119: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11119: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11119: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11119: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11119: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11119: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +11119: Goal: +11119: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +11119: Order: +11119: kbo +11119: Leaf order: +11119: a 4 0 4 1,2 +11119: b 4 0 4 1,2,2 +11119: c 4 0 4 2,2,2,2 +11119: join 17 2 4 0,2,2 +11119: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +11120: Facts: +11120: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11120: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11120: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11120: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11120: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11120: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11120: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11120: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11120: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +11120: Goal: +11120: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +11120: Order: +11120: lpo +11120: Leaf order: +11120: a 4 0 4 1,2 +11120: b 4 0 4 1,2,2 +11120: c 4 0 4 2,2,2,2 +11120: join 17 2 4 0,2,2 +11120: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +11118: Facts: +11118: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +11118: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +11118: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +11118: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +11118: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +11118: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +11118: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +11118: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +11118: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +11118: Goal: +11118: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +11118: Order: +11118: nrkbo +11118: Leaf order: +11118: a 4 0 4 1,2 +11118: b 4 0 4 1,2,2 +11118: c 4 0 4 2,2,2,2 +11118: join 17 2 4 0,2,2 +11118: meet 21 2 6 0,2 +% SZS status Timeout for LAT140-1.p +NO CLASH, using fixed ground order +12763: Facts: +12763: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +12763: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +12763: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +12763: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +12763: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +12763: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +12763: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +12763: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +12763: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +12763: Goal: +12763: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +12763: Order: +12763: nrkbo +12763: Leaf order: +12763: b 3 0 3 1,2,2 +12763: c 3 0 3 2,2,2,2 +12763: a 6 0 6 1,2 +12763: join 16 2 4 0,2,2 +12763: meet 22 2 6 0,2 +NO CLASH, using fixed ground order +12764: Facts: +12764: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +12764: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +12764: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +12764: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +12764: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +12764: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +12764: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +12764: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +12764: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +12764: Goal: +12764: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +12764: Order: +12764: kbo +12764: Leaf order: +12764: b 3 0 3 1,2,2 +12764: c 3 0 3 2,2,2,2 +12764: a 6 0 6 1,2 +12764: join 16 2 4 0,2,2 +12764: meet 22 2 6 0,2 +NO CLASH, using fixed ground order +12765: Facts: +12765: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +12765: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +12765: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +12765: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +12765: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +12765: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +12765: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +12765: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +12765: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 (meet ?28 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join (meet ?26 ?29) (meet ?27 ?29)))) + [29, 28, 27, 26] by equation_H32 ?26 ?27 ?28 ?29 +12765: Goal: +12765: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +12765: Order: +12765: lpo +12765: Leaf order: +12765: b 3 0 3 1,2,2 +12765: c 3 0 3 2,2,2,2 +12765: a 6 0 6 1,2 +12765: join 16 2 4 0,2,2 +12765: meet 22 2 6 0,2 +% SZS status Timeout for LAT145-1.p +NO CLASH, using fixed ground order +13612: Facts: +13612: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13612: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13612: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13612: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13612: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13612: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13612: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13612: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13612: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +13612: Goal: +13612: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (join b d))))) + [] by prove_H43 +13612: Order: +13612: nrkbo +13612: Leaf order: +13612: c 2 0 2 1,2,2,2 +13612: a 3 0 3 1,2 +13612: d 3 0 3 2,2,2,2,2 +13612: b 4 0 4 1,2,2 +13612: meet 19 2 5 0,2 +13612: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +13613: Facts: +13613: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13613: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13613: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13613: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13613: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13613: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13613: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13613: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13613: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =<= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +13613: Goal: +13613: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (join b d))))) + [] by prove_H43 +13613: Order: +13613: kbo +13613: Leaf order: +13613: c 2 0 2 1,2,2,2 +13613: a 3 0 3 1,2 +13613: d 3 0 3 2,2,2,2,2 +13613: b 4 0 4 1,2,2 +13613: meet 19 2 5 0,2 +13613: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +13614: Facts: +13614: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +13614: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +13614: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +13614: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +13614: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +13614: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +13614: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +13614: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +13614: Id : 10, {_}: + meet ?26 (join ?27 (join ?28 (meet ?26 ?29))) + =?= + meet ?26 (join ?27 (join ?28 (meet ?29 (join ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H37 ?26 ?27 ?28 ?29 +13614: Goal: +13614: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (join b d))))) + [] by prove_H43 +13614: Order: +13614: lpo +13614: Leaf order: +13614: c 2 0 2 1,2,2,2 +13614: a 3 0 3 1,2 +13614: d 3 0 3 2,2,2,2,2 +13614: b 4 0 4 1,2,2 +13614: meet 19 2 5 0,2 +13614: join 19 2 5 0,2,2 +% SZS status Timeout for LAT149-1.p +NO CLASH, using fixed ground order +14638: Facts: +14638: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14638: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14638: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14638: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14638: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14638: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14638: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14638: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14638: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +14638: Goal: +14638: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +14638: Order: +14638: nrkbo +14638: Leaf order: +14638: c 2 0 2 2,2,2,2 +14638: b 4 0 4 1,2,2 +14638: a 6 0 6 1,2 +14638: join 18 2 4 0,2,2 +14638: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +14639: Facts: +14639: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14639: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14639: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14639: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14639: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14639: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14639: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14639: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14639: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +14639: Goal: +14639: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +14639: Order: +NO CLASH, using fixed ground order +14640: Facts: +14640: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +14640: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +14640: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +14640: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +14640: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +14640: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +14640: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +14640: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +14640: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?28 (join ?26 ?27))))) + [29, 28, 27, 26] by equation_H40 ?26 ?27 ?28 ?29 +14640: Goal: +14640: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet a (join (meet a b) (meet c (join a b))))) + [] by prove_H7 +14640: Order: +14640: lpo +14640: Leaf order: +14640: c 2 0 2 2,2,2,2 +14640: b 4 0 4 1,2,2 +14640: a 6 0 6 1,2 +14640: join 18 2 4 0,2,2 +14640: meet 20 2 6 0,2 +14639: kbo +14639: Leaf order: +14639: c 2 0 2 2,2,2,2 +14639: b 4 0 4 1,2,2 +14639: a 6 0 6 1,2 +14639: join 18 2 4 0,2,2 +14639: meet 20 2 6 0,2 +% SZS status Timeout for LAT153-1.p +NO CLASH, using fixed ground order +15430: Facts: +15430: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +15430: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +15430: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +15430: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +15430: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +15430: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +15430: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +15430: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +15430: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +15430: Goal: +15430: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +15430: Order: +15430: nrkbo +15430: Leaf order: +15430: a 4 0 4 1,2 +15430: b 4 0 4 1,2,2 +15430: c 4 0 4 2,2,2,2 +15430: join 18 2 4 0,2,2 +15430: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +15431: Facts: +15431: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +15431: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +15431: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +15431: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +15431: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +15431: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +15431: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +15431: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +15431: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +15431: Goal: +15431: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +15431: Order: +15431: kbo +15431: Leaf order: +15431: a 4 0 4 1,2 +15431: b 4 0 4 1,2,2 +15431: c 4 0 4 2,2,2,2 +15431: join 18 2 4 0,2,2 +15431: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +15432: Facts: +15432: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +15432: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +15432: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +15432: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +15432: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +15432: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +15432: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +15432: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +15432: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +15432: Goal: +15432: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join (meet a (join b c)) (meet b c)))) + [] by prove_H2 +15432: Order: +15432: lpo +15432: Leaf order: +15432: a 4 0 4 1,2 +15432: b 4 0 4 1,2,2 +15432: c 4 0 4 2,2,2,2 +15432: join 18 2 4 0,2,2 +15432: meet 20 2 6 0,2 +% SZS status Timeout for LAT157-1.p +NO CLASH, using fixed ground order +16370: Facts: +16370: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +16370: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +16370: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +16370: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +16370: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +16370: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +16370: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +16370: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +16370: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +16370: Goal: +16370: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c (join b d)))) + [] by prove_H49 +16370: Order: +16370: nrkbo +16370: Leaf order: +16370: d 2 0 2 2,2,2,2,2 +16370: b 3 0 3 1,2,2 +16370: c 3 0 3 1,2,2,2 +16370: a 4 0 4 1,2 +16370: meet 19 2 5 0,2 +16370: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +16387: Facts: +16387: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +16387: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +16387: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +16387: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +16387: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +16387: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +16387: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +16387: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +16387: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +16387: Goal: +16387: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c (join b d)))) + [] by prove_H49 +16387: Order: +16387: kbo +16387: Leaf order: +16387: d 2 0 2 2,2,2,2,2 +16387: b 3 0 3 1,2,2 +16387: c 3 0 3 1,2,2,2 +16387: a 4 0 4 1,2 +16387: meet 19 2 5 0,2 +16387: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +16398: Facts: +16398: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +16398: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +16398: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +16398: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +16398: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +16398: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +16398: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +16398: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +16398: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?26 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?26 (meet ?28 (join ?27 ?29))))) + [29, 28, 27, 26] by equation_H50 ?26 ?27 ?28 ?29 +16398: Goal: +16398: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (join (meet a c) (meet c (join b d)))) + [] by prove_H49 +16398: Order: +16398: lpo +16398: Leaf order: +16398: d 2 0 2 2,2,2,2,2 +16398: b 3 0 3 1,2,2 +16398: c 3 0 3 1,2,2,2 +16398: a 4 0 4 1,2 +16398: meet 19 2 5 0,2 +16398: join 19 2 5 0,2,2 +% SZS status Timeout for LAT158-1.p +NO CLASH, using fixed ground order +17619: Facts: +17619: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17619: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17619: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17619: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17619: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17619: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17619: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17619: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17619: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +17619: Goal: +17619: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +17619: Order: +17619: nrkbo +17619: Leaf order: +17619: c 2 0 2 1,2,2,2,2 +17619: b 3 0 3 1,2,2 +17619: d 3 0 3 2,2,2,2,2 +17619: a 4 0 4 1,2 +17619: join 16 2 3 0,2,2 +17619: meet 21 2 7 0,2 +NO CLASH, using fixed ground order +17620: Facts: +17620: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17620: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17620: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17620: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17620: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17620: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17620: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17620: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17620: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +17620: Goal: +NO CLASH, using fixed ground order +17620: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +17620: Order: +17620: kbo +17620: Leaf order: +17620: c 2 0 2 1,2,2,2,2 +17620: b 3 0 3 1,2,2 +17620: d 3 0 3 2,2,2,2,2 +17620: a 4 0 4 1,2 +17620: join 16 2 3 0,2,2 +17620: meet 21 2 7 0,2 +17622: Facts: +17622: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17622: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17622: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17622: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17622: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17622: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17622: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17622: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17622: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +17622: Goal: +17622: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +17622: Order: +17622: lpo +17622: Leaf order: +17622: c 2 0 2 1,2,2,2,2 +17622: b 3 0 3 1,2,2 +17622: d 3 0 3 2,2,2,2,2 +17622: a 4 0 4 1,2 +17622: join 16 2 3 0,2,2 +17622: meet 21 2 7 0,2 +% SZS status Timeout for LAT163-1.p +NO CLASH, using fixed ground order +17778: Facts: +17778: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17778: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17778: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17778: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17778: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17778: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17778: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17778: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17778: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +17778: Goal: +17778: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +17778: Order: +17778: nrkbo +17778: Leaf order: +17778: d 2 0 2 2,2,2,2,2 +17778: a 3 0 3 1,2 +17778: c 3 0 3 1,2,2,2 +17778: b 4 0 4 1,2,2 +17778: join 17 2 4 0,2,2 +17778: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +17779: Facts: +17779: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17779: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17779: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17779: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17779: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17779: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17779: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17779: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17779: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +17779: Goal: +17779: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +17779: Order: +17779: kbo +17779: Leaf order: +17779: d 2 0 2 2,2,2,2,2 +17779: a 3 0 3 1,2 +17779: c 3 0 3 1,2,2,2 +17779: b 4 0 4 1,2,2 +17779: join 17 2 4 0,2,2 +17779: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +17780: Facts: +17780: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +17780: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +17780: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +17780: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +17780: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +17780: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +17780: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +17780: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +17780: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 ?27)))) + [29, 28, 27, 26] by equation_H76 ?26 ?27 ?28 ?29 +17780: Goal: +17780: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +17780: Order: +17780: lpo +17780: Leaf order: +17780: d 2 0 2 2,2,2,2,2 +17780: a 3 0 3 1,2 +17780: c 3 0 3 1,2,2,2 +17780: b 4 0 4 1,2,2 +17780: join 17 2 4 0,2,2 +17780: meet 20 2 6 0,2 +% SZS status Timeout for LAT165-1.p +NO CLASH, using fixed ground order +18025: Facts: +18025: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18025: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18025: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18025: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18025: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18025: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18025: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18025: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18025: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29 +18025: Goal: +18025: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet b (join a d))))) + [] by prove_H78 +18025: Order: +18025: nrkbo +18025: Leaf order: +18025: c 2 0 2 1,2,2,2 +18025: a 3 0 3 1,2 +18025: d 3 0 3 2,2,2,2,2 +18025: b 4 0 4 1,2,2 +18025: join 18 2 5 0,2,2 +18025: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +18026: Facts: +18026: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18026: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18026: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18026: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18026: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18026: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18026: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18026: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18026: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29 +18026: Goal: +18026: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet b (join a d))))) + [] by prove_H78 +18026: Order: +18026: kbo +18026: Leaf order: +18026: c 2 0 2 1,2,2,2 +18026: a 3 0 3 1,2 +18026: d 3 0 3 2,2,2,2,2 +18026: b 4 0 4 1,2,2 +18026: join 18 2 5 0,2,2 +18026: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +18027: Facts: +18027: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18027: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18027: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18027: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18027: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18027: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18027: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18027: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18027: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =?= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?26 (meet ?27 ?28))))) + [29, 28, 27, 26] by equation_H77 ?26 ?27 ?28 ?29 +18027: Goal: +18027: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet b (join a d))))) + [] by prove_H78 +18027: Order: +18027: lpo +18027: Leaf order: +18027: c 2 0 2 1,2,2,2 +18027: a 3 0 3 1,2 +18027: d 3 0 3 2,2,2,2,2 +18027: b 4 0 4 1,2,2 +18027: join 18 2 5 0,2,2 +18027: meet 20 2 5 0,2 +% SZS status Timeout for LAT166-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +18051: Facts: +18051: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18051: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18051: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18051: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18051: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18051: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18051: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18051: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18051: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29))))) + [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29 +18051: Goal: +18051: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +18051: Order: +18051: kbo +18051: Leaf order: +18051: d 2 0 2 2,2,2,2,2 +18051: a 3 0 3 1,2 +18051: c 3 0 3 1,2,2,2 +18051: b 4 0 4 1,2,2 +18051: join 18 2 4 0,2,2 +18051: meet 20 2 6 0,2 +NO CLASH, using fixed ground order +18052: Facts: +18052: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18052: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18052: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18052: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18052: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18052: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18052: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18052: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18052: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29))))) + [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29 +18052: Goal: +18052: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +18052: Order: +18052: lpo +18052: Leaf order: +18052: d 2 0 2 2,2,2,2,2 +18052: a 3 0 3 1,2 +18052: c 3 0 3 1,2,2,2 +18052: b 4 0 4 1,2,2 +18052: join 18 2 4 0,2,2 +18052: meet 20 2 6 0,2 +18050: Facts: +18050: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18050: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18050: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18050: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18050: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18050: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18050: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18050: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18050: Id : 10, {_}: + meet ?26 (join ?27 (meet ?28 (join ?27 ?29))) + =<= + meet ?26 (join ?27 (meet ?28 (join ?29 (meet ?27 (join ?26 ?29))))) + [29, 28, 27, 26] by equation_H78 ?26 ?27 ?28 ?29 +18050: Goal: +18050: Id : 1, {_}: + meet a (join b (meet c (join b d))) + =<= + meet a (join b (meet c (join d (meet a (meet b c))))) + [] by prove_H77 +18050: Order: +18050: nrkbo +18050: Leaf order: +18050: d 2 0 2 2,2,2,2,2 +18050: a 3 0 3 1,2 +18050: c 3 0 3 1,2,2,2 +18050: b 4 0 4 1,2,2 +18050: join 18 2 4 0,2,2 +18050: meet 20 2 6 0,2 +% SZS status Timeout for LAT167-1.p +NO CLASH, using fixed ground order +18084: Facts: +18084: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18084: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18084: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18084: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18084: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18084: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18084: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18084: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18084: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +18084: Goal: +18084: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +18084: Order: +18084: nrkbo +18084: Leaf order: +18084: c 2 0 2 1,2,2,2,2 +18084: b 3 0 3 1,2,2 +18084: d 3 0 3 2,2,2,2,2 +18084: a 4 0 4 1,2 +18084: join 17 2 3 0,2,2 +18084: meet 20 2 7 0,2 +NO CLASH, using fixed ground order +18085: Facts: +18085: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18085: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18085: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18085: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18085: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18085: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18085: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18085: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18085: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +18085: Goal: +18085: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +18085: Order: +18085: kbo +18085: Leaf order: +18085: c 2 0 2 1,2,2,2,2 +18085: b 3 0 3 1,2,2 +18085: d 3 0 3 2,2,2,2,2 +18085: a 4 0 4 1,2 +18085: join 17 2 3 0,2,2 +18085: meet 20 2 7 0,2 +NO CLASH, using fixed ground order +18086: Facts: +18086: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18086: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18086: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18086: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18086: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18086: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18086: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18086: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18086: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +18086: Goal: +18086: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +18086: Order: +18086: lpo +18086: Leaf order: +18086: c 2 0 2 1,2,2,2,2 +18086: b 3 0 3 1,2,2 +18086: d 3 0 3 2,2,2,2,2 +18086: a 4 0 4 1,2 +18086: join 17 2 3 0,2,2 +18086: meet 20 2 7 0,2 +% SZS status Timeout for LAT172-1.p +NO CLASH, using fixed ground order +18325: Facts: +18325: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18325: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18325: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18325: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18325: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18325: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18325: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18325: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18325: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +18325: Goal: +18325: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +18325: Order: +18325: nrkbo +18325: Leaf order: +18325: d 2 0 2 2,2,2,2,2 +18325: b 3 0 3 1,2,2 +18325: c 3 0 3 1,2,2,2 +18325: a 4 0 4 1,2 +18325: meet 18 2 5 0,2 +18325: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +18329: Facts: +18329: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18329: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18329: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18329: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18329: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18329: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18329: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18329: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18329: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =<= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +18329: Goal: +18329: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +18329: Order: +18329: kbo +18329: Leaf order: +18329: d 2 0 2 2,2,2,2,2 +18329: b 3 0 3 1,2,2 +18329: c 3 0 3 1,2,2,2 +18329: a 4 0 4 1,2 +18329: meet 18 2 5 0,2 +18329: join 19 2 5 0,2,2 +NO CLASH, using fixed ground order +18330: Facts: +18330: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +18330: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +18330: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +18330: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +18330: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +18330: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +18330: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +18330: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +18330: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?27 ?29))) + =?= + join ?26 (meet ?27 (join ?28 (meet ?29 (join ?26 ?27)))) + [29, 28, 27, 26] by equation_H76_dual ?26 ?27 ?28 ?29 +18330: Goal: +18330: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join d (meet c (join a b))))) + [] by prove_H40 +18330: Order: +18330: lpo +18330: Leaf order: +18330: d 2 0 2 2,2,2,2,2 +18330: b 3 0 3 1,2,2 +18330: c 3 0 3 1,2,2,2 +18330: a 4 0 4 1,2 +18330: meet 18 2 5 0,2 +18330: join 19 2 5 0,2,2 +% SZS status Timeout for LAT173-1.p +NO CLASH, using fixed ground order +19752: Facts: +19752: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19752: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19752: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19752: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19752: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19752: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19752: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +NO CLASH, using fixed ground order +19755: Facts: +19755: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19755: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19755: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19755: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19755: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19755: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19755: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19755: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +NO CLASH, using fixed ground order +19757: Facts: +19757: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +19757: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +19757: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +19757: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +19757: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +19757: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +19757: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +19757: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19757: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +19757: Goal: +19757: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =>= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +19757: Order: +19757: lpo +19757: Leaf order: +19757: c 2 0 2 1,2,2,2,2 +19757: b 3 0 3 1,2,2 +19757: d 3 0 3 2,2,2,2,2 +19757: a 4 0 4 1,2 +19757: join 18 2 3 0,2,2 +19757: meet 20 2 7 0,2 +19752: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +19752: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +19752: Goal: +19752: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +19752: Order: +19752: nrkbo +19752: Leaf order: +19752: c 2 0 2 1,2,2,2,2 +19752: b 3 0 3 1,2,2 +19752: d 3 0 3 2,2,2,2,2 +19752: a 4 0 4 1,2 +19752: join 18 2 3 0,2,2 +19752: meet 20 2 7 0,2 +19755: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +19755: Goal: +19755: Id : 1, {_}: + meet a (join b (meet a (meet c d))) + =<= + meet a (join b (meet c (join (meet a d) (meet b d)))) + [] by prove_H32 +19755: Order: +19755: kbo +19755: Leaf order: +19755: c 2 0 2 1,2,2,2,2 +19755: b 3 0 3 1,2,2 +19755: d 3 0 3 2,2,2,2,2 +19755: a 4 0 4 1,2 +19755: join 18 2 3 0,2,2 +19755: meet 20 2 7 0,2 +% SZS status Timeout for LAT175-1.p +NO CLASH, using fixed ground order +21153: Facts: +21153: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +21153: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +21153: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +21153: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +21153: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +21153: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +21153: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +21153: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +21153: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +21153: Goal: +21153: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +21153: Order: +21153: nrkbo +21153: Leaf order: +21153: d 2 0 2 2,2,2,2,2 +21153: b 3 0 3 1,2,2 +21153: c 3 0 3 1,2,2,2 +21153: a 4 0 4 1,2 +21153: meet 18 2 5 0,2 +21153: join 20 2 5 0,2,2 +NO CLASH, using fixed ground order +21154: Facts: +21154: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +21154: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +21154: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +21154: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +21154: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +21154: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +21154: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +21154: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +21154: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +21154: Goal: +21154: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =<= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +21154: Order: +21154: kbo +21154: Leaf order: +21154: d 2 0 2 2,2,2,2,2 +21154: b 3 0 3 1,2,2 +21154: c 3 0 3 1,2,2,2 +21154: a 4 0 4 1,2 +21154: meet 18 2 5 0,2 +21154: join 20 2 5 0,2,2 +NO CLASH, using fixed ground order +21155: Facts: +21155: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +21155: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +21155: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +21155: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +21155: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +21155: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +21155: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +21155: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +21155: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =?= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +21155: Goal: +21155: Id : 1, {_}: + meet a (join b (meet c (join a d))) + =>= + meet a (join b (meet c (join b (join d (meet a c))))) + [] by prove_H42 +21155: Order: +21155: lpo +21155: Leaf order: +21155: d 2 0 2 2,2,2,2,2 +21155: b 3 0 3 1,2,2 +21155: c 3 0 3 1,2,2,2 +21155: a 4 0 4 1,2 +21155: meet 18 2 5 0,2 +21155: join 20 2 5 0,2,2 +% SZS status Timeout for LAT176-1.p +NO CLASH, using fixed ground order +23137: Facts: +23137: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +23137: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +23137: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +23137: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +23137: Id : 6, {_}: + add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +23137: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +23137: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +23137: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +23137: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +23137: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29 + [29] by x_fourthed_is_x ?29 +23137: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +23137: Goal: +23137: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +23137: Order: +23137: nrkbo +23137: Leaf order: +23137: b 2 0 1 1,2 +23137: a 2 0 1 2,2 +23137: c 2 0 1 3 +23137: additive_identity 4 0 0 +23137: additive_inverse 2 1 0 +23137: add 14 2 0 +23137: multiply 15 2 1 0,2 +NO CLASH, using fixed ground order +23138: Facts: +23138: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +23138: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +23138: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +23138: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +23138: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +23138: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +23138: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +23138: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +23138: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +23138: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29 + [29] by x_fourthed_is_x ?29 +23138: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +23138: Goal: +23138: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +23138: Order: +23138: kbo +23138: Leaf order: +23138: b 2 0 1 1,2 +23138: a 2 0 1 2,2 +23138: c 2 0 1 3 +23138: additive_identity 4 0 0 +23138: additive_inverse 2 1 0 +23138: add 14 2 0 +23138: multiply 15 2 1 0,2 +NO CLASH, using fixed ground order +23139: Facts: +23139: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +23139: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +23139: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +23139: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +23139: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +23139: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +23139: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +23139: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +23139: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +23139: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 ?29)) =>= ?29 + [29] by x_fourthed_is_x ?29 +23139: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +23139: Goal: +23139: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +23139: Order: +23139: lpo +23139: Leaf order: +23139: b 2 0 1 1,2 +23139: a 2 0 1 2,2 +23139: c 2 0 1 3 +23139: additive_identity 4 0 0 +23139: additive_inverse 2 1 0 +23139: add 14 2 0 +23139: multiply 15 2 1 0,2 +% SZS status Timeout for RNG035-7.p +NO CLASH, using fixed ground order +23161: Facts: +NO CLASH, using fixed ground order +23162: Facts: +23162: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +23162: Goal: +23162: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23162: Order: +23162: kbo +23162: Leaf order: +23162: b 1 0 1 1,2,2 +23162: a 4 0 4 1,1,2 +23162: nand 9 2 3 0,2 +23161: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +23161: Goal: +23161: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23161: Order: +23161: nrkbo +23161: Leaf order: +23161: b 1 0 1 1,2,2 +23161: a 4 0 4 1,1,2 +23161: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23163: Facts: +23163: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +23163: Goal: +23163: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23163: Order: +23163: lpo +23163: Leaf order: +23163: b 1 0 1 1,2,2 +23163: a 4 0 4 1,1,2 +23163: nand 9 2 3 0,2 +% SZS status Timeout for BOO077-1.p +NO CLASH, using fixed ground order +23212: Facts: +23212: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +23212: Goal: +23212: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23212: Order: +23212: nrkbo +23212: Leaf order: +23212: c 2 0 2 2,2,2,2 +23212: a 3 0 3 1,2 +23212: b 3 0 3 1,2,2 +23212: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23213: Facts: +23213: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +23213: Goal: +23213: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23213: Order: +23213: kbo +23213: Leaf order: +23213: c 2 0 2 2,2,2,2 +23213: a 3 0 3 1,2 +23213: b 3 0 3 1,2,2 +23213: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23214: Facts: +23214: Id : 2, {_}: + nand (nand ?2 (nand (nand ?3 ?2) ?2)) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c1 ?2 ?3 ?4 +23214: Goal: +23214: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23214: Order: +23214: lpo +23214: Leaf order: +23214: c 2 0 2 2,2,2,2 +23214: a 3 0 3 1,2 +23214: b 3 0 3 1,2,2 +23214: nand 12 2 6 0,2 +% SZS status Timeout for BOO078-1.p +NO CLASH, using fixed ground order +23320: Facts: +23320: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +23320: Goal: +23320: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23320: Order: +23320: nrkbo +23320: Leaf order: +23320: b 1 0 1 1,2,2 +23320: a 4 0 4 1,1,2 +23320: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23321: Facts: +23321: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +23321: Goal: +23321: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23321: Order: +23321: kbo +23321: Leaf order: +23321: b 1 0 1 1,2,2 +23321: a 4 0 4 1,1,2 +23321: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23322: Facts: +23322: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +23322: Goal: +23322: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23322: Order: +23322: lpo +23322: Leaf order: +23322: b 1 0 1 1,2,2 +23322: a 4 0 4 1,1,2 +23322: nand 9 2 3 0,2 +% SZS status Timeout for BOO079-1.p +NO CLASH, using fixed ground order +23351: Facts: +23351: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +23351: Goal: +NO CLASH, using fixed ground order +23352: Facts: +23352: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +23352: Goal: +23352: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23352: Order: +23352: kbo +23352: Leaf order: +23352: c 2 0 2 2,2,2,2 +23352: a 3 0 3 1,2 +23352: b 3 0 3 1,2,2 +23352: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23353: Facts: +23353: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?2))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c2 ?2 ?3 ?4 +23353: Goal: +23353: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23353: Order: +23353: lpo +23353: Leaf order: +23353: c 2 0 2 2,2,2,2 +23353: a 3 0 3 1,2 +23353: b 3 0 3 1,2,2 +23353: nand 12 2 6 0,2 +23351: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23351: Order: +23351: nrkbo +23351: Leaf order: +23351: c 2 0 2 2,2,2,2 +23351: a 3 0 3 1,2 +23351: b 3 0 3 1,2,2 +23351: nand 12 2 6 0,2 +% SZS status Timeout for BOO080-1.p +NO CLASH, using fixed ground order +23376: Facts: +23376: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +23376: Goal: +23376: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23376: Order: +23376: nrkbo +23376: Leaf order: +23376: b 1 0 1 1,2,2 +23376: a 4 0 4 1,1,2 +23376: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23377: Facts: +23377: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +23377: Goal: +23377: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23377: Order: +23377: kbo +23377: Leaf order: +23377: b 1 0 1 1,2,2 +23377: a 4 0 4 1,1,2 +23377: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23378: Facts: +23378: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +23378: Goal: +23378: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23378: Order: +23378: lpo +23378: Leaf order: +23378: b 1 0 1 1,2,2 +23378: a 4 0 4 1,1,2 +23378: nand 9 2 3 0,2 +% SZS status Timeout for BOO081-1.p +NO CLASH, using fixed ground order +23400: Facts: +23400: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +23400: Goal: +23400: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23400: Order: +23400: nrkbo +23400: Leaf order: +23400: c 2 0 2 2,2,2,2 +23400: a 3 0 3 1,2 +23400: b 3 0 3 1,2,2 +23400: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23401: Facts: +23401: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +23401: Goal: +23401: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23401: Order: +23401: kbo +23401: Leaf order: +23401: c 2 0 2 2,2,2,2 +23401: a 3 0 3 1,2 +23401: b 3 0 3 1,2,2 +23401: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23402: Facts: +23402: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c3 ?2 ?3 ?4 +23402: Goal: +23402: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23402: Order: +23402: lpo +23402: Leaf order: +23402: c 2 0 2 2,2,2,2 +23402: a 3 0 3 1,2 +23402: b 3 0 3 1,2,2 +23402: nand 12 2 6 0,2 +% SZS status Timeout for BOO082-1.p +NO CLASH, using fixed ground order +23425: Facts: +23425: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +23425: Goal: +23425: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23425: Order: +23425: nrkbo +23425: Leaf order: +23425: b 1 0 1 1,2,2 +23425: a 4 0 4 1,1,2 +23425: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23426: Facts: +23426: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +23426: Goal: +23426: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23426: Order: +23426: kbo +23426: Leaf order: +23426: b 1 0 1 1,2,2 +23426: a 4 0 4 1,1,2 +23426: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23427: Facts: +23427: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +23427: Goal: +23427: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23427: Order: +23427: lpo +23427: Leaf order: +23427: b 1 0 1 1,2,2 +23427: a 4 0 4 1,1,2 +23427: nand 9 2 3 0,2 +% SZS status Timeout for BOO083-1.p +NO CLASH, using fixed ground order +23456: Facts: +23456: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +23456: Goal: +23456: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23456: Order: +23456: nrkbo +23456: Leaf order: +23456: c 2 0 2 2,2,2,2 +23456: a 3 0 3 1,2 +23456: b 3 0 3 1,2,2 +23456: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +23458: Facts: +23458: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +23458: Goal: +23458: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23458: Order: +23458: lpo +23458: Leaf order: +23458: c 2 0 2 2,2,2,2 +23458: a 3 0 3 1,2 +23458: b 3 0 3 1,2,2 +23458: nand 12 2 6 0,2 +23457: Facts: +23457: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?2 ?3))) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c4 ?2 ?3 ?4 +23457: Goal: +23457: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23457: Order: +23457: kbo +23457: Leaf order: +23457: c 2 0 2 2,2,2,2 +23457: a 3 0 3 1,2 +23457: b 3 0 3 1,2,2 +23457: nand 12 2 6 0,2 +% SZS status Timeout for BOO084-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +23485: Facts: +23485: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +23485: Goal: +23485: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23485: Order: +23485: kbo +23485: Leaf order: +23485: b 1 0 1 1,2,2 +23485: a 4 0 4 1,1,2 +23485: nand 9 2 3 0,2 +23484: Facts: +23484: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +23484: Goal: +23484: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23484: Order: +23484: nrkbo +23484: Leaf order: +23484: b 1 0 1 1,2,2 +23484: a 4 0 4 1,1,2 +23484: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23486: Facts: +23486: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +23486: Goal: +23486: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23486: Order: +23486: lpo +23486: Leaf order: +23486: b 1 0 1 1,2,2 +23486: a 4 0 4 1,1,2 +23486: nand 9 2 3 0,2 +% SZS status Timeout for BOO085-1.p +NO CLASH, using fixed ground order +23521: Facts: +23521: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +23521: Goal: +23521: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23521: Order: +23521: nrkbo +23521: Leaf order: +23521: c 2 0 2 2,2,2,2 +23521: a 3 0 3 1,2 +23521: b 3 0 3 1,2,2 +23521: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23522: Facts: +23522: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +23522: Goal: +23522: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23522: Order: +23522: kbo +23522: Leaf order: +23522: c 2 0 2 2,2,2,2 +23522: a 3 0 3 1,2 +23522: b 3 0 3 1,2,2 +23522: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23523: Facts: +23523: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c5 ?2 ?3 ?4 +23523: Goal: +23523: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23523: Order: +23523: lpo +23523: Leaf order: +23523: c 2 0 2 2,2,2,2 +23523: a 3 0 3 1,2 +23523: b 3 0 3 1,2,2 +23523: nand 12 2 6 0,2 +% SZS status Timeout for BOO086-1.p +NO CLASH, using fixed ground order +23545: Facts: +23545: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +23545: Goal: +23545: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23545: Order: +23545: nrkbo +23545: Leaf order: +23545: b 1 0 1 1,2,2 +23545: a 4 0 4 1,1,2 +23545: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23546: Facts: +23546: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +23546: Goal: +23546: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23546: Order: +23546: kbo +23546: Leaf order: +23546: b 1 0 1 1,2,2 +23546: a 4 0 4 1,1,2 +23546: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23547: Facts: +23547: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +23547: Goal: +23547: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23547: Order: +23547: lpo +23547: Leaf order: +23547: b 1 0 1 1,2,2 +23547: a 4 0 4 1,1,2 +23547: nand 9 2 3 0,2 +% SZS status Timeout for BOO087-1.p +NO CLASH, using fixed ground order +23572: Facts: +23572: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +23572: Goal: +23572: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23572: Order: +23572: nrkbo +23572: Leaf order: +23572: c 2 0 2 2,2,2,2 +23572: a 3 0 3 1,2 +23572: b 3 0 3 1,2,2 +23572: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23573: Facts: +23573: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +23573: Goal: +23573: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23573: Order: +23573: kbo +23573: Leaf order: +23573: c 2 0 2 2,2,2,2 +23573: a 3 0 3 1,2 +23573: b 3 0 3 1,2,2 +23573: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23574: Facts: +23574: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?4))) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c6 ?2 ?3 ?4 +23574: Goal: +23574: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23574: Order: +23574: lpo +23574: Leaf order: +23574: c 2 0 2 2,2,2,2 +23574: a 3 0 3 1,2 +23574: b 3 0 3 1,2,2 +23574: nand 12 2 6 0,2 +% SZS status Timeout for BOO088-1.p +NO CLASH, using fixed ground order +23605: Facts: +23605: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +23605: Goal: +23605: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23605: Order: +23605: nrkbo +23605: Leaf order: +23605: b 1 0 1 1,2,2 +23605: a 4 0 4 1,1,2 +23605: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23606: Facts: +23606: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +23606: Goal: +23606: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23606: Order: +23606: kbo +23606: Leaf order: +23606: b 1 0 1 1,2,2 +23606: a 4 0 4 1,1,2 +23606: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23607: Facts: +23607: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +23607: Goal: +23607: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23607: Order: +23607: lpo +23607: Leaf order: +23607: b 1 0 1 1,2,2 +23607: a 4 0 4 1,1,2 +23607: nand 9 2 3 0,2 +% SZS status Timeout for BOO089-1.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +23696: Facts: +23696: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +23696: Goal: +23696: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23696: Order: +23696: kbo +23696: Leaf order: +23696: c 2 0 2 2,2,2,2 +23696: a 3 0 3 1,2 +23696: b 3 0 3 1,2,2 +23696: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23697: Facts: +23697: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +23697: Goal: +23697: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23697: Order: +23697: lpo +23697: Leaf order: +23697: c 2 0 2 2,2,2,2 +23697: a 3 0 3 1,2 +23697: b 3 0 3 1,2,2 +23697: nand 12 2 6 0,2 +23695: Facts: +23695: Id : 2, {_}: + nand (nand ?2 (nand ?2 (nand ?3 ?3))) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c7 ?2 ?3 ?4 +23695: Goal: +23695: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23695: Order: +23695: nrkbo +23695: Leaf order: +23695: c 2 0 2 2,2,2,2 +23695: a 3 0 3 1,2 +23695: b 3 0 3 1,2,2 +23695: nand 12 2 6 0,2 +% SZS status Timeout for BOO090-1.p +NO CLASH, using fixed ground order +23723: Facts: +23723: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +23723: Goal: +23723: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23723: Order: +23723: nrkbo +23723: Leaf order: +23723: b 1 0 1 1,2,2 +23723: a 4 0 4 1,1,2 +23723: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23724: Facts: +23724: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +23724: Goal: +23724: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23724: Order: +23724: kbo +23724: Leaf order: +23724: b 1 0 1 1,2,2 +23724: a 4 0 4 1,1,2 +23724: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23725: Facts: +23725: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +23725: Goal: +23725: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23725: Order: +23725: lpo +23725: Leaf order: +23725: b 1 0 1 1,2,2 +23725: a 4 0 4 1,1,2 +23725: nand 9 2 3 0,2 +% SZS status Timeout for BOO091-1.p +NO CLASH, using fixed ground order +23747: Facts: +23747: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +23747: Goal: +23747: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23747: Order: +23747: nrkbo +23747: Leaf order: +23747: c 2 0 2 2,2,2,2 +23747: a 3 0 3 1,2 +23747: b 3 0 3 1,2,2 +23747: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23748: Facts: +23748: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +23748: Goal: +23748: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23748: Order: +23748: kbo +23748: Leaf order: +23748: c 2 0 2 2,2,2,2 +23748: a 3 0 3 1,2 +23748: b 3 0 3 1,2,2 +23748: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23749: Facts: +23749: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c8 ?2 ?3 ?4 +23749: Goal: +23749: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23749: Order: +23749: lpo +23749: Leaf order: +23749: c 2 0 2 2,2,2,2 +23749: a 3 0 3 1,2 +23749: b 3 0 3 1,2,2 +23749: nand 12 2 6 0,2 +% SZS status Timeout for BOO092-1.p +NO CLASH, using fixed ground order +23772: Facts: +23772: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +23772: Goal: +NO CLASH, using fixed ground order +23773: Facts: +23773: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +23773: Goal: +23773: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23773: Order: +23773: kbo +23773: Leaf order: +23773: b 1 0 1 1,2,2 +23773: a 4 0 4 1,1,2 +23773: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23774: Facts: +23774: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +23774: Goal: +23774: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23774: Order: +23774: lpo +23774: Leaf order: +23774: b 1 0 1 1,2,2 +23774: a 4 0 4 1,1,2 +23774: nand 9 2 3 0,2 +23772: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23772: Order: +23772: nrkbo +23772: Leaf order: +23772: b 1 0 1 1,2,2 +23772: a 4 0 4 1,1,2 +23772: nand 9 2 3 0,2 +% SZS status Timeout for BOO093-1.p +NO CLASH, using fixed ground order +23798: Facts: +23798: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +23798: Goal: +23798: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23798: Order: +23798: nrkbo +23798: Leaf order: +23798: c 2 0 2 2,2,2,2 +23798: a 3 0 3 1,2 +23798: b 3 0 3 1,2,2 +23798: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23799: Facts: +23799: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +23799: Goal: +23799: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23799: Order: +23799: kbo +23799: Leaf order: +23799: c 2 0 2 2,2,2,2 +23799: a 3 0 3 1,2 +23799: b 3 0 3 1,2,2 +23799: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23800: Facts: +23800: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?3)) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c9 ?2 ?3 ?4 +23800: Goal: +23800: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23800: Order: +23800: lpo +23800: Leaf order: +23800: c 2 0 2 2,2,2,2 +23800: a 3 0 3 1,2 +23800: b 3 0 3 1,2,2 +23800: nand 12 2 6 0,2 +% SZS status Timeout for BOO094-1.p +NO CLASH, using fixed ground order +23822: Facts: +23822: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +23822: Goal: +23822: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23822: Order: +23822: nrkbo +23822: Leaf order: +23822: b 1 0 1 1,2,2 +23822: a 4 0 4 1,1,2 +23822: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23823: Facts: +23823: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +23823: Goal: +23823: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23823: Order: +23823: kbo +23823: Leaf order: +23823: b 1 0 1 1,2,2 +23823: a 4 0 4 1,1,2 +23823: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23824: Facts: +23824: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +23824: Goal: +23824: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23824: Order: +23824: lpo +23824: Leaf order: +23824: b 1 0 1 1,2,2 +23824: a 4 0 4 1,1,2 +23824: nand 9 2 3 0,2 +% SZS status Timeout for BOO095-1.p +NO CLASH, using fixed ground order +23854: Facts: +23854: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +23854: Goal: +23854: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23854: Order: +23854: nrkbo +23854: Leaf order: +23854: c 2 0 2 2,2,2,2 +23854: a 3 0 3 1,2 +23854: b 3 0 3 1,2,2 +23854: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23855: Facts: +23855: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +23855: Goal: +23855: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23855: Order: +23855: kbo +23855: Leaf order: +23855: c 2 0 2 2,2,2,2 +23855: a 3 0 3 1,2 +23855: b 3 0 3 1,2,2 +23855: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23856: Facts: +23856: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c10 ?2 ?3 ?4 +23856: Goal: +23856: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23856: Order: +23856: lpo +23856: Leaf order: +23856: c 2 0 2 2,2,2,2 +23856: a 3 0 3 1,2 +23856: b 3 0 3 1,2,2 +23856: nand 12 2 6 0,2 +% SZS status Timeout for BOO096-1.p +NO CLASH, using fixed ground order +23878: Facts: +23878: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +23878: Goal: +23878: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23878: Order: +23878: nrkbo +23878: Leaf order: +23878: b 1 0 1 1,2,2 +23878: a 4 0 4 1,1,2 +23878: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23879: Facts: +23879: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +23879: Goal: +23879: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23879: Order: +23879: kbo +23879: Leaf order: +23879: b 1 0 1 1,2,2 +23879: a 4 0 4 1,1,2 +23879: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23880: Facts: +23880: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +23880: Goal: +23880: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23880: Order: +23880: lpo +23880: Leaf order: +23880: b 1 0 1 1,2,2 +23880: a 4 0 4 1,1,2 +23880: nand 9 2 3 0,2 +% SZS status Timeout for BOO097-1.p +NO CLASH, using fixed ground order +23905: Facts: +23905: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +23905: Goal: +23905: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23905: Order: +23905: nrkbo +23905: Leaf order: +23905: c 2 0 2 2,2,2,2 +23905: a 3 0 3 1,2 +23905: b 3 0 3 1,2,2 +23905: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23906: Facts: +23906: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +23906: Goal: +23906: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23906: Order: +23906: kbo +23906: Leaf order: +23906: c 2 0 2 2,2,2,2 +23906: a 3 0 3 1,2 +23906: b 3 0 3 1,2,2 +23906: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23907: Facts: +23907: Id : 2, {_}: + nand (nand (nand ?2 (nand ?3 ?4)) ?2) (nand ?4 (nand ?2 ?3)) =>= ?4 + [4, 3, 2] by c11 ?2 ?3 ?4 +23907: Goal: +23907: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23907: Order: +23907: lpo +23907: Leaf order: +23907: c 2 0 2 2,2,2,2 +23907: a 3 0 3 1,2 +23907: b 3 0 3 1,2,2 +23907: nand 12 2 6 0,2 +% SZS status Timeout for BOO098-1.p +NO CLASH, using fixed ground order +23950: Facts: +23950: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +23950: Goal: +23950: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23950: Order: +23950: kbo +23950: Leaf order: +23950: b 1 0 1 1,2,2 +23950: a 4 0 4 1,1,2 +23950: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23951: Facts: +23951: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +23951: Goal: +23951: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23951: Order: +23951: lpo +23951: Leaf order: +23951: b 1 0 1 1,2,2 +23951: a 4 0 4 1,1,2 +23951: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +23949: Facts: +23949: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +23949: Goal: +23949: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +23949: Order: +23949: nrkbo +23949: Leaf order: +23949: b 1 0 1 1,2,2 +23949: a 4 0 4 1,1,2 +23949: nand 9 2 3 0,2 +% SZS status Timeout for BOO099-1.p +NO CLASH, using fixed ground order +23972: Facts: +23972: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +23972: Goal: +23972: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23972: Order: +23972: nrkbo +23972: Leaf order: +23972: c 2 0 2 2,2,2,2 +23972: a 3 0 3 1,2 +23972: b 3 0 3 1,2,2 +23972: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23973: Facts: +23973: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +23973: Goal: +23973: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23973: Order: +23973: kbo +23973: Leaf order: +23973: c 2 0 2 2,2,2,2 +23973: a 3 0 3 1,2 +23973: b 3 0 3 1,2,2 +23973: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +23974: Facts: +23974: Id : 2, {_}: + nand (nand (nand ?2 (nand ?2 ?3)) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c12 ?2 ?3 ?4 +23974: Goal: +23974: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +23974: Order: +23974: lpo +23974: Leaf order: +23974: c 2 0 2 2,2,2,2 +23974: a 3 0 3 1,2 +23974: b 3 0 3 1,2,2 +23974: nand 12 2 6 0,2 +% SZS status Timeout for BOO100-1.p +NO CLASH, using fixed ground order +24933: Facts: +24933: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +24933: Goal: +24933: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +24933: Order: +24933: nrkbo +24933: Leaf order: +24933: b 1 0 1 1,2,2 +24933: a 4 0 4 1,1,2 +24933: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +24934: Facts: +24934: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +24934: Goal: +24934: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +24934: Order: +24934: kbo +24934: Leaf order: +24934: b 1 0 1 1,2,2 +24934: a 4 0 4 1,1,2 +24934: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +24935: Facts: +24935: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +24935: Goal: +24935: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +24935: Order: +24935: lpo +24935: Leaf order: +24935: b 1 0 1 1,2,2 +24935: a 4 0 4 1,1,2 +24935: nand 9 2 3 0,2 +% SZS status Timeout for BOO101-1.p +NO CLASH, using fixed ground order +24957: Facts: +NO CLASH, using fixed ground order +24958: Facts: +24958: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +24958: Goal: +24958: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +24958: Order: +24958: kbo +24958: Leaf order: +24958: c 2 0 2 2,2,2,2 +24958: a 3 0 3 1,2 +24958: b 3 0 3 1,2,2 +24958: nand 12 2 6 0,2 +24957: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +24957: Goal: +24957: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +24957: Order: +24957: nrkbo +24957: Leaf order: +24957: c 2 0 2 2,2,2,2 +24957: a 3 0 3 1,2 +24957: b 3 0 3 1,2,2 +24957: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +24959: Facts: +24959: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c13 ?2 ?3 ?4 +24959: Goal: +24959: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +24959: Order: +24959: lpo +24959: Leaf order: +24959: c 2 0 2 2,2,2,2 +24959: a 3 0 3 1,2 +24959: b 3 0 3 1,2,2 +24959: nand 12 2 6 0,2 +% SZS status Timeout for BOO102-1.p +NO CLASH, using fixed ground order +24983: Facts: +24983: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +24983: Goal: +24983: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +24983: Order: +24983: nrkbo +24983: Leaf order: +24983: b 1 0 1 1,2,2 +24983: a 4 0 4 1,1,2 +24983: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +24984: Facts: +24984: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +24984: Goal: +24984: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +24984: Order: +24984: kbo +24984: Leaf order: +24984: b 1 0 1 1,2,2 +24984: a 4 0 4 1,1,2 +24984: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +24985: Facts: +24985: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +24985: Goal: +24985: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +24985: Order: +24985: lpo +24985: Leaf order: +24985: b 1 0 1 1,2,2 +24985: a 4 0 4 1,1,2 +24985: nand 9 2 3 0,2 +% SZS status Timeout for BOO103-1.p +NO CLASH, using fixed ground order +25006: Facts: +25006: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +25006: Goal: +25006: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25006: Order: +25006: nrkbo +25006: Leaf order: +25006: c 2 0 2 2,2,2,2 +25006: a 3 0 3 1,2 +25006: b 3 0 3 1,2,2 +25006: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +25007: Facts: +25007: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +25007: Goal: +25007: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25007: Order: +25007: kbo +25007: Leaf order: +25007: c 2 0 2 2,2,2,2 +25007: a 3 0 3 1,2 +25007: b 3 0 3 1,2,2 +25007: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +25008: Facts: +25008: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?2) ?2) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c14 ?2 ?3 ?4 +25008: Goal: +25008: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25008: Order: +25008: lpo +25008: Leaf order: +25008: c 2 0 2 2,2,2,2 +25008: a 3 0 3 1,2 +25008: b 3 0 3 1,2,2 +25008: nand 12 2 6 0,2 +% SZS status Timeout for BOO104-1.p +NO CLASH, using fixed ground order +25030: Facts: +25030: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +25030: Goal: +25030: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +25030: Order: +25030: nrkbo +25030: Leaf order: +25030: b 1 0 1 1,2,2 +25030: a 4 0 4 1,1,2 +25030: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +25031: Facts: +25031: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +25031: Goal: +25031: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +25031: Order: +25031: kbo +25031: Leaf order: +25031: b 1 0 1 1,2,2 +25031: a 4 0 4 1,1,2 +25031: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +25032: Facts: +25032: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +25032: Goal: +25032: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +25032: Order: +25032: lpo +25032: Leaf order: +25032: b 1 0 1 1,2,2 +25032: a 4 0 4 1,1,2 +25032: nand 9 2 3 0,2 +% SZS status Timeout for BOO105-1.p +NO CLASH, using fixed ground order +25053: Facts: +25053: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +25053: Goal: +25053: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25053: Order: +25053: nrkbo +25053: Leaf order: +25053: c 2 0 2 2,2,2,2 +25053: a 3 0 3 1,2 +25053: b 3 0 3 1,2,2 +25053: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +25054: Facts: +25054: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +25054: Goal: +25054: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25054: Order: +25054: kbo +25054: Leaf order: +25054: c 2 0 2 2,2,2,2 +25054: a 3 0 3 1,2 +25054: b 3 0 3 1,2,2 +25054: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +25055: Facts: +25055: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?2 ?4)) =>= ?3 + [4, 3, 2] by c15 ?2 ?3 ?4 +25055: Goal: +25055: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25055: Order: +25055: lpo +25055: Leaf order: +25055: c 2 0 2 2,2,2,2 +25055: a 3 0 3 1,2 +25055: b 3 0 3 1,2,2 +25055: nand 12 2 6 0,2 +% SZS status Timeout for BOO106-1.p +NO CLASH, using fixed ground order +25082: Facts: +25082: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +25082: Goal: +25082: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +25082: Order: +25082: nrkbo +25082: Leaf order: +25082: b 1 0 1 1,2,2 +25082: a 4 0 4 1,1,2 +25082: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +25083: Facts: +25083: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +25083: Goal: +25083: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +25083: Order: +25083: kbo +25083: Leaf order: +25083: b 1 0 1 1,2,2 +25083: a 4 0 4 1,1,2 +25083: nand 9 2 3 0,2 +NO CLASH, using fixed ground order +25084: Facts: +25084: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +25084: Goal: +25084: Id : 1, {_}: nand (nand a a) (nand b a) =>= a [] by prove_meredith_2_basis_1 +25084: Order: +25084: lpo +25084: Leaf order: +25084: b 1 0 1 1,2,2 +25084: a 4 0 4 1,1,2 +25084: nand 9 2 3 0,2 +% SZS status Timeout for BOO107-1.p +NO CLASH, using fixed ground order +25109: Facts: +25109: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +25109: Goal: +25109: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25109: Order: +25109: nrkbo +25109: Leaf order: +25109: c 2 0 2 2,2,2,2 +25109: a 3 0 3 1,2 +25109: b 3 0 3 1,2,2 +25109: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +25110: Facts: +25110: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +25110: Goal: +25110: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25110: Order: +25110: kbo +25110: Leaf order: +25110: c 2 0 2 2,2,2,2 +25110: a 3 0 3 1,2 +25110: b 3 0 3 1,2,2 +25110: nand 12 2 6 0,2 +NO CLASH, using fixed ground order +25111: Facts: +25111: Id : 2, {_}: + nand (nand (nand (nand ?2 ?3) ?4) ?4) (nand ?3 (nand ?4 ?2)) =>= ?3 + [4, 3, 2] by c16 ?2 ?3 ?4 +25111: Goal: +25111: Id : 1, {_}: + nand a (nand b (nand a c)) =<= nand (nand (nand c b) b) a + [] by prove_meredith_2_basis_2 +25111: Order: +25111: lpo +25111: Leaf order: +25111: c 2 0 2 2,2,2,2 +25111: a 3 0 3 1,2 +25111: b 3 0 3 1,2,2 +25111: nand 12 2 6 0,2 +% SZS status Timeout for BOO108-1.p +CLASH, statistics insufficient +25136: Facts: +25136: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25136: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25136: Goal: +25136: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25136: Order: +25136: nrkbo +25136: Leaf order: +25136: s 1 0 0 +25136: b 1 0 0 +25136: f 3 1 3 0,2,2 +25136: apply 14 2 3 0,2 +CLASH, statistics insufficient +25137: Facts: +25137: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25137: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25137: Goal: +25137: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25137: Order: +25137: kbo +25137: Leaf order: +25137: s 1 0 0 +25137: b 1 0 0 +25137: f 3 1 3 0,2,2 +25137: apply 14 2 3 0,2 +CLASH, statistics insufficient +25138: Facts: +25138: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25138: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25138: Goal: +25138: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25138: Order: +25138: lpo +25138: Leaf order: +25138: s 1 0 0 +25138: b 1 0 0 +25138: f 3 1 3 0,2,2 +25138: apply 14 2 3 0,2 +% SZS status Timeout for COL067-1.p +CLASH, statistics insufficient +25159: Facts: +25159: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25159: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25159: Goal: +25159: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +25159: Order: +25159: nrkbo +25159: Leaf order: +25159: s 1 0 0 +25159: b 1 0 0 +25159: combinator 1 0 1 1,3 +25159: apply 12 2 1 0,3 +CLASH, statistics insufficient +25160: Facts: +25160: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25160: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25160: Goal: +25160: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +25160: Order: +25160: kbo +25160: Leaf order: +25160: s 1 0 0 +25160: b 1 0 0 +25160: combinator 1 0 1 1,3 +25160: apply 12 2 1 0,3 +CLASH, statistics insufficient +25161: Facts: +25161: Id : 2, {_}: + apply (apply (apply s ?3) ?4) ?5 + =?= + apply (apply ?3 ?5) (apply ?4 ?5) + [5, 4, 3] by s_definition ?3 ?4 ?5 +25161: Id : 3, {_}: + apply (apply (apply b ?7) ?8) ?9 =>= apply ?7 (apply ?8 ?9) + [9, 8, 7] by b_definition ?7 ?8 ?9 +25161: Goal: +25161: Id : 1, {_}: ?1 =<= apply combinator ?1 [1] by prove_fixed_point ?1 +25161: Order: +25161: lpo +25161: Leaf order: +25161: s 1 0 0 +25161: b 1 0 0 +25161: combinator 1 0 1 1,3 +25161: apply 12 2 1 0,3 +% SZS status Timeout for COL068-1.p +CLASH, statistics insufficient +25183: Facts: +25183: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25183: Id : 3, {_}: + apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8) + [8, 7] by l_definition ?7 ?8 +25183: Goal: +25183: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25183: Order: +25183: nrkbo +25183: Leaf order: +25183: b 1 0 0 +25183: l 1 0 0 +25183: f 3 1 3 0,2,2 +25183: apply 12 2 3 0,2 +CLASH, statistics insufficient +25184: Facts: +25184: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25184: Id : 3, {_}: + apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8) + [8, 7] by l_definition ?7 ?8 +25184: Goal: +25184: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25184: Order: +25184: kbo +25184: Leaf order: +25184: b 1 0 0 +25184: l 1 0 0 +25184: f 3 1 3 0,2,2 +25184: apply 12 2 3 0,2 +CLASH, statistics insufficient +25185: Facts: +25185: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by b_definition ?3 ?4 ?5 +25185: Id : 3, {_}: + apply (apply l ?7) ?8 =?= apply ?7 (apply ?8 ?8) + [8, 7] by l_definition ?7 ?8 +25185: Goal: +25185: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by prove_fixed_point ?1 +25185: Order: +25185: lpo +25185: Leaf order: +25185: b 1 0 0 +25185: l 1 0 0 +25185: f 3 1 3 0,2,2 +25185: apply 12 2 3 0,2 +% SZS status Timeout for COL069-1.p +CLASH, statistics insufficient +25251: Facts: +25251: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by definition_B ?3 ?4 ?5 +25251: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7 +25251: Goal: +25251: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by strong_fixpoint ?1 +25251: Order: +25251: nrkbo +25251: Leaf order: +25251: b 1 0 0 +25251: m 1 0 0 +25251: f 3 1 3 0,2,2 +25251: apply 10 2 3 0,2 +CLASH, statistics insufficient +25252: Facts: +25252: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by definition_B ?3 ?4 ?5 +25252: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7 +25252: Goal: +25252: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by strong_fixpoint ?1 +25252: Order: +25252: kbo +25252: Leaf order: +25252: b 1 0 0 +25252: m 1 0 0 +25252: f 3 1 3 0,2,2 +25252: apply 10 2 3 0,2 +CLASH, statistics insufficient +25253: Facts: +25253: Id : 2, {_}: + apply (apply (apply b ?3) ?4) ?5 =>= apply ?3 (apply ?4 ?5) + [5, 4, 3] by definition_B ?3 ?4 ?5 +25253: Id : 3, {_}: apply m ?7 =?= apply ?7 ?7 [7] by definition_M ?7 +25253: Goal: +25253: Id : 1, {_}: + apply ?1 (f ?1) =<= apply (f ?1) (apply ?1 (f ?1)) + [1] by strong_fixpoint ?1 +25253: Order: +25253: lpo +25253: Leaf order: +25253: b 1 0 0 +25253: m 1 0 0 +25253: f 3 1 3 0,2,2 +25253: apply 10 2 3 0,2 +% SZS status Timeout for COL087-1.p +NO CLASH, using fixed ground order +25281: Facts: +25281: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25281: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25281: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25281: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25281: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25281: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =?= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25281: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =?= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25281: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25281: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25281: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25281: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25281: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25281: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25281: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25281: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25281: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1 +25281: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2 +25281: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3 +25281: Goal: +25281: Id : 1, {_}: + least_upper_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + multiply (greatest_lower_bound a b) (greatest_lower_bound a c) + [] by prove_p08a +25281: Order: +25281: nrkbo +25281: Leaf order: +25281: identity 5 0 0 +25281: b 5 0 3 1,2,1,2 +25281: c 5 0 3 2,2,1,2 +25281: a 7 0 5 1,1,2 +25281: inverse 1 1 0 +25281: least_upper_bound 17 2 1 0,2 +25281: greatest_lower_bound 18 2 5 0,1,2 +25281: multiply 21 2 3 0,2,1,2 +NO CLASH, using fixed ground order +25282: Facts: +25282: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25282: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25282: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25282: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25282: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25282: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25282: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25282: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25282: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25282: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25282: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25282: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =<= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25282: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =<= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25282: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =<= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25282: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =<= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25282: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1 +25282: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2 +25282: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3 +25282: Goal: +25282: Id : 1, {_}: + least_upper_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + multiply (greatest_lower_bound a b) (greatest_lower_bound a c) + [] by prove_p08a +25282: Order: +25282: kbo +25282: Leaf order: +25282: identity 5 0 0 +25282: b 5 0 3 1,2,1,2 +25282: c 5 0 3 2,2,1,2 +25282: a 7 0 5 1,1,2 +25282: inverse 1 1 0 +25282: least_upper_bound 17 2 1 0,2 +25282: greatest_lower_bound 18 2 5 0,1,2 +25282: multiply 21 2 3 0,2,1,2 +NO CLASH, using fixed ground order +25283: Facts: +25283: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2 +25283: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4 +25283: Id : 4, {_}: + multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) + [8, 7, 6] by associativity ?6 ?7 ?8 +25283: Id : 5, {_}: + greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 + [11, 10] by symmetry_of_glb ?10 ?11 +25283: Id : 6, {_}: + least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 + [14, 13] by symmetry_of_lub ?13 ?14 +25283: Id : 7, {_}: + greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) + =<= + greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 + [18, 17, 16] by associativity_of_glb ?16 ?17 ?18 +25283: Id : 8, {_}: + least_upper_bound ?20 (least_upper_bound ?21 ?22) + =<= + least_upper_bound (least_upper_bound ?20 ?21) ?22 + [22, 21, 20] by associativity_of_lub ?20 ?21 ?22 +25283: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24 +25283: Id : 10, {_}: + greatest_lower_bound ?26 ?26 =>= ?26 + [26] by idempotence_of_gld ?26 +25283: Id : 11, {_}: + least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 + [29, 28] by lub_absorbtion ?28 ?29 +25283: Id : 12, {_}: + greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 + [32, 31] by glb_absorbtion ?31 ?32 +25283: Id : 13, {_}: + multiply ?34 (least_upper_bound ?35 ?36) + =>= + least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) + [36, 35, 34] by monotony_lub1 ?34 ?35 ?36 +25283: Id : 14, {_}: + multiply ?38 (greatest_lower_bound ?39 ?40) + =>= + greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) + [40, 39, 38] by monotony_glb1 ?38 ?39 ?40 +25283: Id : 15, {_}: + multiply (least_upper_bound ?42 ?43) ?44 + =>= + least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) + [44, 43, 42] by monotony_lub2 ?42 ?43 ?44 +25283: Id : 16, {_}: + multiply (greatest_lower_bound ?46 ?47) ?48 + =>= + greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) + [48, 47, 46] by monotony_glb2 ?46 ?47 ?48 +25283: Id : 17, {_}: least_upper_bound identity a =>= a [] by p08a_1 +25283: Id : 18, {_}: least_upper_bound identity b =>= b [] by p08a_2 +25283: Id : 19, {_}: least_upper_bound identity c =>= c [] by p08a_3 +25283: Goal: +25283: Id : 1, {_}: + least_upper_bound (greatest_lower_bound a (multiply b c)) + (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) + =>= + multiply (greatest_lower_bound a b) (greatest_lower_bound a c) + [] by prove_p08a +25283: Order: +25283: lpo +25283: Leaf order: +25283: identity 5 0 0 +25283: b 5 0 3 1,2,1,2 +25283: c 5 0 3 2,2,1,2 +25283: a 7 0 5 1,1,2 +25283: inverse 1 1 0 +25283: least_upper_bound 17 2 1 0,2 +25283: greatest_lower_bound 18 2 5 0,1,2 +25283: multiply 21 2 3 0,2,1,2 +% SZS status Timeout for GRP177-1.p +NO CLASH, using fixed ground order +25304: Facts: +25304: Id : 2, {_}: + f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5)) + =>= + ?3 + [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5 +25304: Goal: +25304: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25304: Order: +25304: nrkbo +25304: Leaf order: +25304: a 3 0 3 1,2 +25304: c 3 0 3 2,1,2,2 +25304: b 4 0 4 1,1,2,2 +25304: f 17 2 8 0,2 +NO CLASH, using fixed ground order +25305: Facts: +25305: Id : 2, {_}: + f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5)) + =>= + ?3 + [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5 +25305: Goal: +25305: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25305: Order: +25305: kbo +25305: Leaf order: +25305: a 3 0 3 1,2 +25305: c 3 0 3 2,1,2,2 +25305: b 4 0 4 1,1,2,2 +25305: f 17 2 8 0,2 +NO CLASH, using fixed ground order +25306: Facts: +25306: Id : 2, {_}: + f (f ?2 ?3) (f (f (f (f ?2 ?3) ?3) (f ?4 ?3)) (f (f ?3 ?3) ?5)) + =>= + ?3 + [5, 4, 3, 2] by oml_21C ?2 ?3 ?4 ?5 +25306: Goal: +25306: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25306: Order: +25306: lpo +25306: Leaf order: +25306: a 3 0 3 1,2 +25306: c 3 0 3 2,1,2,2 +25306: b 4 0 4 1,1,2,2 +25306: f 17 2 8 0,2 +% SZS status Timeout for LAT071-1.p +NO CLASH, using fixed ground order +25332: Facts: +25332: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5 +25332: Goal: +25332: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25332: Order: +25332: nrkbo +25332: Leaf order: +25332: a 3 0 3 1,2 +25332: c 3 0 3 2,1,2,2 +25332: b 4 0 4 1,1,2,2 +25332: f 18 2 8 0,2 +NO CLASH, using fixed ground order +25333: Facts: +25333: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5 +25333: Goal: +25333: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25333: Order: +25333: kbo +25333: Leaf order: +25333: a 3 0 3 1,2 +25333: c 3 0 3 2,1,2,2 +25333: b 4 0 4 1,1,2,2 +25333: f 18 2 8 0,2 +NO CLASH, using fixed ground order +25334: Facts: +25334: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f ?4 (f (f ?3 ?3) ?4)) ?4)) + =>= + ?3 + [5, 4, 3, 2] by oml_23A ?2 ?3 ?4 ?5 +25334: Goal: +25334: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25334: Order: +25334: lpo +25334: Leaf order: +25334: a 3 0 3 1,2 +25334: c 3 0 3 2,1,2,2 +25334: b 4 0 4 1,1,2,2 +25334: f 18 2 8 0,2 +% SZS status Timeout for LAT072-1.p +NO CLASH, using fixed ground order +25355: Facts: +25355: Id : 2, {_}: + f (f (f ?2 (f ?3 ?2)) ?2) + (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5)))) + =>= + ?3 + [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5 +25355: Goal: +25355: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +25355: Order: +25355: nrkbo +25355: Leaf order: +25355: b 3 0 3 1,2,2 +25355: c 3 0 3 1,2,2,2,2 +25355: a 4 0 4 1,2 +25355: f 18 2 8 0,2 +NO CLASH, using fixed ground order +25356: Facts: +25356: Id : 2, {_}: + f (f (f ?2 (f ?3 ?2)) ?2) + (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5)))) + =>= + ?3 + [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5 +25356: Goal: +25356: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +25356: Order: +25356: kbo +25356: Leaf order: +25356: b 3 0 3 1,2,2 +25356: c 3 0 3 1,2,2,2,2 +25356: a 4 0 4 1,2 +25356: f 18 2 8 0,2 +NO CLASH, using fixed ground order +25357: Facts: +25357: Id : 2, {_}: + f (f (f ?2 (f ?3 ?2)) ?2) + (f ?3 (f ?4 (f (f ?3 ?2) (f (f ?4 ?4) ?5)))) + =>= + ?3 + [5, 4, 3, 2] by mol_23C ?2 ?3 ?4 ?5 +25357: Goal: +25357: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +25357: Order: +25357: lpo +25357: Leaf order: +25357: b 3 0 3 1,2,2 +25357: c 3 0 3 1,2,2,2,2 +25357: a 4 0 4 1,2 +25357: f 18 2 8 0,2 +% SZS status Timeout for LAT073-1.p +NO CLASH, using fixed ground order +25379: Facts: +NO CLASH, using fixed ground order +25381: Facts: +25381: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +25381: Goal: +25381: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25381: Order: +25381: lpo +25381: Leaf order: +25381: a 3 0 3 1,2 +25381: c 3 0 3 2,1,2,2 +25381: b 4 0 4 1,1,2,2 +25381: f 19 2 8 0,2 +NO CLASH, using fixed ground order +25380: Facts: +25380: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +25380: Goal: +25380: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25380: Order: +25380: kbo +25380: Leaf order: +25380: a 3 0 3 1,2 +25380: c 3 0 3 2,1,2,2 +25380: b 4 0 4 1,1,2,2 +25380: f 19 2 8 0,2 +25379: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +25379: Goal: +25379: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25379: Order: +25379: nrkbo +25379: Leaf order: +25379: a 3 0 3 1,2 +25379: c 3 0 3 2,1,2,2 +25379: b 4 0 4 1,1,2,2 +25379: f 19 2 8 0,2 +% SZS status Timeout for LAT074-1.p +NO CLASH, using fixed ground order +25407: Facts: +25407: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +25407: Goal: +25407: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +25407: Order: +25407: nrkbo +25407: Leaf order: +25407: b 3 0 3 1,2,2 +25407: c 3 0 3 1,2,2,2,2 +25407: a 4 0 4 1,2 +25407: f 19 2 8 0,2 +NO CLASH, using fixed ground order +25408: Facts: +25408: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +25408: Goal: +25408: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +25408: Order: +25408: kbo +25408: Leaf order: +25408: b 3 0 3 1,2,2 +25408: c 3 0 3 1,2,2,2,2 +25408: a 4 0 4 1,2 +25408: f 19 2 8 0,2 +NO CLASH, using fixed ground order +25409: Facts: +25409: Id : 2, {_}: + f (f ?2 ?3) + (f (f (f ?3 ?3) ?4) (f (f (f (f (f ?3 ?2) ?4) ?4) ?3) (f ?3 ?5))) + =>= + ?3 + [5, 4, 3, 2] by mol_25A ?2 ?3 ?4 ?5 +25409: Goal: +25409: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +25409: Order: +25409: lpo +25409: Leaf order: +25409: b 3 0 3 1,2,2 +25409: c 3 0 3 1,2,2,2,2 +25409: a 4 0 4 1,2 +25409: f 19 2 8 0,2 +% SZS status Timeout for LAT075-1.p +NO CLASH, using fixed ground order +25460: Facts: +25460: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +25460: Goal: +25460: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25460: Order: +25460: nrkbo +25460: Leaf order: +25460: a 3 0 3 1,2 +25460: c 3 0 3 2,1,2,2 +25460: b 4 0 4 1,1,2,2 +25460: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25461: Facts: +25461: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +25461: Goal: +25461: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25461: Order: +25461: kbo +25461: Leaf order: +25461: a 3 0 3 1,2 +25461: c 3 0 3 2,1,2,2 +25461: b 4 0 4 1,1,2,2 +25461: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25462: Facts: +25462: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +25462: Goal: +25462: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25462: Order: +25462: lpo +25462: Leaf order: +25462: a 3 0 3 1,2 +25462: c 3 0 3 2,1,2,2 +25462: b 4 0 4 1,1,2,2 +25462: f 20 2 8 0,2 +% SZS status Timeout for LAT076-1.p +NO CLASH, using fixed ground order +25483: Facts: +25483: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +25483: Goal: +25483: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +25483: Order: +25483: nrkbo +25483: Leaf order: +25483: b 3 0 3 1,2,2 +25483: c 3 0 3 1,2,2,2,2 +25483: a 4 0 4 1,2 +25483: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25484: Facts: +25484: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +25484: Goal: +25484: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +25484: Order: +25484: kbo +25484: Leaf order: +25484: b 3 0 3 1,2,2 +25484: c 3 0 3 1,2,2,2,2 +25484: a 4 0 4 1,2 +25484: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25485: Facts: +25485: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?4 ?3)) ?5) + (f ?3 (f (f (f (f (f (f ?2 ?2) ?3) ?4) ?4) ?3) ?2)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B1 ?2 ?3 ?4 ?5 +25485: Goal: +25485: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +25485: Order: +25485: lpo +25485: Leaf order: +25485: b 3 0 3 1,2,2 +25485: c 3 0 3 1,2,2,2,2 +25485: a 4 0 4 1,2 +25485: f 20 2 8 0,2 +% SZS status Timeout for LAT077-1.p +NO CLASH, using fixed ground order +25507: Facts: +25507: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +25507: Goal: +25507: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25507: Order: +25507: nrkbo +25507: Leaf order: +25507: a 3 0 3 1,2 +25507: c 3 0 3 2,1,2,2 +25507: b 4 0 4 1,1,2,2 +25507: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25508: Facts: +25508: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +25508: Goal: +25508: Id : 1, {_}: + f a (f (f b c) (f b c)) =<= f c (f (f b a) (f b a)) + [] by associativity +25508: Order: +25508: kbo +25508: Leaf order: +25508: a 3 0 3 1,2 +25508: c 3 0 3 2,1,2,2 +25508: b 4 0 4 1,1,2,2 +25508: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25509: Facts: +25509: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +25509: Goal: +25509: Id : 1, {_}: + f a (f (f b c) (f b c)) =>= f c (f (f b a) (f b a)) + [] by associativity +25509: Order: +25509: lpo +25509: Leaf order: +25509: a 3 0 3 1,2 +25509: c 3 0 3 2,1,2,2 +25509: b 4 0 4 1,1,2,2 +25509: f 20 2 8 0,2 +% SZS status Timeout for LAT078-1.p +NO CLASH, using fixed ground order +25531: Facts: +25531: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +25531: Goal: +25531: Id : 1, {_}: + f a (f b (f a (f c c))) =<= f a (f c (f a (f b b))) + [] by modularity +25531: Order: +25531: nrkbo +25531: Leaf order: +25531: b 3 0 3 1,2,2 +25531: c 3 0 3 1,2,2,2,2 +25531: a 4 0 4 1,2 +25531: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25532: Facts: +25532: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +25532: Goal: +25532: Id : 1, {_}: + f a (f b (f a (f c c))) =?= f a (f c (f a (f b b))) + [] by modularity +25532: Order: +25532: kbo +25532: Leaf order: +25532: b 3 0 3 1,2,2 +25532: c 3 0 3 1,2,2,2,2 +25532: a 4 0 4 1,2 +25532: f 20 2 8 0,2 +NO CLASH, using fixed ground order +25533: Facts: +25533: Id : 2, {_}: + f (f (f (f ?2 ?3) (f ?3 ?4)) ?5) + (f ?3 (f (f (f ?2 (f ?2 (f (f ?4 ?4) ?3))) ?3) ?4)) + =>= + ?3 + [5, 4, 3, 2] by mol_27B2 ?2 ?3 ?4 ?5 +25533: Goal: +25533: Id : 1, {_}: + f a (f b (f a (f c c))) =>= f a (f c (f a (f b b))) + [] by modularity +25533: Order: +25533: lpo +25533: Leaf order: +25533: b 3 0 3 1,2,2 +25533: c 3 0 3 1,2,2,2,2 +25533: a 4 0 4 1,2 +25533: f 20 2 8 0,2 +% SZS status Timeout for LAT079-1.p +NO CLASH, using fixed ground order +25631: Facts: +25631: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25631: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25631: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25631: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25631: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25631: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25631: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25631: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25631: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H11 ?26 ?27 ?28 +25631: Goal: +25631: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +25631: Order: +25631: nrkbo +25631: Leaf order: +25631: b 3 0 3 1,2,2 +25631: c 3 0 3 2,2,2,2 +25631: a 4 0 4 1,2 +25631: join 16 2 3 0,2,2 +25631: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +25633: Facts: +25633: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25633: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25633: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25633: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25633: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25633: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25633: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25633: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25633: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =?= + meet ?26 + (join ?27 + (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H11 ?26 ?27 ?28 +25633: Goal: +25633: Id : 1, {_}: + meet a (join b (meet a c)) + =>= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +25633: Order: +25633: lpo +25633: Leaf order: +25633: b 3 0 3 1,2,2 +25633: c 3 0 3 2,2,2,2 +25633: a 4 0 4 1,2 +25633: join 16 2 3 0,2,2 +25633: meet 20 2 5 0,2 +NO CLASH, using fixed ground order +25632: Facts: +25632: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25632: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25632: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25632: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25632: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25632: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25632: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25632: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25632: Id : 10, {_}: + meet ?26 (join ?27 (meet ?26 ?28)) + =<= + meet ?26 + (join ?27 + (meet ?28 (join ?26 (meet ?27 (join ?28 (meet ?26 ?27)))))) + [28, 27, 26] by equation_H11 ?26 ?27 ?28 +25632: Goal: +25632: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join b (meet c (join a (meet b c)))) + [] by prove_H10 +25632: Order: +25632: kbo +25632: Leaf order: +25632: b 3 0 3 1,2,2 +25632: c 3 0 3 2,2,2,2 +25632: a 4 0 4 1,2 +25632: join 16 2 3 0,2,2 +25632: meet 20 2 5 0,2 +% SZS status Timeout for LAT139-1.p +NO CLASH, using fixed ground order +25659: Facts: +25659: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25659: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25659: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25659: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25659: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25659: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25659: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25659: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25659: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +25659: Goal: +25659: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25659: Order: +25659: nrkbo +25659: Leaf order: +25659: b 3 0 3 1,2,2 +25659: c 3 0 3 2,2,2,2 +25659: a 6 0 6 1,2 +25659: join 17 2 4 0,2,2 +25659: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +25660: Facts: +25660: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25660: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25660: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25660: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25660: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25660: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25660: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25660: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25660: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +25660: Goal: +25660: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25660: Order: +25660: kbo +25660: Leaf order: +25660: b 3 0 3 1,2,2 +25660: c 3 0 3 2,2,2,2 +25660: a 6 0 6 1,2 +25660: join 17 2 4 0,2,2 +25660: meet 21 2 6 0,2 +NO CLASH, using fixed ground order +25661: Facts: +25661: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25661: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25661: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25661: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25661: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25661: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25661: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25661: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25661: Id : 10, {_}: + join (meet ?26 ?27) (meet ?26 ?28) + =<= + meet ?26 + (join (meet ?27 (join ?26 (meet ?27 ?28))) + (meet ?28 (join ?26 ?27))) + [28, 27, 26] by equation_H21 ?26 ?27 ?28 +25661: Goal: +25661: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25661: Order: +25661: lpo +25661: Leaf order: +25661: b 3 0 3 1,2,2 +25661: c 3 0 3 2,2,2,2 +25661: a 6 0 6 1,2 +25661: join 17 2 4 0,2,2 +25661: meet 21 2 6 0,2 +% SZS status Timeout for LAT141-1.p +NO CLASH, using fixed ground order +25683: Facts: +25683: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25683: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25683: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25683: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25683: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25683: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25683: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25683: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25683: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H58 ?26 ?27 ?28 +25683: Goal: +25683: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +25683: Order: +25683: nrkbo +25683: Leaf order: +25683: c 2 0 2 2,1,2,2 +25683: d 2 0 2 2,2,2,2 +25683: a 3 0 3 1,2 +25683: b 5 0 5 1,1,2,2 +25683: join 18 2 5 0,1,2,2 +25683: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +25684: Facts: +25684: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25684: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25684: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25684: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25684: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25684: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25684: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25684: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25684: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H58 ?26 ?27 ?28 +25684: Goal: +25684: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +25684: Order: +25684: kbo +25684: Leaf order: +25684: c 2 0 2 2,1,2,2 +25684: d 2 0 2 2,2,2,2 +25684: a 3 0 3 1,2 +25684: b 5 0 5 1,1,2,2 +25684: join 18 2 5 0,1,2,2 +25684: meet 18 2 5 0,2 +NO CLASH, using fixed ground order +25685: Facts: +25685: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25685: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25685: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25685: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25685: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25685: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25685: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25685: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25685: Id : 10, {_}: + meet ?26 (join ?27 ?28) + =<= + meet ?26 (join ?27 (meet (join ?26 ?27) (join ?28 (meet ?26 ?27)))) + [28, 27, 26] by equation_H58 ?26 ?27 ?28 +25685: Goal: +25685: Id : 1, {_}: + meet a (meet (join b c) (join b d)) + =<= + meet a (join b (meet (join b d) (join c (meet a b)))) + [] by prove_H59 +25685: Order: +25685: lpo +25685: Leaf order: +25685: c 2 0 2 2,1,2,2 +25685: d 2 0 2 2,2,2,2 +25685: a 3 0 3 1,2 +25685: b 5 0 5 1,1,2,2 +25685: join 18 2 5 0,1,2,2 +25685: meet 18 2 5 0,2 +% SZS status Timeout for LAT161-1.p +NO CLASH, using fixed ground order +25706: Facts: +25706: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25706: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25706: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25706: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25706: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25706: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25706: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =?= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25706: Id : 9, {_}: + join (join ?22 ?23) ?24 =?= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +NO CLASH, using fixed ground order +25707: Facts: +25707: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25707: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25707: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25707: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25707: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25707: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25707: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25707: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25707: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +25707: Goal: +25707: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25707: Order: +25707: kbo +25707: Leaf order: +25707: b 3 0 3 1,2,2 +25707: c 3 0 3 2,2,2,2 +25707: a 6 0 6 1,2 +25707: join 19 2 4 0,2,2 +25707: meet 19 2 6 0,2 +NO CLASH, using fixed ground order +25708: Facts: +25708: Id : 2, {_}: meet ?2 ?2 =>= ?2 [2] by idempotence_of_meet ?2 +25708: Id : 3, {_}: join ?4 ?4 =>= ?4 [4] by idempotence_of_join ?4 +25708: Id : 4, {_}: meet ?6 (join ?6 ?7) =>= ?6 [7, 6] by absorption1 ?6 ?7 +25708: Id : 5, {_}: join ?9 (meet ?9 ?10) =>= ?9 [10, 9] by absorption2 ?9 ?10 +25708: Id : 6, {_}: + meet ?12 ?13 =?= meet ?13 ?12 + [13, 12] by commutativity_of_meet ?12 ?13 +25708: Id : 7, {_}: + join ?15 ?16 =?= join ?16 ?15 + [16, 15] by commutativity_of_join ?15 ?16 +25708: Id : 8, {_}: + meet (meet ?18 ?19) ?20 =>= meet ?18 (meet ?19 ?20) + [20, 19, 18] by associativity_of_meet ?18 ?19 ?20 +25708: Id : 9, {_}: + join (join ?22 ?23) ?24 =>= join ?22 (join ?23 ?24) + [24, 23, 22] by associativity_of_join ?22 ?23 ?24 +25708: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +25708: Goal: +25708: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25708: Order: +25708: lpo +25708: Leaf order: +25708: b 3 0 3 1,2,2 +25708: c 3 0 3 2,2,2,2 +25708: a 6 0 6 1,2 +25708: join 19 2 4 0,2,2 +25708: meet 19 2 6 0,2 +25706: Id : 10, {_}: + join ?26 (meet ?27 (join ?28 (meet ?26 ?29))) + =<= + join ?26 (meet (join ?26 (meet ?27 (join ?26 ?28))) (join ?28 ?29)) + [29, 28, 27, 26] by equation_H79_dual ?26 ?27 ?28 ?29 +25706: Goal: +25706: Id : 1, {_}: + meet a (join b (meet a c)) + =<= + meet a (join (meet a (join b (meet a c))) (meet c (join a b))) + [] by prove_H6 +25706: Order: +25706: nrkbo +25706: Leaf order: +25706: b 3 0 3 1,2,2 +25706: c 3 0 3 2,2,2,2 +25706: a 6 0 6 1,2 +25706: join 19 2 4 0,2,2 +25706: meet 19 2 6 0,2 +% SZS status Timeout for LAT177-1.p +NO CLASH, using fixed ground order +25759: Facts: +25759: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3 +25759: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associative_addition ?5 ?6 ?7 +25759: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9 +25759: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11 +25759: Id : 6, {_}: + add ?13 (additive_inverse ?13) =>= additive_identity + [13] by right_additive_inverse ?13 +25759: Id : 7, {_}: + add (additive_inverse ?15) ?15 =>= additive_identity + [15] by left_additive_inverse ?15 +25759: Id : 8, {_}: + additive_inverse additive_identity =>= additive_identity + [] by additive_inverse_identity +25759: Id : 9, {_}: + add ?18 (add (additive_inverse ?18) ?19) =>= ?19 + [19, 18] by property_of_inverse_and_add ?18 ?19 +25759: Id : 10, {_}: + additive_inverse (add ?21 ?22) + =<= + add (additive_inverse ?21) (additive_inverse ?22) + [22, 21] by distribute_additive_inverse ?21 ?22 +25759: Id : 11, {_}: + additive_inverse (additive_inverse ?24) =>= ?24 + [24] by additive_inverse_additive_inverse ?24 +25759: Id : 12, {_}: + multiply ?26 additive_identity =>= additive_identity + [26] by multiply_additive_id1 ?26 +25759: Id : 13, {_}: + multiply additive_identity ?28 =>= additive_identity + [28] by multiply_additive_id2 ?28 +25759: Id : 14, {_}: + multiply (additive_inverse ?30) (additive_inverse ?31) + =>= + multiply ?30 ?31 + [31, 30] by product_of_inverse ?30 ?31 +25759: Id : 15, {_}: + multiply ?33 (additive_inverse ?34) + =>= + additive_inverse (multiply ?33 ?34) + [34, 33] by multiply_additive_inverse1 ?33 ?34 +25759: Id : 16, {_}: + multiply (additive_inverse ?36) ?37 + =>= + additive_inverse (multiply ?36 ?37) + [37, 36] by multiply_additive_inverse2 ?36 ?37 +25759: Id : 17, {_}: + multiply ?39 (add ?40 ?41) + =<= + add (multiply ?39 ?40) (multiply ?39 ?41) + [41, 40, 39] by distribute1 ?39 ?40 ?41 +25759: Id : 18, {_}: + multiply (add ?43 ?44) ?45 + =<= + add (multiply ?43 ?45) (multiply ?44 ?45) + [45, 44, 43] by distribute2 ?43 ?44 ?45 +25759: Id : 19, {_}: + multiply (multiply ?47 ?48) ?48 =?= multiply ?47 (multiply ?48 ?48) + [48, 47] by right_alternative ?47 ?48 +25759: Id : 20, {_}: + associator ?50 ?51 ?52 + =<= + add (multiply (multiply ?50 ?51) ?52) + (additive_inverse (multiply ?50 (multiply ?51 ?52))) + [52, 51, 50] by associator ?50 ?51 ?52 +25759: Id : 21, {_}: + commutator ?54 ?55 + =<= + add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55)) + [55, 54] by commutator ?54 ?55 +25759: Id : 22, {_}: + multiply (multiply (associator ?57 ?57 ?58) ?57) + (associator ?57 ?57 ?58) + =>= + additive_identity + [58, 57] by middle_associator ?57 ?58 +25759: Id : 23, {_}: + multiply (multiply ?60 ?60) ?61 =?= multiply ?60 (multiply ?60 ?61) + [61, 60] by left_alternative ?60 ?61 +25759: Id : 24, {_}: + s ?63 ?64 ?65 ?66 + =<= + add + (add (associator (multiply ?63 ?64) ?65 ?66) + (additive_inverse (multiply ?64 (associator ?63 ?65 ?66)))) + (additive_inverse (multiply (associator ?64 ?65 ?66) ?63)) + [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66 +25759: Id : 25, {_}: + multiply ?68 (multiply ?69 (multiply ?70 ?69)) + =?= + multiply (multiply (multiply ?68 ?69) ?70) ?69 + [70, 69, 68] by right_moufang ?68 ?69 ?70 +25759: Id : 26, {_}: + multiply (multiply ?72 (multiply ?73 ?72)) ?74 + =?= + multiply ?72 (multiply ?73 (multiply ?72 ?74)) + [74, 73, 72] by left_moufang ?72 ?73 ?74 +25759: Id : 27, {_}: + multiply (multiply ?76 ?77) (multiply ?78 ?76) + =?= + multiply (multiply ?76 (multiply ?77 ?78)) ?76 + [78, 77, 76] by middle_moufang ?76 ?77 ?78 +25759: Goal: +25759: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25759: Order: +25759: nrkbo +25759: Leaf order: +25759: a 2 0 2 1,2 +25759: b 2 0 2 2,2 +25759: c 2 0 2 3,2 +25759: d 2 0 2 4,2 +25759: additive_identity 11 0 0 +25759: additive_inverse 20 1 1 0,3 +25759: commutator 1 2 0 +25759: add 22 2 0 +25759: multiply 51 2 0 +25759: associator 6 3 0 +25759: s 3 4 2 0,2 +NO CLASH, using fixed ground order +25760: Facts: +25760: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3 +25760: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associative_addition ?5 ?6 ?7 +25760: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9 +25760: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11 +25760: Id : 6, {_}: + add ?13 (additive_inverse ?13) =>= additive_identity + [13] by right_additive_inverse ?13 +25760: Id : 7, {_}: + add (additive_inverse ?15) ?15 =>= additive_identity + [15] by left_additive_inverse ?15 +25760: Id : 8, {_}: + additive_inverse additive_identity =>= additive_identity + [] by additive_inverse_identity +25760: Id : 9, {_}: + add ?18 (add (additive_inverse ?18) ?19) =>= ?19 + [19, 18] by property_of_inverse_and_add ?18 ?19 +25760: Id : 10, {_}: + additive_inverse (add ?21 ?22) + =<= + add (additive_inverse ?21) (additive_inverse ?22) + [22, 21] by distribute_additive_inverse ?21 ?22 +25760: Id : 11, {_}: + additive_inverse (additive_inverse ?24) =>= ?24 + [24] by additive_inverse_additive_inverse ?24 +25760: Id : 12, {_}: + multiply ?26 additive_identity =>= additive_identity + [26] by multiply_additive_id1 ?26 +25760: Id : 13, {_}: + multiply additive_identity ?28 =>= additive_identity + [28] by multiply_additive_id2 ?28 +25760: Id : 14, {_}: + multiply (additive_inverse ?30) (additive_inverse ?31) + =>= + multiply ?30 ?31 + [31, 30] by product_of_inverse ?30 ?31 +25760: Id : 15, {_}: + multiply ?33 (additive_inverse ?34) + =>= + additive_inverse (multiply ?33 ?34) + [34, 33] by multiply_additive_inverse1 ?33 ?34 +25760: Id : 16, {_}: + multiply (additive_inverse ?36) ?37 + =>= + additive_inverse (multiply ?36 ?37) + [37, 36] by multiply_additive_inverse2 ?36 ?37 +25760: Id : 17, {_}: + multiply ?39 (add ?40 ?41) + =<= + add (multiply ?39 ?40) (multiply ?39 ?41) + [41, 40, 39] by distribute1 ?39 ?40 ?41 +25760: Id : 18, {_}: + multiply (add ?43 ?44) ?45 + =<= + add (multiply ?43 ?45) (multiply ?44 ?45) + [45, 44, 43] by distribute2 ?43 ?44 ?45 +25760: Id : 19, {_}: + multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48) + [48, 47] by right_alternative ?47 ?48 +25760: Id : 20, {_}: + associator ?50 ?51 ?52 + =<= + add (multiply (multiply ?50 ?51) ?52) + (additive_inverse (multiply ?50 (multiply ?51 ?52))) + [52, 51, 50] by associator ?50 ?51 ?52 +25760: Id : 21, {_}: + commutator ?54 ?55 + =<= + add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55)) + [55, 54] by commutator ?54 ?55 +25760: Id : 22, {_}: + multiply (multiply (associator ?57 ?57 ?58) ?57) + (associator ?57 ?57 ?58) + =>= + additive_identity + [58, 57] by middle_associator ?57 ?58 +25760: Id : 23, {_}: + multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61) + [61, 60] by left_alternative ?60 ?61 +25760: Id : 24, {_}: + s ?63 ?64 ?65 ?66 + =<= + add + (add (associator (multiply ?63 ?64) ?65 ?66) + (additive_inverse (multiply ?64 (associator ?63 ?65 ?66)))) + (additive_inverse (multiply (associator ?64 ?65 ?66) ?63)) + [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66 +25760: Id : 25, {_}: + multiply ?68 (multiply ?69 (multiply ?70 ?69)) + =<= + multiply (multiply (multiply ?68 ?69) ?70) ?69 + [70, 69, 68] by right_moufang ?68 ?69 ?70 +25760: Id : 26, {_}: + multiply (multiply ?72 (multiply ?73 ?72)) ?74 + =>= + multiply ?72 (multiply ?73 (multiply ?72 ?74)) + [74, 73, 72] by left_moufang ?72 ?73 ?74 +25760: Id : 27, {_}: + multiply (multiply ?76 ?77) (multiply ?78 ?76) + =<= + multiply (multiply ?76 (multiply ?77 ?78)) ?76 + [78, 77, 76] by middle_moufang ?76 ?77 ?78 +25760: Goal: +25760: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25760: Order: +25760: kbo +25760: Leaf order: +25760: a 2 0 2 1,2 +25760: b 2 0 2 2,2 +25760: c 2 0 2 3,2 +25760: d 2 0 2 4,2 +25760: additive_identity 11 0 0 +25760: additive_inverse 20 1 1 0,3 +25760: commutator 1 2 0 +25760: add 22 2 0 +25760: multiply 51 2 0 +25760: associator 6 3 0 +25760: s 3 4 2 0,2 +NO CLASH, using fixed ground order +25761: Facts: +25761: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutative_addition ?2 ?3 +25761: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associative_addition ?5 ?6 ?7 +25761: Id : 4, {_}: add ?9 additive_identity =>= ?9 [9] by right_identity ?9 +25761: Id : 5, {_}: add additive_identity ?11 =>= ?11 [11] by left_identity ?11 +25761: Id : 6, {_}: + add ?13 (additive_inverse ?13) =>= additive_identity + [13] by right_additive_inverse ?13 +25761: Id : 7, {_}: + add (additive_inverse ?15) ?15 =>= additive_identity + [15] by left_additive_inverse ?15 +25761: Id : 8, {_}: + additive_inverse additive_identity =>= additive_identity + [] by additive_inverse_identity +25761: Id : 9, {_}: + add ?18 (add (additive_inverse ?18) ?19) =>= ?19 + [19, 18] by property_of_inverse_and_add ?18 ?19 +25761: Id : 10, {_}: + additive_inverse (add ?21 ?22) + =<= + add (additive_inverse ?21) (additive_inverse ?22) + [22, 21] by distribute_additive_inverse ?21 ?22 +25761: Id : 11, {_}: + additive_inverse (additive_inverse ?24) =>= ?24 + [24] by additive_inverse_additive_inverse ?24 +25761: Id : 12, {_}: + multiply ?26 additive_identity =>= additive_identity + [26] by multiply_additive_id1 ?26 +25761: Id : 13, {_}: + multiply additive_identity ?28 =>= additive_identity + [28] by multiply_additive_id2 ?28 +25761: Id : 14, {_}: + multiply (additive_inverse ?30) (additive_inverse ?31) + =>= + multiply ?30 ?31 + [31, 30] by product_of_inverse ?30 ?31 +25761: Id : 15, {_}: + multiply ?33 (additive_inverse ?34) + =>= + additive_inverse (multiply ?33 ?34) + [34, 33] by multiply_additive_inverse1 ?33 ?34 +25761: Id : 16, {_}: + multiply (additive_inverse ?36) ?37 + =>= + additive_inverse (multiply ?36 ?37) + [37, 36] by multiply_additive_inverse2 ?36 ?37 +25761: Id : 17, {_}: + multiply ?39 (add ?40 ?41) + =>= + add (multiply ?39 ?40) (multiply ?39 ?41) + [41, 40, 39] by distribute1 ?39 ?40 ?41 +25761: Id : 18, {_}: + multiply (add ?43 ?44) ?45 + =>= + add (multiply ?43 ?45) (multiply ?44 ?45) + [45, 44, 43] by distribute2 ?43 ?44 ?45 +25761: Id : 19, {_}: + multiply (multiply ?47 ?48) ?48 =>= multiply ?47 (multiply ?48 ?48) + [48, 47] by right_alternative ?47 ?48 +25761: Id : 20, {_}: + associator ?50 ?51 ?52 + =>= + add (multiply (multiply ?50 ?51) ?52) + (additive_inverse (multiply ?50 (multiply ?51 ?52))) + [52, 51, 50] by associator ?50 ?51 ?52 +25761: Id : 21, {_}: + commutator ?54 ?55 + =<= + add (multiply ?55 ?54) (additive_inverse (multiply ?54 ?55)) + [55, 54] by commutator ?54 ?55 +25761: Id : 22, {_}: + multiply (multiply (associator ?57 ?57 ?58) ?57) + (associator ?57 ?57 ?58) + =>= + additive_identity + [58, 57] by middle_associator ?57 ?58 +25761: Id : 23, {_}: + multiply (multiply ?60 ?60) ?61 =>= multiply ?60 (multiply ?60 ?61) + [61, 60] by left_alternative ?60 ?61 +25761: Id : 24, {_}: + s ?63 ?64 ?65 ?66 + =>= + add + (add (associator (multiply ?63 ?64) ?65 ?66) + (additive_inverse (multiply ?64 (associator ?63 ?65 ?66)))) + (additive_inverse (multiply (associator ?64 ?65 ?66) ?63)) + [66, 65, 64, 63] by defines_s ?63 ?64 ?65 ?66 +25761: Id : 25, {_}: + multiply ?68 (multiply ?69 (multiply ?70 ?69)) + =<= + multiply (multiply (multiply ?68 ?69) ?70) ?69 + [70, 69, 68] by right_moufang ?68 ?69 ?70 +25761: Id : 26, {_}: + multiply (multiply ?72 (multiply ?73 ?72)) ?74 + =>= + multiply ?72 (multiply ?73 (multiply ?72 ?74)) + [74, 73, 72] by left_moufang ?72 ?73 ?74 +25761: Id : 27, {_}: + multiply (multiply ?76 ?77) (multiply ?78 ?76) + =<= + multiply (multiply ?76 (multiply ?77 ?78)) ?76 + [78, 77, 76] by middle_moufang ?76 ?77 ?78 +25761: Goal: +25761: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25761: Order: +25761: lpo +25761: Leaf order: +25761: a 2 0 2 1,2 +25761: b 2 0 2 2,2 +25761: c 2 0 2 3,2 +25761: d 2 0 2 4,2 +25761: additive_identity 11 0 0 +25761: additive_inverse 20 1 1 0,3 +25761: commutator 1 2 0 +25761: add 22 2 0 +25761: multiply 51 2 0 +25761: associator 6 3 0 +25761: s 3 4 2 0,2 +% SZS status Timeout for RNG010-5.p +NO CLASH, using fixed ground order +25787: Facts: +25787: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25787: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25787: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25787: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25787: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25787: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25787: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25787: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25787: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25787: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25787: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25787: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25787: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25787: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25787: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25787: Id : 17, {_}: + s ?44 ?45 ?46 ?47 + =<= + add + (add (associator (multiply ?44 ?45) ?46 ?47) + (additive_inverse (multiply ?45 (associator ?44 ?46 ?47)))) + (additive_inverse (multiply (associator ?45 ?46 ?47) ?44)) + [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47 +25787: Id : 18, {_}: + multiply ?49 (multiply ?50 (multiply ?51 ?50)) + =?= + multiply (multiply (multiply ?49 ?50) ?51) ?50 + [51, 50, 49] by right_moufang ?49 ?50 ?51 +25787: Id : 19, {_}: + multiply (multiply ?53 (multiply ?54 ?53)) ?55 + =?= + multiply ?53 (multiply ?54 (multiply ?53 ?55)) + [55, 54, 53] by left_moufang ?53 ?54 ?55 +25787: Id : 20, {_}: + multiply (multiply ?57 ?58) (multiply ?59 ?57) + =?= + multiply (multiply ?57 (multiply ?58 ?59)) ?57 + [59, 58, 57] by middle_moufang ?57 ?58 ?59 +25787: Goal: +25787: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25787: Order: +25787: nrkbo +25787: Leaf order: +25787: a 2 0 2 1,2 +25787: b 2 0 2 2,2 +25787: c 2 0 2 3,2 +25787: d 2 0 2 4,2 +25787: additive_identity 8 0 0 +25787: additive_inverse 9 1 1 0,3 +25787: commutator 1 2 0 +25787: add 18 2 0 +25787: multiply 43 2 0 +25787: associator 4 3 0 +25787: s 3 4 2 0,2 +NO CLASH, using fixed ground order +25788: Facts: +25788: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25788: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25788: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25788: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25788: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25788: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25788: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25788: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25788: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25788: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25788: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25788: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25788: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25788: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25788: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25788: Id : 17, {_}: + s ?44 ?45 ?46 ?47 + =<= + add + (add (associator (multiply ?44 ?45) ?46 ?47) + (additive_inverse (multiply ?45 (associator ?44 ?46 ?47)))) + (additive_inverse (multiply (associator ?45 ?46 ?47) ?44)) + [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47 +25788: Id : 18, {_}: + multiply ?49 (multiply ?50 (multiply ?51 ?50)) + =<= + multiply (multiply (multiply ?49 ?50) ?51) ?50 + [51, 50, 49] by right_moufang ?49 ?50 ?51 +25788: Id : 19, {_}: + multiply (multiply ?53 (multiply ?54 ?53)) ?55 + =>= + multiply ?53 (multiply ?54 (multiply ?53 ?55)) + [55, 54, 53] by left_moufang ?53 ?54 ?55 +25788: Id : 20, {_}: + multiply (multiply ?57 ?58) (multiply ?59 ?57) + =<= + multiply (multiply ?57 (multiply ?58 ?59)) ?57 + [59, 58, 57] by middle_moufang ?57 ?58 ?59 +25788: Goal: +25788: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25788: Order: +25788: kbo +25788: Leaf order: +25788: a 2 0 2 1,2 +25788: b 2 0 2 2,2 +25788: c 2 0 2 3,2 +25788: d 2 0 2 4,2 +25788: additive_identity 8 0 0 +25788: additive_inverse 9 1 1 0,3 +25788: commutator 1 2 0 +25788: add 18 2 0 +25788: multiply 43 2 0 +25788: associator 4 3 0 +25788: s 3 4 2 0,2 +NO CLASH, using fixed ground order +25789: Facts: +25789: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25789: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25789: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25789: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25789: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25789: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25789: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25789: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25789: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25789: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25789: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25789: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25789: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25789: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25789: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25789: Id : 17, {_}: + s ?44 ?45 ?46 ?47 + =>= + add + (add (associator (multiply ?44 ?45) ?46 ?47) + (additive_inverse (multiply ?45 (associator ?44 ?46 ?47)))) + (additive_inverse (multiply (associator ?45 ?46 ?47) ?44)) + [47, 46, 45, 44] by defines_s ?44 ?45 ?46 ?47 +25789: Id : 18, {_}: + multiply ?49 (multiply ?50 (multiply ?51 ?50)) + =<= + multiply (multiply (multiply ?49 ?50) ?51) ?50 + [51, 50, 49] by right_moufang ?49 ?50 ?51 +25789: Id : 19, {_}: + multiply (multiply ?53 (multiply ?54 ?53)) ?55 + =>= + multiply ?53 (multiply ?54 (multiply ?53 ?55)) + [55, 54, 53] by left_moufang ?53 ?54 ?55 +25789: Id : 20, {_}: + multiply (multiply ?57 ?58) (multiply ?59 ?57) + =<= + multiply (multiply ?57 (multiply ?58 ?59)) ?57 + [59, 58, 57] by middle_moufang ?57 ?58 ?59 +25789: Goal: +25789: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25789: Order: +25789: lpo +25789: Leaf order: +25789: a 2 0 2 1,2 +25789: b 2 0 2 2,2 +25789: c 2 0 2 3,2 +25789: d 2 0 2 4,2 +25789: additive_identity 8 0 0 +25789: additive_inverse 9 1 1 0,3 +25789: commutator 1 2 0 +25789: add 18 2 0 +25789: multiply 43 2 0 +25789: associator 4 3 0 +25789: s 3 4 2 0,2 +% SZS status Timeout for RNG010-6.p +NO CLASH, using fixed ground order +25814: Facts: +25814: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25814: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25814: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25814: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25814: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25814: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25814: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25814: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25814: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25814: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25814: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25814: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25814: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25814: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25814: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25814: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25814: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25814: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25814: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25814: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25814: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25814: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25814: Id : 24, {_}: + s ?69 ?70 ?71 ?72 + =<= + add + (add (associator (multiply ?69 ?70) ?71 ?72) + (additive_inverse (multiply ?70 (associator ?69 ?71 ?72)))) + (additive_inverse (multiply (associator ?70 ?71 ?72) ?69)) + [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72 +25814: Id : 25, {_}: + multiply ?74 (multiply ?75 (multiply ?76 ?75)) + =?= + multiply (multiply (multiply ?74 ?75) ?76) ?75 + [76, 75, 74] by right_moufang ?74 ?75 ?76 +25814: Id : 26, {_}: + multiply (multiply ?78 (multiply ?79 ?78)) ?80 + =?= + multiply ?78 (multiply ?79 (multiply ?78 ?80)) + [80, 79, 78] by left_moufang ?78 ?79 ?80 +25814: Id : 27, {_}: + multiply (multiply ?82 ?83) (multiply ?84 ?82) + =?= + multiply (multiply ?82 (multiply ?83 ?84)) ?82 + [84, 83, 82] by middle_moufang ?82 ?83 ?84 +25814: Goal: +25814: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25814: Order: +25814: nrkbo +25814: Leaf order: +25814: a 2 0 2 1,2 +25814: b 2 0 2 2,2 +25814: c 2 0 2 3,2 +25814: d 2 0 2 4,2 +25814: additive_identity 8 0 0 +25814: additive_inverse 25 1 1 0,3 +25814: commutator 1 2 0 +25814: add 26 2 0 +25814: multiply 61 2 0 +25814: associator 4 3 0 +25814: s 3 4 2 0,2 +NO CLASH, using fixed ground order +25815: Facts: +NO CLASH, using fixed ground order +25816: Facts: +25816: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25816: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25816: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25816: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25816: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25816: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25816: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25816: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25816: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25816: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25816: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25816: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25816: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25816: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25816: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25816: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25816: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25816: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25816: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25816: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25816: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25816: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25816: Id : 24, {_}: + s ?69 ?70 ?71 ?72 + =>= + add + (add (associator (multiply ?69 ?70) ?71 ?72) + (additive_inverse (multiply ?70 (associator ?69 ?71 ?72)))) + (additive_inverse (multiply (associator ?70 ?71 ?72) ?69)) + [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72 +25816: Id : 25, {_}: + multiply ?74 (multiply ?75 (multiply ?76 ?75)) + =<= + multiply (multiply (multiply ?74 ?75) ?76) ?75 + [76, 75, 74] by right_moufang ?74 ?75 ?76 +25816: Id : 26, {_}: + multiply (multiply ?78 (multiply ?79 ?78)) ?80 + =>= + multiply ?78 (multiply ?79 (multiply ?78 ?80)) + [80, 79, 78] by left_moufang ?78 ?79 ?80 +25816: Id : 27, {_}: + multiply (multiply ?82 ?83) (multiply ?84 ?82) + =<= + multiply (multiply ?82 (multiply ?83 ?84)) ?82 + [84, 83, 82] by middle_moufang ?82 ?83 ?84 +25816: Goal: +25816: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25816: Order: +25816: lpo +25816: Leaf order: +25816: a 2 0 2 1,2 +25816: b 2 0 2 2,2 +25816: c 2 0 2 3,2 +25816: d 2 0 2 4,2 +25816: additive_identity 8 0 0 +25816: additive_inverse 25 1 1 0,3 +25816: commutator 1 2 0 +25816: add 26 2 0 +25816: multiply 61 2 0 +25816: associator 4 3 0 +25816: s 3 4 2 0,2 +25815: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +25815: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +25815: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +25815: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +25815: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +25815: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +25815: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +25815: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +25815: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +25815: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +25815: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +25815: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25815: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +25815: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +25815: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +25815: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +25815: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +25815: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +25815: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +25815: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +25815: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +25815: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +25815: Id : 24, {_}: + s ?69 ?70 ?71 ?72 + =<= + add + (add (associator (multiply ?69 ?70) ?71 ?72) + (additive_inverse (multiply ?70 (associator ?69 ?71 ?72)))) + (additive_inverse (multiply (associator ?70 ?71 ?72) ?69)) + [72, 71, 70, 69] by defines_s ?69 ?70 ?71 ?72 +25815: Id : 25, {_}: + multiply ?74 (multiply ?75 (multiply ?76 ?75)) + =<= + multiply (multiply (multiply ?74 ?75) ?76) ?75 + [76, 75, 74] by right_moufang ?74 ?75 ?76 +25815: Id : 26, {_}: + multiply (multiply ?78 (multiply ?79 ?78)) ?80 + =>= + multiply ?78 (multiply ?79 (multiply ?78 ?80)) + [80, 79, 78] by left_moufang ?78 ?79 ?80 +25815: Id : 27, {_}: + multiply (multiply ?82 ?83) (multiply ?84 ?82) + =<= + multiply (multiply ?82 (multiply ?83 ?84)) ?82 + [84, 83, 82] by middle_moufang ?82 ?83 ?84 +25815: Goal: +25815: Id : 1, {_}: + s a b c d =<= additive_inverse (s b a c d) + [] by prove_skew_symmetry +25815: Order: +25815: kbo +25815: Leaf order: +25815: a 2 0 2 1,2 +25815: b 2 0 2 2,2 +25815: c 2 0 2 3,2 +25815: d 2 0 2 4,2 +25815: additive_identity 8 0 0 +25815: additive_inverse 25 1 1 0,3 +25815: commutator 1 2 0 +25815: add 26 2 0 +25815: multiply 61 2 0 +25815: associator 4 3 0 +25815: s 3 4 2 0,2 +% SZS status Timeout for RNG010-7.p +NO CLASH, using fixed ground order +25837: Facts: +25837: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +25837: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +25837: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +25837: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +25837: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +25837: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +25837: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +25837: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +25837: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +25837: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +25837: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +25837: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25837: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +25837: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +25837: Goal: +25837: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +25837: Order: +25837: nrkbo +25837: Leaf order: +25837: y 6 0 6 3,1,1,2 +25837: additive_identity 9 0 1 3 +25837: x 12 0 12 1,1,1,2 +25837: additive_inverse 6 1 0 +25837: commutator 1 2 0 +25837: add 17 2 1 0,2 +25837: multiply 22 2 4 0,1,2 +25837: associator 7 3 6 0,1,1,2 +NO CLASH, using fixed ground order +25838: Facts: +25838: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +25838: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +25838: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +25838: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +25838: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +25838: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +25838: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +25838: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +25838: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +25838: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +25838: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +25838: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25838: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +25838: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +25838: Goal: +25838: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +25838: Order: +25838: kbo +25838: Leaf order: +25838: y 6 0 6 3,1,1,2 +25838: additive_identity 9 0 1 3 +25838: x 12 0 12 1,1,1,2 +25838: additive_inverse 6 1 0 +25838: commutator 1 2 0 +25838: add 17 2 1 0,2 +25838: multiply 22 2 4 0,1,2 +25838: associator 7 3 6 0,1,1,2 +NO CLASH, using fixed ground order +25839: Facts: +25839: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +25839: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +25839: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +25839: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +25839: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +25839: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +25839: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +25839: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +25839: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +25839: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +25839: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +25839: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25839: Id : 14, {_}: + associator ?34 ?35 ?36 + =>= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +25839: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +25839: Goal: +25839: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +25839: Order: +25839: lpo +25839: Leaf order: +25839: y 6 0 6 3,1,1,2 +25839: additive_identity 9 0 1 3 +25839: x 12 0 12 1,1,1,2 +25839: additive_inverse 6 1 0 +25839: commutator 1 2 0 +25839: add 17 2 1 0,2 +25839: multiply 22 2 4 0,1,2 +25839: associator 7 3 6 0,1,1,2 +% SZS status Timeout for RNG030-6.p +NO CLASH, using fixed ground order +25861: Facts: +25861: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +25861: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +25861: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +25861: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +25861: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +25861: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +25861: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +25861: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +25861: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +25861: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +25861: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +25861: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +25861: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +25861: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +25861: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +25861: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +25861: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +25861: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +25861: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +25861: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +25861: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +25861: Goal: +25861: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +25861: Order: +25861: nrkbo +25861: Leaf order: +25861: y 6 0 6 3,1,1,2 +25861: additive_identity 9 0 1 3 +25861: x 12 0 12 1,1,1,2 +25861: additive_inverse 22 1 0 +25861: commutator 1 2 0 +25861: add 25 2 1 0,2 +25861: multiply 40 2 4 0,1,2add +25861: associator 7 3 6 0,1,1,2 +NO CLASH, using fixed ground order +25862: Facts: +NO CLASH, using fixed ground order +25863: Facts: +25863: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +25863: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +25863: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +25863: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +25863: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +25863: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +25863: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +25863: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +25863: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +25863: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +25863: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +25863: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +25863: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +25863: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +25863: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +25863: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +25863: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +25863: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +25863: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +25863: Id : 21, {_}: + associator ?59 ?60 ?61 + =>= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +25863: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +25863: Goal: +25863: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +25863: Order: +25863: lpo +25863: Leaf order: +25863: y 6 0 6 3,1,1,2 +25863: additive_identity 9 0 1 3 +25863: x 12 0 12 1,1,1,2 +25863: additive_inverse 22 1 0 +25863: commutator 1 2 0 +25863: add 25 2 1 0,2 +25863: multiply 40 2 4 0,1,2add +25863: associator 7 3 6 0,1,1,2 +25862: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +25862: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +25862: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +25862: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +25862: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +25862: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +25862: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +25862: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +25862: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +25862: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +25862: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +25862: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +25862: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +25862: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +25862: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +25862: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +25862: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +25862: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +25862: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +25862: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +25862: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +25862: Goal: +25862: Id : 1, {_}: + add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_1 +25862: Order: +25862: kbo +25862: Leaf order: +25862: y 6 0 6 3,1,1,2 +25862: additive_identity 9 0 1 3 +25862: x 12 0 12 1,1,1,2 +25862: additive_inverse 22 1 0 +25862: commutator 1 2 0 +25862: add 25 2 1 0,2 +25862: multiply 40 2 4 0,1,2add +25862: associator 7 3 6 0,1,1,2 +% SZS status Timeout for RNG030-7.p +NO CLASH, using fixed ground order +25886: Facts: +25886: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +25886: Id : 3, {_}: + add ?5 (add ?6 ?7) =?= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +25886: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +25886: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +25886: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +25886: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +25886: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +25886: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +25886: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +25886: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +25886: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +25886: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25886: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +25886: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +25886: Goal: +25886: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +25886: Order: +25886: nrkbo +25886: Leaf order: +25886: additive_identity 9 0 1 3 +25886: y 18 0 18 3,1,1,1,1,1,1,2 +25886: x 36 0 36 1,1,1,1,1,1,1,2 +25886: additive_inverse 6 1 0 +25886: commutator 1 2 0 +25886: add 21 2 5 0,2 +25886: multiply 30 2 12 0,1,1,1,1,1,2 +25886: associator 19 3 18 0,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +25887: Facts: +25887: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +25887: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +25887: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +25887: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +25887: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +25887: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +25887: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +25887: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +25887: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +25887: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +25887: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +25887: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25887: Id : 14, {_}: + associator ?34 ?35 ?36 + =<= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +25887: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +25887: Goal: +25887: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +25887: Order: +25887: kbo +25887: Leaf order: +25887: additive_identity 9 0 1 3 +25887: y 18 0 18 3,1,1,1,1,1,1,2 +25887: x 36 0 36 1,1,1,1,1,1,1,2 +25887: additive_inverse 6 1 0 +25887: commutator 1 2 0 +25887: add 21 2 5 0,2 +25887: multiply 30 2 12 0,1,1,1,1,1,2 +25887: associator 19 3 18 0,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +25888: Facts: +25888: Id : 2, {_}: + add ?2 ?3 =?= add ?3 ?2 + [3, 2] by commutativity_for_addition ?2 ?3 +25888: Id : 3, {_}: + add ?5 (add ?6 ?7) =<= add (add ?5 ?6) ?7 + [7, 6, 5] by associativity_for_addition ?5 ?6 ?7 +25888: Id : 4, {_}: add additive_identity ?9 =>= ?9 [9] by left_additive_identity ?9 +25888: Id : 5, {_}: + add ?11 additive_identity =>= ?11 + [11] by right_additive_identity ?11 +25888: Id : 6, {_}: + multiply additive_identity ?13 =>= additive_identity + [13] by left_multiplicative_zero ?13 +25888: Id : 7, {_}: + multiply ?15 additive_identity =>= additive_identity + [15] by right_multiplicative_zero ?15 +25888: Id : 8, {_}: + add (additive_inverse ?17) ?17 =>= additive_identity + [17] by left_additive_inverse ?17 +25888: Id : 9, {_}: + add ?19 (additive_inverse ?19) =>= additive_identity + [19] by right_additive_inverse ?19 +25888: Id : 10, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +25888: Id : 11, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +25888: Id : 12, {_}: + additive_inverse (additive_inverse ?29) =>= ?29 + [29] by additive_inverse_additive_inverse ?29 +25888: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +25888: Id : 14, {_}: + associator ?34 ?35 ?36 + =>= + add (multiply (multiply ?34 ?35) ?36) + (additive_inverse (multiply ?34 (multiply ?35 ?36))) + [36, 35, 34] by associator ?34 ?35 ?36 +25888: Id : 15, {_}: + commutator ?38 ?39 + =<= + add (multiply ?39 ?38) (additive_inverse (multiply ?38 ?39)) + [39, 38] by commutator ?38 ?39 +25888: Goal: +25888: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +25888: Order: +25888: lpo +25888: Leaf order: +25888: additive_identity 9 0 1 3 +25888: y 18 0 18 3,1,1,1,1,1,1,2 +25888: x 36 0 36 1,1,1,1,1,1,1,2 +25888: additive_inverse 6 1 0 +25888: commutator 1 2 0 +25888: add 21 2 5 0,2 +25888: multiply 30 2 12 0,1,1,1,1,1,2 +25888: associator 19 3 18 0,1,1,1,1,1,1,2 +% SZS status Timeout for RNG032-6.p +NO CLASH, using fixed ground order +25915: Facts: +25915: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +25915: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +25915: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +25915: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +25915: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +25915: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +25915: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +25915: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +25915: Id : 10, {_}: + add ?30 (add ?31 ?32) =?= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +25915: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +25915: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +25915: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +25915: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +25915: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +25915: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +25915: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +25915: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +25915: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +25915: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =?= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +25915: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +25915: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +25915: Goal: +25915: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +25915: Order: +25915: nrkbo +25915: Leaf order: +25915: additive_identity 9 0 1 3 +25915: y 18 0 18 3,1,1,1,1,1,1,2 +25915: x 36 0 36 1,1,1,1,1,1,1,2 +25915: additive_inverse 22 1 0 +25915: commutator 1 2 0 +25915: add 29 2 5 0,2 +25915: multiply 48 2 12 0,1,1,1,1,1,2add +25915: associator 19 3 18 0,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +25916: Facts: +25916: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +25916: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +25916: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +25916: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =<= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +25916: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =<= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +25916: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =<= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +25916: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =<= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +25916: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +25916: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +25916: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +25916: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +25916: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +25916: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +25916: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +25916: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +25916: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =<= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +25916: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =<= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +25916: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +25916: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +25916: Id : 21, {_}: + associator ?59 ?60 ?61 + =<= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +25916: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +25916: Goal: +25916: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +25916: Order: +25916: kbo +25916: Leaf order: +25916: additive_identity 9 0 1 3 +25916: y 18 0 18 3,1,1,1,1,1,1,2 +25916: x 36 0 36 1,1,1,1,1,1,1,2 +25916: additive_inverse 22 1 0 +25916: commutator 1 2 0 +25916: add 29 2 5 0,2 +25916: multiply 48 2 12 0,1,1,1,1,1,2add +25916: associator 19 3 18 0,1,1,1,1,1,1,2 +NO CLASH, using fixed ground order +25917: Facts: +25917: Id : 2, {_}: + multiply (additive_inverse ?2) (additive_inverse ?3) + =>= + multiply ?2 ?3 + [3, 2] by product_of_inverses ?2 ?3 +25917: Id : 3, {_}: + multiply (additive_inverse ?5) ?6 + =>= + additive_inverse (multiply ?5 ?6) + [6, 5] by inverse_product1 ?5 ?6 +25917: Id : 4, {_}: + multiply ?8 (additive_inverse ?9) + =>= + additive_inverse (multiply ?8 ?9) + [9, 8] by inverse_product2 ?8 ?9 +25917: Id : 5, {_}: + multiply ?11 (add ?12 (additive_inverse ?13)) + =>= + add (multiply ?11 ?12) (additive_inverse (multiply ?11 ?13)) + [13, 12, 11] by distributivity_of_difference1 ?11 ?12 ?13 +25917: Id : 6, {_}: + multiply (add ?15 (additive_inverse ?16)) ?17 + =>= + add (multiply ?15 ?17) (additive_inverse (multiply ?16 ?17)) + [17, 16, 15] by distributivity_of_difference2 ?15 ?16 ?17 +25917: Id : 7, {_}: + multiply (additive_inverse ?19) (add ?20 ?21) + =>= + add (additive_inverse (multiply ?19 ?20)) + (additive_inverse (multiply ?19 ?21)) + [21, 20, 19] by distributivity_of_difference3 ?19 ?20 ?21 +25917: Id : 8, {_}: + multiply (add ?23 ?24) (additive_inverse ?25) + =>= + add (additive_inverse (multiply ?23 ?25)) + (additive_inverse (multiply ?24 ?25)) + [25, 24, 23] by distributivity_of_difference4 ?23 ?24 ?25 +25917: Id : 9, {_}: + add ?27 ?28 =?= add ?28 ?27 + [28, 27] by commutativity_for_addition ?27 ?28 +25917: Id : 10, {_}: + add ?30 (add ?31 ?32) =<= add (add ?30 ?31) ?32 + [32, 31, 30] by associativity_for_addition ?30 ?31 ?32 +25917: Id : 11, {_}: + add additive_identity ?34 =>= ?34 + [34] by left_additive_identity ?34 +25917: Id : 12, {_}: + add ?36 additive_identity =>= ?36 + [36] by right_additive_identity ?36 +25917: Id : 13, {_}: + multiply additive_identity ?38 =>= additive_identity + [38] by left_multiplicative_zero ?38 +25917: Id : 14, {_}: + multiply ?40 additive_identity =>= additive_identity + [40] by right_multiplicative_zero ?40 +25917: Id : 15, {_}: + add (additive_inverse ?42) ?42 =>= additive_identity + [42] by left_additive_inverse ?42 +25917: Id : 16, {_}: + add ?44 (additive_inverse ?44) =>= additive_identity + [44] by right_additive_inverse ?44 +25917: Id : 17, {_}: + multiply ?46 (add ?47 ?48) + =>= + add (multiply ?46 ?47) (multiply ?46 ?48) + [48, 47, 46] by distribute1 ?46 ?47 ?48 +25917: Id : 18, {_}: + multiply (add ?50 ?51) ?52 + =>= + add (multiply ?50 ?52) (multiply ?51 ?52) + [52, 51, 50] by distribute2 ?50 ?51 ?52 +25917: Id : 19, {_}: + additive_inverse (additive_inverse ?54) =>= ?54 + [54] by additive_inverse_additive_inverse ?54 +25917: Id : 20, {_}: + multiply (multiply ?56 ?57) ?57 =>= multiply ?56 (multiply ?57 ?57) + [57, 56] by right_alternative ?56 ?57 +25917: Id : 21, {_}: + associator ?59 ?60 ?61 + =>= + add (multiply (multiply ?59 ?60) ?61) + (additive_inverse (multiply ?59 (multiply ?60 ?61))) + [61, 60, 59] by associator ?59 ?60 ?61 +25917: Id : 22, {_}: + commutator ?63 ?64 + =<= + add (multiply ?64 ?63) (additive_inverse (multiply ?63 ?64)) + [64, 63] by commutator ?63 ?64 +25917: Goal: +25917: Id : 1, {_}: + add + (add + (add + (add + (add + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y)))) + (multiply (associator x x y) + (multiply (associator x x y) (associator x x y))) + =>= + additive_identity + [] by prove_conjecture_3 +25917: Order: +25917: lpo +25917: Leaf order: +25917: additive_identity 9 0 1 3 +25917: y 18 0 18 3,1,1,1,1,1,1,2 +25917: x 36 0 36 1,1,1,1,1,1,1,2 +25917: additive_inverse 22 1 0 +25917: commutator 1 2 0 +25917: add 29 2 5 0,2 +25917: multiply 48 2 12 0,1,1,1,1,1,2add +25917: associator 19 3 18 0,1,1,1,1,1,1,2 +% SZS status Timeout for RNG032-7.p +NO CLASH, using fixed ground order +26009: Facts: +26009: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26009: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26009: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26009: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26009: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26009: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26009: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26009: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26009: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26009: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26009: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +NO CLASH, using fixed ground order +26010: Facts: +26010: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26010: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26010: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26010: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26010: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26010: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26010: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26010: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26010: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26010: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26010: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26010: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26010: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26010: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26010: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26010: Goal: +26010: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26010: Order: +26010: lpo +26010: Leaf order: +26010: x 4 0 4 1,1,1,2 +26010: y 4 0 4 2,1,1,2 +26010: z 4 0 4 2,1,2 +26010: w 4 0 4 3,1,2 +26010: additive_identity 8 0 0 +26010: additive_inverse 6 1 0 +26010: commutator 2 2 1 0,3,2,2 +26010: add 18 2 2 0,2 +26010: multiply 25 2 3 0,1,1,2 +26010: associator 5 3 4 0,1,2 +26009: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26009: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26009: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26009: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26009: Goal: +26009: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26009: Order: +26009: kbo +26009: Leaf order: +26009: x 4 0 4 1,1,1,2 +26009: y 4 0 4 2,1,1,2 +26009: z 4 0 4 2,1,2 +26009: w 4 0 4 3,1,2 +26009: additive_identity 8 0 0 +26009: additive_inverse 6 1 0 +26009: commutator 2 2 1 0,3,2,2 +26009: add 18 2 2 0,2 +26009: multiply 25 2 3 0,1,1,2 +26009: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26008: Facts: +26008: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26008: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26008: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26008: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26008: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26008: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26008: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26008: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26008: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26008: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26008: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26008: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26008: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26008: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26008: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26008: Goal: +26008: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26008: Order: +26008: nrkbo +26008: Leaf order: +26008: x 4 0 4 1,1,1,2 +26008: y 4 0 4 2,1,1,2 +26008: z 4 0 4 2,1,2 +26008: w 4 0 4 3,1,2 +26008: additive_identity 8 0 0 +26008: additive_inverse 6 1 0 +26008: commutator 2 2 1 0,3,2,2 +26008: add 18 2 2 0,2 +26008: multiply 25 2 3 0,1,1,2 +26008: associator 5 3 4 0,1,2 +% SZS status Timeout for RNG033-6.p +NO CLASH, using fixed ground order +26035: Facts: +26035: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26035: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26035: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26035: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26035: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26035: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26035: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26035: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26035: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26035: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26035: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26035: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26035: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26035: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26035: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26035: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26035: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26035: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26035: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26035: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26035: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26035: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26035: Goal: +26035: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26035: Order: +26035: nrkbo +26035: Leaf order: +26035: x 4 0 4 1,1,1,2 +26035: y 4 0 4 2,1,1,2 +26035: z 4 0 4 2,1,2 +26035: w 4 0 4 3,1,2 +26035: additive_identity 8 0 0 +26035: additive_inverse 22 1 0 +26035: commutator 2 2 1 0,3,2,2 +26035: add 26 2 2 0,2 +26035: multiply 43 2 3 0,1,1,2 +26035: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26036: Facts: +26036: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26036: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26036: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26036: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26036: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26036: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26036: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26036: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26036: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26036: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26036: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26036: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26036: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26036: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26036: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26036: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26036: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26036: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26036: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26036: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26036: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26036: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26036: Goal: +26036: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26036: Order: +26036: kbo +26036: Leaf order: +26036: x 4 0 4 1,1,1,2 +26036: y 4 0 4 2,1,1,2 +26036: z 4 0 4 2,1,2 +26036: w 4 0 4 3,1,2 +26036: additive_identity 8 0 0 +26036: additive_inverse 22 1 0 +26036: commutator 2 2 1 0,3,2,2 +26036: add 26 2 2 0,2 +26036: multiply 43 2 3 0,1,1,2 +26036: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26037: Facts: +26037: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26037: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26037: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26037: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26037: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26037: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26037: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26037: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26037: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26037: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26037: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26037: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26037: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26037: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26037: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26037: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26037: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26037: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26037: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26037: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26037: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26037: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26037: Goal: +26037: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26037: Order: +26037: lpo +26037: Leaf order: +26037: x 4 0 4 1,1,1,2 +26037: y 4 0 4 2,1,1,2 +26037: z 4 0 4 2,1,2 +26037: w 4 0 4 3,1,2 +26037: additive_identity 8 0 0 +26037: additive_inverse 22 1 0 +26037: commutator 2 2 1 0,3,2,2 +26037: add 26 2 2 0,2 +26037: multiply 43 2 3 0,1,1,2 +26037: associator 5 3 4 0,1,2 +% SZS status Timeout for RNG033-7.p +NO CLASH, using fixed ground order +26058: Facts: +26058: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26058: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26058: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26058: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26058: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26058: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26058: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26058: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26058: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26058: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26058: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26058: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26058: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26058: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26058: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26058: Id : 17, {_}: + multiply ?44 (multiply ?45 (multiply ?46 ?45)) + =?= + multiply (multiply (multiply ?44 ?45) ?46) ?45 + [46, 45, 44] by right_moufang ?44 ?45 ?46 +26058: Goal: +26058: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26058: Order: +26058: nrkbo +26058: Leaf order: +26058: x 4 0 4 1,1,1,2 +26058: y 4 0 4 2,1,1,2 +26058: z 4 0 4 2,1,2 +26058: w 4 0 4 3,1,2 +26058: additive_identity 8 0 0 +26058: additive_inverse 6 1 0 +26058: commutator 2 2 1 0,3,2,2 +26058: add 18 2 2 0,2 +26058: multiply 31 2 3 0,1,1,2 +26058: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26059: Facts: +26059: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26059: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26059: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26059: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26059: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26059: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26059: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26059: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26059: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26059: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26059: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26059: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26059: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26059: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26059: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26059: Id : 17, {_}: + multiply ?44 (multiply ?45 (multiply ?46 ?45)) + =<= + multiply (multiply (multiply ?44 ?45) ?46) ?45 + [46, 45, 44] by right_moufang ?44 ?45 ?46 +26059: Goal: +26059: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26059: Order: +26059: kbo +26059: Leaf order: +26059: x 4 0 4 1,1,1,2 +26059: y 4 0 4 2,1,1,2 +26059: z 4 0 4 2,1,2 +26059: w 4 0 4 3,1,2 +26059: additive_identity 8 0 0 +26059: additive_inverse 6 1 0 +26059: commutator 2 2 1 0,3,2,2 +26059: add 18 2 2 0,2 +26059: multiply 31 2 3 0,1,1,2 +26059: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26060: Facts: +26060: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26060: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26060: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26060: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26060: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26060: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26060: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26060: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26060: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26060: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26060: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26060: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26060: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26060: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26060: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26060: Id : 17, {_}: + multiply ?44 (multiply ?45 (multiply ?46 ?45)) + =<= + multiply (multiply (multiply ?44 ?45) ?46) ?45 + [46, 45, 44] by right_moufang ?44 ?45 ?46 +26060: Goal: +26060: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26060: Order: +26060: lpo +26060: Leaf order: +26060: x 4 0 4 1,1,1,2 +26060: y 4 0 4 2,1,1,2 +26060: z 4 0 4 2,1,2 +26060: w 4 0 4 3,1,2 +26060: additive_identity 8 0 0 +26060: additive_inverse 6 1 0 +26060: commutator 2 2 1 0,3,2,2 +26060: add 18 2 2 0,2 +26060: multiply 31 2 3 0,1,1,2 +26060: associator 5 3 4 0,1,2 +% SZS status Timeout for RNG033-8.p +NO CLASH, using fixed ground order +26087: Facts: +26087: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26087: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26087: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26087: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26087: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26087: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26087: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26087: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26087: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26087: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26087: Id : 12, {_}: + add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26087: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26087: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26087: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26087: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26087: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26087: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26087: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26087: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26087: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26087: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26087: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26087: Id : 24, {_}: + multiply ?69 (multiply ?70 (multiply ?71 ?70)) + =?= + multiply (multiply (multiply ?69 ?70) ?71) ?70 + [71, 70, 69] by right_moufang ?69 ?70 ?71 +26087: Goal: +26087: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26087: Order: +26087: nrkbo +26087: Leaf order: +26087: x 4 0 4 1,1,1,2 +26087: y 4 0 4 2,1,1,2 +26087: z 4 0 4 2,1,2 +26087: w 4 0 4 3,1,2 +26087: additive_identity 8 0 0 +26087: additive_inverse 22 1 0 +26087: commutator 2 2 1 0,3,2,2 +26087: add 26 2 2 0,2 +26087: multiply 49 2 3 0,1,1,2 +26087: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26089: Facts: +26089: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26089: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26089: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26089: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26089: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26089: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26089: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26089: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =>= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26089: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =>= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26089: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26089: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26089: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26089: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26089: Id : 15, {_}: + associator ?37 ?38 ?39 + =>= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26089: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26089: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26089: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26089: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26089: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =>= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26089: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =>= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26089: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =>= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26089: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =>= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26089: Id : 24, {_}: + multiply ?69 (multiply ?70 (multiply ?71 ?70)) + =<= + multiply (multiply (multiply ?69 ?70) ?71) ?70 + [71, 70, 69] by right_moufang ?69 ?70 ?71 +26089: Goal: +26089: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26089: Order: +26089: lpo +26089: Leaf order: +26089: x 4 0 4 1,1,1,2 +26089: y 4 0 4 2,1,1,2 +26089: z 4 0 4 2,1,2 +26089: w 4 0 4 3,1,2 +26089: additive_identity 8 0 0 +26089: additive_inverse 22 1 0 +26089: commutator 2 2 1 0,3,2,2 +26089: add 26 2 2 0,2 +26089: multiply 49 2 3 0,1,1,2 +26089: associator 5 3 4 0,1,2 +NO CLASH, using fixed ground order +26088: Facts: +26088: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26088: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26088: Id : 4, {_}: + multiply additive_identity ?6 =>= additive_identity + [6] by left_multiplicative_zero ?6 +26088: Id : 5, {_}: + multiply ?8 additive_identity =>= additive_identity + [8] by right_multiplicative_zero ?8 +26088: Id : 6, {_}: + add (additive_inverse ?10) ?10 =>= additive_identity + [10] by left_additive_inverse ?10 +26088: Id : 7, {_}: + add ?12 (additive_inverse ?12) =>= additive_identity + [12] by right_additive_inverse ?12 +26088: Id : 8, {_}: + additive_inverse (additive_inverse ?14) =>= ?14 + [14] by additive_inverse_additive_inverse ?14 +26088: Id : 9, {_}: + multiply ?16 (add ?17 ?18) + =<= + add (multiply ?16 ?17) (multiply ?16 ?18) + [18, 17, 16] by distribute1 ?16 ?17 ?18 +26088: Id : 10, {_}: + multiply (add ?20 ?21) ?22 + =<= + add (multiply ?20 ?22) (multiply ?21 ?22) + [22, 21, 20] by distribute2 ?20 ?21 ?22 +26088: Id : 11, {_}: + add ?24 ?25 =?= add ?25 ?24 + [25, 24] by commutativity_for_addition ?24 ?25 +26088: Id : 12, {_}: + add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 + [29, 28, 27] by associativity_for_addition ?27 ?28 ?29 +26088: Id : 13, {_}: + multiply (multiply ?31 ?32) ?32 =>= multiply ?31 (multiply ?32 ?32) + [32, 31] by right_alternative ?31 ?32 +26088: Id : 14, {_}: + multiply (multiply ?34 ?34) ?35 =>= multiply ?34 (multiply ?34 ?35) + [35, 34] by left_alternative ?34 ?35 +26088: Id : 15, {_}: + associator ?37 ?38 ?39 + =<= + add (multiply (multiply ?37 ?38) ?39) + (additive_inverse (multiply ?37 (multiply ?38 ?39))) + [39, 38, 37] by associator ?37 ?38 ?39 +26088: Id : 16, {_}: + commutator ?41 ?42 + =<= + add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42)) + [42, 41] by commutator ?41 ?42 +26088: Id : 17, {_}: + multiply (additive_inverse ?44) (additive_inverse ?45) + =>= + multiply ?44 ?45 + [45, 44] by product_of_inverses ?44 ?45 +26088: Id : 18, {_}: + multiply (additive_inverse ?47) ?48 + =>= + additive_inverse (multiply ?47 ?48) + [48, 47] by inverse_product1 ?47 ?48 +26088: Id : 19, {_}: + multiply ?50 (additive_inverse ?51) + =>= + additive_inverse (multiply ?50 ?51) + [51, 50] by inverse_product2 ?50 ?51 +26088: Id : 20, {_}: + multiply ?53 (add ?54 (additive_inverse ?55)) + =<= + add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55)) + [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55 +26088: Id : 21, {_}: + multiply (add ?57 (additive_inverse ?58)) ?59 + =<= + add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59)) + [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59 +26088: Id : 22, {_}: + multiply (additive_inverse ?61) (add ?62 ?63) + =<= + add (additive_inverse (multiply ?61 ?62)) + (additive_inverse (multiply ?61 ?63)) + [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63 +26088: Id : 23, {_}: + multiply (add ?65 ?66) (additive_inverse ?67) + =<= + add (additive_inverse (multiply ?65 ?67)) + (additive_inverse (multiply ?66 ?67)) + [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67 +26088: Id : 24, {_}: + multiply ?69 (multiply ?70 (multiply ?71 ?70)) + =<= + multiply (multiply (multiply ?69 ?70) ?71) ?70 + [71, 70, 69] by right_moufang ?69 ?70 ?71 +26088: Goal: +26088: Id : 1, {_}: + add (associator (multiply x y) z w) (associator x y (commutator z w)) + =>= + add (multiply x (associator y z w)) (multiply (associator x z w) y) + [] by prove_challenge +26088: Order: +26088: kbo +26088: Leaf order: +26088: x 4 0 4 1,1,1,2 +26088: y 4 0 4 2,1,1,2 +26088: z 4 0 4 2,1,2 +26088: w 4 0 4 3,1,2 +26088: additive_identity 8 0 0 +26088: additive_inverse 22 1 0 +26088: commutator 2 2 1 0,3,2,2 +26088: add 26 2 2 0,2 +26088: multiply 49 2 3 0,1,1,2 +26088: associator 5 3 4 0,1,2 +% SZS status Timeout for RNG033-9.p +NO CLASH, using fixed ground order +NO CLASH, using fixed ground order +26115: Facts: +26115: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26116: Facts: +26116: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26116: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26116: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +26116: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +26116: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +26116: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +26116: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +26116: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +26115: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26116: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +26115: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +26115: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +26115: Id : 6, {_}: + add ?10 (add ?11 ?12) =?= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +26115: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +26115: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =?= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +26115: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =<= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +26115: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =<= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +26115: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29 + [29] by x_fifthed_is_x ?29 +26115: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +26115: Goal: +NO CLASH, using fixed ground order +26117: Facts: +26117: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2 +26117: Id : 3, {_}: + add ?4 additive_identity =>= ?4 + [4] by right_additive_identity ?4 +26117: Id : 4, {_}: + add (additive_inverse ?6) ?6 =>= additive_identity + [6] by left_additive_inverse ?6 +26117: Id : 5, {_}: + add ?8 (additive_inverse ?8) =>= additive_identity + [8] by right_additive_inverse ?8 +26117: Id : 6, {_}: + add ?10 (add ?11 ?12) =<= add (add ?10 ?11) ?12 + [12, 11, 10] by associativity_for_addition ?10 ?11 ?12 +26117: Id : 7, {_}: + add ?14 ?15 =?= add ?15 ?14 + [15, 14] by commutativity_for_addition ?14 ?15 +26117: Id : 8, {_}: + multiply ?17 (multiply ?18 ?19) =<= multiply (multiply ?17 ?18) ?19 + [19, 18, 17] by associativity_for_multiplication ?17 ?18 ?19 +26117: Id : 9, {_}: + multiply ?21 (add ?22 ?23) + =>= + add (multiply ?21 ?22) (multiply ?21 ?23) + [23, 22, 21] by distribute1 ?21 ?22 ?23 +26117: Id : 10, {_}: + multiply (add ?25 ?26) ?27 + =>= + add (multiply ?25 ?27) (multiply ?26 ?27) + [27, 26, 25] by distribute2 ?25 ?26 ?27 +26117: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29 + [29] by x_fifthed_is_x ?29 +26117: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +26117: Goal: +26117: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +26117: Order: +26117: lpo +26117: Leaf order: +26117: b 2 0 1 1,2 +26117: a 2 0 1 2,2 +26117: c 2 0 1 3 +26117: additive_identity 4 0 0 +26117: additive_inverse 2 1 0 +26117: add 14 2 0 +26117: multiply 16 2 1 0,2 +26116: Id : 11, {_}: + multiply ?29 (multiply ?29 (multiply ?29 (multiply ?29 ?29))) =>= ?29 + [29] by x_fifthed_is_x ?29 +26116: Id : 12, {_}: multiply a b =>= c [] by a_times_b_is_c +26116: Goal: +26116: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +26116: Order: +26116: kbo +26116: Leaf order: +26116: b 2 0 1 1,2 +26116: a 2 0 1 2,2 +26116: c 2 0 1 3 +26116: additive_identity 4 0 0 +26116: additive_inverse 2 1 0 +26116: add 14 2 0 +26116: multiply 16 2 1 0,2 +26115: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity +26115: Order: +26115: nrkbo +26115: Leaf order: +26115: b 2 0 1 1,2 +26115: a 2 0 1 2,2 +26115: c 2 0 1 3 +26115: additive_identity 4 0 0 +26115: additive_inverse 2 1 0 +26115: add 14 2 0 +26115: multiply 16 2 1 0,2 +% SZS status Timeout for RNG036-7.p +NO CLASH, using fixed ground order +26159: Facts: +26159: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26159: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26159: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26159: Goal: +26159: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26159: Order: +26159: nrkbo +26159: Leaf order: +26159: a 2 0 2 1,1,1,2 +26159: b 3 0 3 1,2,1,1,2 +26159: negate 9 1 5 0,1,2 +26159: add 12 2 3 0,2 +NO CLASH, using fixed ground order +26160: Facts: +26160: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26160: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26160: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26160: Goal: +26160: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26160: Order: +26160: kbo +26160: Leaf order: +26160: a 2 0 2 1,1,1,2 +26160: b 3 0 3 1,2,1,1,2 +26160: negate 9 1 5 0,1,2 +26160: add 12 2 3 0,2 +NO CLASH, using fixed ground order +26161: Facts: +26161: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26161: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26161: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26161: Goal: +26161: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26161: Order: +26161: lpo +26161: Leaf order: +26161: a 2 0 2 1,1,1,2 +26161: b 3 0 3 1,2,1,1,2 +26161: negate 9 1 5 0,1,2 +26161: add 12 2 3 0,2 +% SZS status Timeout for ROB001-1.p +NO CLASH, using fixed ground order +26183: Facts: +26183: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26183: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26183: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26183: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +26183: Goal: +26183: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26183: Order: +26183: nrkbo +26183: Leaf order: +26183: a 3 0 2 1,1,1,2 +26183: b 5 0 3 1,2,1,1,2 +26183: negate 11 1 5 0,1,2 +26183: add 13 2 3 0,2 +NO CLASH, using fixed ground order +26184: Facts: +26184: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26184: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26184: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26184: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +26184: Goal: +26184: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26184: Order: +26184: kbo +26184: Leaf order: +26184: a 3 0 2 1,1,1,2 +26184: b 5 0 3 1,2,1,1,2 +26184: negate 11 1 5 0,1,2 +26184: add 13 2 3 0,2 +NO CLASH, using fixed ground order +26185: Facts: +26185: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26185: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26185: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26185: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +26185: Goal: +26185: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26185: Order: +26185: lpo +26185: Leaf order: +26185: a 3 0 2 1,1,1,2 +26185: b 5 0 3 1,2,1,1,2 +26185: negate 11 1 5 0,1,2 +26185: add 13 2 3 0,2 +% SZS status Timeout for ROB007-1.p +NO CLASH, using fixed ground order +26215: Facts: +26215: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +26215: Id : 3, {_}: + add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +26215: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +26215: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +26215: Goal: +26215: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +26215: Order: +26215: nrkbo +26215: Leaf order: +26215: a 1 0 0 +26215: b 2 0 0 +26215: negate 6 1 0 +26215: add 11 2 1 0,2 +NO CLASH, using fixed ground order +26216: Facts: +26216: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +26216: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +26216: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +26216: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +26216: Goal: +26216: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +26216: Order: +26216: kbo +26216: Leaf order: +26216: a 1 0 0 +26216: b 2 0 0 +26216: negate 6 1 0 +26216: add 11 2 1 0,2 +NO CLASH, using fixed ground order +26217: Facts: +26217: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +26217: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +26217: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +26217: Id : 5, {_}: negate (add a b) =>= negate b [] by condition +26217: Goal: +26217: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +26217: Order: +26217: lpo +26217: Leaf order: +26217: a 1 0 0 +26217: b 2 0 0 +26217: negate 6 1 0 +26217: add 11 2 1 0,2 +% SZS status Timeout for ROB007-2.p +NO CLASH, using fixed ground order +26249: Facts: +26249: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26249: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26249: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26249: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +26249: Goal: +26249: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26249: Order: +26249: nrkbo +26249: Leaf order: +26249: a 3 0 2 1,1,1,2 +26249: b 5 0 3 1,2,1,1,2 +26249: negate 11 1 5 0,1,2 +26249: add 13 2 3 0,2 +NO CLASH, using fixed ground order +26250: Facts: +26250: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26250: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26250: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26250: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +26250: Goal: +26250: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26250: Order: +26250: kbo +26250: Leaf order: +26250: a 3 0 2 1,1,1,2 +26250: b 5 0 3 1,2,1,1,2 +26250: negate 11 1 5 0,1,2 +26250: add 13 2 3 0,2 +NO CLASH, using fixed ground order +26251: Facts: +26251: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26251: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26251: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26251: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +26251: Goal: +26251: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26251: Order: +26251: lpo +26251: Leaf order: +26251: a 3 0 2 1,1,1,2 +26251: b 5 0 3 1,2,1,1,2 +26251: negate 11 1 5 0,1,2 +26251: add 13 2 3 0,2 +% SZS status Timeout for ROB020-1.p +NO CLASH, using fixed ground order +26275: Facts: +26275: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +26275: Id : 3, {_}: + add (add ?6 ?7) ?8 =?= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +26275: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +26275: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +26275: Goal: +26275: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +26275: Order: +26275: nrkbo +26275: Leaf order: +26275: a 1 0 0 +26275: b 2 0 0 +26275: negate 6 1 0 +26275: add 11 2 1 0,2 +NO CLASH, using fixed ground order +26276: Facts: +26276: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +26276: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +26276: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +26276: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +26276: Goal: +26276: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +26276: Order: +26276: kbo +26276: Leaf order: +26276: a 1 0 0 +26276: b 2 0 0 +26276: negate 6 1 0 +26276: add 11 2 1 0,2 +NO CLASH, using fixed ground order +26277: Facts: +26277: Id : 2, {_}: add ?3 ?4 =?= add ?4 ?3 [4, 3] by commutativity_of_add ?3 ?4 +26277: Id : 3, {_}: + add (add ?6 ?7) ?8 =>= add ?6 (add ?7 ?8) + [8, 7, 6] by associativity_of_add ?6 ?7 ?8 +26277: Id : 4, {_}: + negate (add (negate (add ?10 ?11)) (negate (add ?10 (negate ?11)))) + =>= + ?10 + [11, 10] by robbins_axiom ?10 ?11 +26277: Id : 5, {_}: negate (add a (negate b)) =>= b [] by condition1 +26277: Goal: +26277: Id : 1, {_}: add ?1 ?1 =>= ?1 [1] by prove_idempotence ?1 +26277: Order: +26277: lpo +26277: Leaf order: +26277: a 1 0 0 +26277: b 2 0 0 +26277: negate 6 1 0 +26277: add 11 2 1 0,2 +% SZS status Timeout for ROB020-2.p +NO CLASH, using fixed ground order +26303: Facts: +26303: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26303: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26303: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26303: Id : 5, {_}: + negate (add (negate (add a (add a b))) (negate (add a (negate b)))) + =>= + a + [] by the_condition +26303: Goal: +26303: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26303: Order: +26303: nrkbo +26303: Leaf order: +26303: b 5 0 3 1,2,1,1,2 +26303: a 6 0 2 1,1,1,2 +26303: negate 13 1 5 0,1,2 +26303: add 16 2 3 0,2 +NO CLASH, using fixed ground order +26304: Facts: +26304: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26304: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26304: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26304: Id : 5, {_}: + negate (add (negate (add a (add a b))) (negate (add a (negate b)))) + =>= + a + [] by the_condition +26304: Goal: +26304: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26304: Order: +26304: kbo +26304: Leaf order: +26304: b 5 0 3 1,2,1,1,2 +26304: a 6 0 2 1,1,1,2 +26304: negate 13 1 5 0,1,2 +26304: add 16 2 3 0,2 +NO CLASH, using fixed ground order +26305: Facts: +26305: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26305: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26305: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26305: Id : 5, {_}: + negate (add (negate (add a (add a b))) (negate (add a (negate b)))) + =>= + a + [] by the_condition +26305: Goal: +26305: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26305: Order: +26305: lpo +26305: Leaf order: +26305: b 5 0 3 1,2,1,1,2 +26305: a 6 0 2 1,1,1,2 +26305: negate 13 1 5 0,1,2 +26305: add 16 2 3 0,2 +% SZS status Timeout for ROB024-1.p +NO CLASH, using fixed ground order +26392: Facts: +26392: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26392: Id : 3, {_}: + add (add ?5 ?6) ?7 =?= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26392: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26392: Id : 5, {_}: negate (negate c) =>= c [] by double_negation +26392: Goal: +26392: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26392: Order: +26392: nrkbo +26392: Leaf order: +26392: c 2 0 0 +26392: a 2 0 2 1,1,1,2 +26392: b 3 0 3 1,2,1,1,2 +26392: negate 11 1 5 0,1,2 +26392: add 12 2 3 0,2 +NO CLASH, using fixed ground order +26393: Facts: +26393: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26393: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26393: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26393: Id : 5, {_}: negate (negate c) =>= c [] by double_negation +26393: Goal: +26393: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26393: Order: +26393: kbo +26393: Leaf order: +26393: c 2 0 0 +26393: a 2 0 2 1,1,1,2 +26393: b 3 0 3 1,2,1,1,2 +26393: negate 11 1 5 0,1,2 +26393: add 12 2 3 0,2 +NO CLASH, using fixed ground order +26394: Facts: +26394: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3 +26394: Id : 3, {_}: + add (add ?5 ?6) ?7 =>= add ?5 (add ?6 ?7) + [7, 6, 5] by associativity_of_add ?5 ?6 ?7 +26394: Id : 4, {_}: + negate (add (negate (add ?9 ?10)) (negate (add ?9 (negate ?10)))) + =>= + ?9 + [10, 9] by robbins_axiom ?9 ?10 +26394: Id : 5, {_}: negate (negate c) =>= c [] by double_negation +26394: Goal: +26394: Id : 1, {_}: + add (negate (add a (negate b))) (negate (add (negate a) (negate b))) + =>= + b + [] by prove_huntingtons_axiom +26394: Order: +26394: lpo +26394: Leaf order: +26394: c 2 0 0 +26394: a 2 0 2 1,1,1,2 +26394: b 3 0 3 1,2,1,1,2 +26394: negate 11 1 5 0,1,2 +26394: add 12 2 3 0,2 +% SZS status Timeout for ROB027-1.p +NO CLASH, using fixed ground order +26415: Facts: +26415: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +26415: Id : 3, {_}: + add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +26415: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +26415: Goal: +26415: Id : 1, {_}: + negate (add ?1 ?2) =>= negate ?2 + [2, 1] by prove_absorption_within_negation ?1 ?2 +26415: Order: +26415: nrkbo +26415: Leaf order: +26415: negate 6 1 2 0,2 +26415: add 10 2 1 0,1,2 +NO CLASH, using fixed ground order +26416: Facts: +26416: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +26416: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +26416: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +26416: Goal: +26416: Id : 1, {_}: + negate (add ?1 ?2) =>= negate ?2 + [2, 1] by prove_absorption_within_negation ?1 ?2 +26416: Order: +26416: kbo +26416: Leaf order: +26416: negate 6 1 2 0,2 +26416: add 10 2 1 0,1,2 +NO CLASH, using fixed ground order +26417: Facts: +26417: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +26417: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +26417: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +26417: Goal: +26417: Id : 1, {_}: + negate (add ?1 ?2) =>= negate ?2 + [2, 1] by prove_absorption_within_negation ?1 ?2 +26417: Order: +26417: lpo +26417: Leaf order: +26417: negate 6 1 2 0,2 +26417: add 10 2 1 0,1,2 +% SZS status Timeout for ROB031-1.p +NO CLASH, using fixed ground order +26440: Facts: +26440: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +26440: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +26440: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +26440: Goal: +26440: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2 +26440: Order: +26440: kbo +26440: Leaf order: +26440: negate 4 1 0 +26440: add 10 2 1 0,2 +NO CLASH, using fixed ground order +26441: Facts: +26441: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +26441: Id : 3, {_}: + add (add ?7 ?8) ?9 =>= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +26441: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +26441: Goal: +26441: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2 +26441: Order: +26441: lpo +26441: Leaf order: +26441: negate 4 1 0 +26441: add 10 2 1 0,2 +NO CLASH, using fixed ground order +26439: Facts: +26439: Id : 2, {_}: add ?4 ?5 =?= add ?5 ?4 [5, 4] by commutativity_of_add ?4 ?5 +26439: Id : 3, {_}: + add (add ?7 ?8) ?9 =?= add ?7 (add ?8 ?9) + [9, 8, 7] by associativity_of_add ?7 ?8 ?9 +26439: Id : 4, {_}: + negate (add (negate (add ?11 ?12)) (negate (add ?11 (negate ?12)))) + =>= + ?11 + [12, 11] by robbins_axiom ?11 ?12 +26439: Goal: +26439: Id : 1, {_}: add ?1 ?2 =>= ?2 [2, 1] by prove_absorbtion ?1 ?2 +26439: Order: +26439: nrkbo +26439: Leaf order: +26439: negate 4 1 0 +26439: add 10 2 1 0,2 +% SZS status Timeout for ROB032-1.p diff --git a/helm/software/components/binaries/matitaprover/matitaprover.ml b/helm/software/components/binaries/matitaprover/matitaprover.ml index 1172bbb5d..627f2604b 100644 --- a/helm/software/components/binaries/matitaprover/matitaprover.ml +++ b/helm/software/components/binaries/matitaprover/matitaprover.ml @@ -163,7 +163,11 @@ end name, (n_occ, arity, n_gocc, g_pos, Stats.dependencies name passives)) data in - List.sort Pervasives.compare data + List.sort + (fun (n1,(o1,a1,go1,p1,d1)) (n2,(o2,a2,go2,p2,d2)) -> + Pervasives.compare + (a1,o1,go1,p1,d1) (a2,o2,go2,p2,d2)) + data ;; let worker order goal hypotheses = @@ -272,11 +276,9 @@ usage: matitaprover [options] problemfile"; [ (fun () -> worker `NRKBO goal hypotheses) ; -(* (fun () -> worker `KBO goal hypotheses) ; (fun () -> worker `LPO goal hypotheses) -*) ]; let rec aux () = if List.length !childs = 0 then -- 2.39.2